Question
Hint:
We can apply L'Hopital's rule, also commonly spelled L'Hospital's rule, whenever direct substitution of a limit yields an indeterminate form. This means that the limit of a quotient of functions (i.e., an algebraic fraction) is equal to the limit of their derivatives.
In this question, we have to find value of
.
The correct answer is: ![fraction numerator 2 m squared over denominator n squared end fraction](data:image/png;base64,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)
![Lt subscript x not stretchy rightwards arrow 0 end subscript fraction numerator 1 minus cos space 2 m x over denominator sin squared space n x end fraction left parenthesis m comma n element of Z right parenthesis](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAANkAAAAmCAYAAABJej66AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAXQ/cXWQAABbZJREFUeNrtnGGEHVcUx6/neWI9YcV6nnjKihURa6lYa8UKURUr1lJVVRXLqogVVSofKh/yJfIhYuXbqv0QtVRVVESIiIgVJSKqIkpUP0RVWLVqPc8yPcf+n97O3jtz79zZ2Tez58eRnTsz19yX+59z7rl3rlLVZYzsG7KXFWzbNNkPZJtkPbTxUyUIBXOHbJEsqmDbnpB9QtbE8QmydZQJQuFEB6Sd75H9Iv/dQhVFNg3P0iX7g+yz2PlZslcI6/jf84Y6Rskek23hebM+c9dQdpXsa7IW2TLZX2R/kp3D+WGym2QbCD+vaPcukF031HkN5wRhz0U2QfaObI6shnHgd9r5SbI3ZCdxfBLHU7F6nlvE58MUQsY430NozxFO1uH1fidr4wXxMco7EGpLu/9F7PgC2W3pVkJRIuPkw1LK+VmDZ7sbK9uCR8nKIbKf4VXj/Eb2yFD/W7IVS3lbO/4Qno45i7oEwVtkkYOZ4PDqcEK9fL4RK2ugXGcuIHExDNF+YDhXg4CHPMvjPCSbUTtZzCPSpYQiPVmU8XzPUNaEZ3mFsNOFUQjsmOX8JMZ6oeWX8czj0p2EokX2LidPpnMF46A0jkOUQwnXsGdcDSzvz8ndVDJFIOyDyFYcxmTnDaHhjwn31CyeTqeFhEY95TrOJi4GlLOn/AlCbiJ54hMuXlTm7GSVuY52i8hygjshp+3nIY6jZN9q50+pnWziCRyP43g6oc4FS8imcw+eLA0W87mM5SNk92Oi4qTNHcffhtv67IC+2NdtoXVUQXG5JC9C4TQ+Z/a2kRiIey7umK/hnX6FJ7M96zY6djsgUaPDc1+HDPenlTcguKOGa9bUTsbRpaNNVKxP9aMM22/fwzXvkz3NIrINiTwFjxfPegmek6OBWxgDb2kCygKPpb/Sjp9CbF4ii6TvCI7cILs04M84j8jiC4ihEVAXT+bHJ+iXTOPRyCM8EYQkHpCdNpSHLPGycRUehOtchUfaUMkJqQ6811AObZ1R5kQWr8B5JJ5M2Cs2LZ4hdImXstS5BIHNqP8SUN0EES1bxsZZws37lvGtcapGRCbkxbalPHSJl63ORUsOwTbd8BZiDKGFcddIwjW9KoksEtt3SxNZXku84tf8Yyivp9zbU/5L6HSaCIlHU66rlMiEwQ8X81ri5XLNVMq9IZ6M7+MJ+umU60oXLvbnml6r3avahcHjoaET5rHEK697bwWMyVYd782U+OjlEMdmYQoD4iOwx2r391jCYGFK4Ycu8bIlMBY8yvt0kHxperaL94z50vHaS/gdvET2UtkXiPIAcFxzpw+QNXJ9MyQ19i6yRn1Ow10Lg4tpMjpkiRezhj46F1CnDmcx+/NkEyp9HejnEK8r1snopIHgGbUzrxFZwrk1/M3zHPMeD7OCDNFkQnxfi8XEmxXoiPpSHO6QxyomtGfq/+v3si7xShKZb51x4is+thOczd8pGtHHoNZlVaGwp7sM0Zi4mPKQ3MAxx7Fgr0KdsYbf5kXFRLYXC4TXHDzUIGBdIBzKMhITvstTWJS8Mv2UoyerV8STxelWsE0ciuX1qcsEwrv6gLf5hsNYMhNn8Zbhr3pHMmRrfMZk/Pe9inXGGSR3BDu8iqN1UBvfQQdpIuy5lnP9/TmPYQj4yYCFDKFTG22EF6OiI8FEAwO8Me34jfJPjaYxi+RI2sLPsolsDF65LV1JEPKHhcWLSw/LTyEcZFx29o0sxx/Bq3cR4nZi17HAjns+j+tnHbLzr1AaXHb2NYmMBcZZpv6E/AW1O7GRZWGqz2cdsvOvUApcdvY1iexMrMxlByoXfD7rkJ1/hVLgsrNvlHKcVu5Kls86ZOdfoRSk7exblMiyfNYhO/8KpcK2s29RIvP9rEN2/hVKh21cVZTIfD7rCN35VxD2BdvOvkWJzPWzjtCdfwWhUFx29i1KZC6fdeSx86+QM/8CCN45m3uNYZYAAAGqdEVYdE1hdGhNTAA8bWF0aCB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMTk5OC9NYXRoL01hdGhNTCI+PG1zdWI+PG1pPkx0PC9taT48bXJvdz48bWk+eDwvbWk+PG1vIHN0cmV0Y2h5PSJmYWxzZSI+JiN4MjE5Mjs8L21vPjxtbj4wPC9tbj48L21yb3c+PC9tc3ViPjxtZnJhYz48bXJvdz48bW4+MTwvbW4+PG1vPiYjeDIyMTI7PC9tbz48bWk+Y29zPC9taT48bW8+JiN4QTA7PC9tbz48bW4+MjwvbW4+PG1pPm08L21pPjxtaT54PC9taT48L21yb3c+PG1yb3c+PG1zdXA+PG1pPnNpbjwvbWk+PG1uPjI8L21uPjwvbXN1cD48bW8+JiN4QTA7PC9tbz48bWk+bjwvbWk+PG1pPng8L21pPjwvbXJvdz48L21mcmFjPjxtbz4oPC9tbz48bWk+bTwvbWk+PG1vPiw8L21vPjxtaT5uPC9taT48bW8+JiN4MjIwODs8L21vPjxtaT5aPC9taT48bW8+KTwvbW8+PC9tYXRoPsCgjFgAAAAASUVORK5CYII=)
We first try substitution:
= ![Lt subscript x not stretchy rightwards arrow 0 end subscript fraction numerator 1 minus cos space 0 over denominator space sin squared space 0 end fraction equals 0 over 0](data:image/png;base64,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)
Since the limit is in the form 0 over 0, it is indeterminate—we don’t yet know what is it. We need to do some work to put it in a form where we can determine the limit.
( cos2x = 1 - 2sin2x )
(
)
so, simply
= ![fraction numerator 2 m squared over denominator n squared end fraction](data:image/png;base64,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)
We can only apply the L’Hospital’s rule if the direct substitution returns an indeterminate form, that means
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Consider the situation shown in figure. Water
is filled in a breaker upto a height of 10 cm. A plane mirror fixed at a height of 5 cm from the surface of water. Distance of image from the mirror after reflection from it of an object O at the bottom of the beaker is
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAASoAAACjCAYAAAA98lOLAAAgAElEQVR4nO29eWwc533//57Z++ZyeZPLWxQvHaQoSrIoU5JlS7Ilu67t5kSQAkmaFD3+KlCgfxT9q03/KAoUPVLgGydpjLptnDhIfEnUTUoUJeswdVDiJV4iuST3JPecnfn9wd8z3ntnlyvx8PMCCIncnc8+z+zMZ57nczKCIAigUCiUDQy73gOgUCiUdFBFRaFQNjxUUVEolA0PVVQUCmXDQxUVhULZ8FBFRaFQNjxUUVEolA0PVVQUCmXDQxUVhULZ8FBFRaFQNjxUUVEolA2PfL0HsNmhqZIUKTAMs95D2NRQRbUGeJ6niooiCYZhwLJ0A5MtVFGtAZ7nEQ6H13sYlE0AwzBQKBR0ZZUlVFGtAY7jEAqF6KqKkhaZTAaFQrHew9i0UEWVJYIgIBQKwefzrfdQKBscQRCgUCig0WjoiipLqKJaA4FAACsrK3RFRUmLSqWCyWRa72FsWqiiWgOBQADLy8vgeZ4+KSlJEQQBHMfRB9oaoIpqDfh8PrhcLnoBUlIiCAJ4nhe9xPShljlUUWWJIAjwer2w2+1UUVFSQhQVvU6yhyqqNUBiY+gFSEnFWlZRRMHxPB/191h5ya5BhmHE63Qzr+QY2oUme/x+P0Kh0HoPg7IJkMlkGXv9eJ7H8vIy3G43/H5/1GtEAQGrSirZbSyTyaDX62EwGKBWq7OfwDpDFdUaoKeOkgmZKCligB8YGEBPTw/GxsbEyHaGYRAOh0W7l0wmg1wuj7seBUGAVqtFZ2cnXnrpJVit1pzO53lCt35rYDMvpSmbA5PJhIaGBuj1+qjrbXl5GZcuXQLHcThx4gTUanXCB6darUZFRQWUSuXzHHbOoYqKQtmAMAwDuVyOxsZG1NfXi6laxF714MEDjIyMwO/346WXXsL27dshk8niHp5EjkwmW49p5AyqqCiUDQpRMnL5l7cpsVv19fXh888/RyAQwJUrV1BXVweDwbBlE5+35qwolC0Kx3GYn59Hf38/xsfHMT09jZs3b8Jut8d5BrcSVFFRKJsEnufhdDrxySefwOFwQKfTwWQywe1248yZM2KWxFaEbv0olE0Cx3Gw2+0YGhpCV1cXtFotQqEQuru7MTc3h5WVFeh0ui25/aOKikLZJLjdbszOzqKjowONjY3wer1wuVw4fPgwlpaWMDc3B51Oh7y8vPUeas6hiopC2STwPA+j0YjTp08jGAyCZVnwPI+SkhI0Nzdjenp6vYf4zKCKikLZJJhMJmi1Wmg0GiwuLopxUzKZDFqtFrW1tZs+DCEZVFFRKJsElUoFlUoV93eSyyc1qJOk3GwmW9bmGSmFQskJwWAQHo9nU9XIoisqCmWLQvIFl5eXRaXEsiyGh4dx48YNfO1rX0NBQcGm2C5SRUWhbGEcDgd+9rOfwWaziRUXpqen4fP58Nprr8Fisaz3ECVBFRWFskXheR52ux3vvvsuTCYTtm/fDrVajYKCAjQ0NCAvL2/T2KmooqJQtjAkUr27uxvf/va3kZeXB5lMJjabSFYBhNiuIiPdU703UX0s8rdcVBmhiopC2eKwLAuDwYDi4mKYzWaxykIqBcJxHDwej9gTgBTgY1kWwWAQPM9DpVKB53l4vV7I5XLxdZfLBY7joNfrodfrE3oqM4UqKgplixNZ3z8YDEKn00Gv10MulydUVjzPY3FxEe+99x5++ctfgmEYGI1GvPHGGzCZTLhx4wa8Xi8OHTqE+fl5XLhwAYWFhfijP/ojmM1m/Pu//ztmZ2dx6tQpvPnmm2hoaFjzHKiiolC2KAzDQKVSoby8HPfu3cM///M/AwAaGxvx8ssvo76+HkqlMkpZcRwHp9OJ//u//8PNmzdx4sQJ5OfnY2ZmBsXFxSgrK8PQ0BDu3LmD8vJylJSU4ODBg7h69SreffddHD9+HB0dHRgaGoLNZoPT6cxJ5x2qqCiULYzZbMZ3v/tdLCwswOv1YmxsDBcuXIDNZsNf/MVfoLCwUAxPEAQBfr8fAwMDuHr1KkpLS/Hnf/7nUKvVmJ+fh8FggFKpxM2bNxEMBqHX63Hw4EEEAgHcu3cPs7OzKCsrg9VqhUKhgMPhyFkVXKqoKJQtCsMwMJlMeOutt8DzPDiOw8zMDP7lX/4Fn376KU6fPg2TyQSNRgNgVVF5PB589NFHKCwsxOnTp1FQUAC5XC4a3mdnZ+F0OlFYWIg9e/agrq4OAwMDMJlMaGpqQldXF6ampmCz2VBRUZHSYJ8Jm8M3SaFQMoak1qhUKmg0Guh0OhQVFaGqqgqhUAizs7Nx3W0CgQBGRkZgtVqxfft2yOVysCwrJkA/ffoUHo8HLS0taGxsBAA8fvwY5eXleOGFF2A0GrGysoLp6WlYrdacxWnRFRWFskUJhUJiSze1Wg25XI5QKASe56FUKqFWq6Oi0gVBQDgchsPhgFwuh8FgQDgchs/nQzAYhEqlwuzsLAKBAKqrq6HRaBAKhfD48WOUlZWhuroaMpkMTqcT4+PjKCwshE6ny8lcqKKiULYos7OzuHz5Mh49eoTu7m7U19djZGQET548gdVqRW1trbjtA76s0V5QUIBAIICnT59CpVLh7t27GBoawje+8Q243W5oNBpUV1dDqVTC6/Xi6dOn4jbP5/PBZrNBoVCIbb2oMX2dIX3VgC+X2bSFFiURkW3dIwMhn+X1QqotjI6OYnR0FHq9HhzHwWw2o6urCyUlJVErKoZhoNfrcfz4cdy9exc//vGPYTKZUF5ejvb2diiVSthsNqjVatTV1Ym/ezweWCwW5Ofnw263Y35+HisrK+jt7UVxcTFqamrWPBeqqLJEEAQ4nU54PB4AgFKphNls3tTdaCnPjmAwCJvNhnA4LMYlGY3GZ5oQbDQasXv3bni9XkxMTGBlZQX5+floa2vDrl27xABNAlFUJ0+ehEajwcjICAwGA3bs2IF9+/aBZVns3LkTwWBQ9Ozp9Xr84R/+Idrb26FWq6FSqbB7924oFApUVFTkTBHTTslZwvM8bt++jdHRUfA8D7PZjLa2NhQVFa330CgbDEEQYLfbceXKFfh8PshkMmzbtg3Nzc1ZR23Pz8/jn/7pn2C32/F3f/d3KCsrS/i54XBYtEuR1RxpwZVoBxB5DFGqCoVCjGYnHZrJ1o7neQSDQVGmIAjisSzLiseuFbqiyhJBELC4uIjR0VGEw2GUlJSIXhAKJRJBEBAIBPDkyRMsLy9DLpcjPz9fbCoqlXA4jHA4DIVCESc/Nr8OSNwXMB3pjolNYpbJZHF2rlykzMR9bs4lfoXgOA7BYBDBYBAcx23ZVkWUtUNWHoFAAMFgUDQyZ4LP58PCwgJ8Pl/UtSYIAoLBIBwOBwKBQK6HviGgimqNPA+jKGVrsNZrxeVy4f79+xgcHMTKyoooy+/3Y2RkBFeuXMH8/HyOR70xoFu/NUCVE2UtZHr9GAwGmEwm/OpXv0JLS4uYFnPz5k1MTExg//79MBgMz2i06wtVVBTKJkGv16OsrAx+vx8ff/wxhoeHAazajQoKClBXVwej0bjOo3w20K0fhbJJYBgGZrMZb731FhwOBx4+fIiHDx9iamoK+/btg8lk2hT1z7OBrqjWADGGklwohmE2TVcPyvODFJ5ba0AwwzBQq9VoaWnBjh07MDg4CJ/Ph6amJnR0dECj0WxZcwRVVGuE53kEAgF4PB44HA7odDqqrChRMAwDu90Or9eLcDicUbhAZOgBQafToaurC1988QVsNhs6OjpQUFAAAAlDHraCw4cqqjVALsAHDx5gdnYW77//PrRaLVVUlDg4jkMgEEBHRwesVqukY0iZ30AgEKeASEmVxcVFtLW1IRQKwW63x8kgcVE6nU5yg9KNCFVUa0Sj0aC8vFwsn5GXl0cVFSUKhmGwsrKCkZERyQ8yEht14cIFXL9+XUzVIvKCwSDGxsbg9XrxH//xHzAYDHErLwCQy+UoKSnB6dOnN3VAMlVUa0AQBOh0OtTW1qKoqAhdXV0oLy/POOKYsrVhGAYLCwv46KOP4PF4JCsqks4SDofBcVzU64FAAHa7HeFwGDKZDKFQKE5uZCeZzR6MTBVVDuB5XsyPIlHHFAqBZVkx/y2TY1QqFU6ePIljx46JSocosNHRUfzkJz+B3+/Hn/7pn6Kqqiqhx49U9djM2z6AKqo1EWmcZBgGMpksYWePbJ5oqcrGRJYMyYUsIk+qLCIvEWRcUsdGPKZrlUXmt9bzlY2cdOc3W4iyisyd43kePp8PN27cwK1bt+D3+9Hf34+qqirodLpN01A0U6iiygEk6ZQUFYutOySXy6FUKiVfRIIgiHmEiXLCiDyp3qNQKCT+xCKTyaBQKMRs+nSEw+GkuY0Mw0CpVEKhUEieK6lAGbvaiD1v6TxWuZBDmhskkyOTyaBUKsVKAuSYZN8VOSaXSbqkAmdvby+GhoYQDodx7do1vPzyy3FlW7YSVFGtEYZhEAgE0NfXh9/+9rfgOC7qIjaZTDh06BBeffVV0YWcCpZl4fP5cPv2bXz88cd4/Phx1LKf4zi0tbXh+PHjOHDgQMqVAinR8fDhQ3z22Wfo7e2Null5nofVasXx48dx8OBBmEymlNsTmUyGubk5nDlzBleuXIHD4YjqYKJSqfDqq6/i6NGjKC8vj7OrxI4tGAzizJkzOHfuHCYnJ6MUr1qtRkdHB06fPo2qqqqkMWoMwyAUCuHcuXPo6enBkydPohSJSqVCe3s7Tp8+jZqaGrAsm1ROOBzGpUuXcObMGYyPj0fFxpE6S6dOnUJ9fb041lAohLt37+Kjjz7Co0ePxO9fEASwLIu6ujqcPn0a1dXVSc+FVARBgNvtRk9PD2ZmZsCyLGQyGebn59Hb24s/+IM/gMFg2NRhCMmgimqNkGC+8vJyNDU1QaPRRN0IpBpiZCkMKfJKSkqwb9++uOqI4XAYVqsVxcXFkrZF4XAY+fn52L17t3gRRypSs9mMyspKKBSKtLIEQYBWq0VjYyMUCgV8Pl+ULLlcjoaGBmi1WklbSZZlUV1djUOHDsHhcEStBhQKBSorK8WUkGRjIwqhqqoKXV1daG5ujpIjl8thtVrFbiip5sgwDKxWK7q6utDY2Bgnp7y8HGazOWrOLMuiqKgInZ2dqK6uFms4EXkFBQUoLS3NyUqH4zjY7XbcvHkTbW1tYFkW4XAYe/fuxcjICLxeL7RabUZxWpsFWjgvS8LhMD777DPcvHkTPM+jsLAQhw4dSuj1I8b2TCDbhtinIylWlkmZEGJDSXSzELtLJjaqdHalTI3GydI+yLik2pbI+Yp9f6ZyyE8iL1qi8x6ZmRALeZjYbDZ88sknYvvzzs5OHDp0CFqtNu2YCA6HA/fu3cO1a9ewe/dunDlzBh6PB9/85jcxPT2NnTt3oqamBnq9XrLMzcLWU73rALkYidcvF65gss3LBZFu7o0kC8id63w95aQ7Jld2I7/fD5Zl8a1vfQuCIODcuXPgeR7V1dXYuXMnnjx5Ar/fTxUVhUKRRqQnMFfpK3l5eWhuboZer8fS0pL4d7lcDqPRiIaGhk0fhpAMqqieMem2G5lcwLmUtRnkpZO5HuOTMh6yuuY4TiwdnMjjmilqtRpqtTpO8REzQa566G1EqKJ6xiRKKgUyTxRNFe9EZEjNzo+MWE5kh0kVSyRlfIn6uJHtTybzTTZGIieTc5gqlkqKHCnjIeeN53n09vbi7NmzePz4MVpaWrB3716EQqE1V0/4qkIV1TOCYRgsLy9jYGAA9+7dg9vtjrrQNBoNduzYgc7OTphMprRPar/fjwcPHuD69etwOBzi30lHkPr6enR2dqKioiLtuMLhMMbHx3H9+nVMTk6KrxH7U3V1NTo6OtDa2irJCM2yLJaWlnDr1i3cu3cPy8vLomISBAEKhQIdHR3YvXs3CgoKJNm3OI7D8PAwrl+/jrm5OVH5EUVaWVmJzs5O1NbWpryByTmanp7GwMAARkZGRGVPlFdpaSna29uxa9cuyGSyhPMNh8MYGxvDwMAApqenwfO8OB6GYVBWVobOzk40NDSIv+/duxdWqxUVFRUoLi7G0tISzQPNEqqonhHkJlhZWYHD4RDd72TlYTAYsLy8LNl7RyKSHQ6HeMGTm1ClUsHtdov5XlJu3GAwCJfLFXXzEAN+fn5+xk0CwuEwVlZWYLfb4Xa74xSV1+vNyDlAgmidTqeY00YUg0wmg8lkQjAYlJw3FwqF4PF4sLS0JCpKopi1Wi18Pl/KeDSSJEzGExsvpdPpEAgExPE1NTWhpaVFXKnNz8/j0aNHkudPiYaGJ2RJZHhCOBxGYWEhDhw4gLKysqgndqQSiCQy1ibT7Vos2cqK3ZJGRtNnu/UjY8zV1i/R+cvVfGPlpfLOrWU8DMNgcXFxzeEJkUjp67eVoCuqZ0iyWChCMptTMlkkHSSZLCkBoJGyUt3omeQSAqlz5DIdX+QYkymP5z3fXI6HkjlUUeWY2Bshl+U1yFYlV7JyeVM9i5t0o8032/F8lY3guYIqqhwS+dRNdFOsxdWeyU32VZCVa5nPUk4uY6m+qlBFlSPI05aUjY28sMm2KFnqCYlsjrRtAdGKL5PQA47j4raV5FiyFZUaLU2qJMSuDMl4SPqLlBs9MvUnk/OTjMjzFmszyuS8keMjjeyRY1uLHDKObLsjU1ahiioHMMxqJYCRkRHcunUrqmws8XpVVFSgoaEBFosl6liWZTE/P4/Hjx9jamoq6mYQBAH5+fnYtm0bKisroVQq067KXC4XhoeHMTExgUAgECVPoVCgsbERtbW1aZtQMMxqVYLHjx9jdHQ0ypNHZFmtVjQ1NUnqJRcOhzE9PY2hoSE4nc44ZVBUVITGxkaUlJRIUsgsy8LhcGB4eBhjY2NRBnxBEKDX61FfX4+amhrodLqkW3CWZeF0OjEyMoLR0dG4Vuk6nU6Uo9frU8pxu90YGRnByMiI6BUkY/L7/Zibm4Ner9+y0ePPEqqocgSpYX3nzh3YbDbxAuV5XixZUlRUFKWoyNN2cXERN27cwMDAQNSTOxwOo6amBiqVCmVlZVCpVGmVy/LyMu7du4e+vr6oeCae56HVasGyLEpLS2EwGFLaW0i81fDwMC5cuIDZ2dmopF+NRoN9+/bBarVmpKguXbqEycnJqPAKuVyO5uZm5Ofno7i4WLKicrlc+OKLL3DhwgXwPB8118LCQgBAaWlpyohtomAGBwdx4cIFhEKhKDkWiwU8z6OkpCRlF2KGYeDxeHD//n2cP39ezMsDvqyIYbFYUFVVlXZulHhoeEKWxIYn5OXlYceOHdBqtWI8DfBl+ROdTgez2QyVShWX/rC8vAyXyxUXFAqspk2YTCYYDIa0zSVJYKjT6cTy8nJcJDTLssjPz4fBYEir9MjYSVxU7OpMJpNBr9cjPz8fCoUirXIhcVYOhyMucZtlWWg0GpjNZmi1WkmKimEYeL1euN1uuFyuuLkoFArk5eXBYDCkXIkyDAOfzyfKiV0xKRQKmEwmGI1GSXI8Hg+cTmfc/NxuNwYGBiAIAtRqNQ1PyBC6osoRCoUCFosFFRUVCdNSkqVwkG2K0WhM6TqX4j0kN0FZWVlaN7xUt35hYSGKi4uTfp7UMAaZTIa8vDzk5+evWRZ5v1arhV6vR3l5edy4I+WlkklWhzqdLu5mz0aOVqtFaWmpeDz5d2FhAY8ePcLy8rKk+WXCV2GtQRVVDiGG1Ew9fuS4dBHlyY5NJCvVMcleSzRGoiTXU1YyeanOG1EysTKftZxYhUbsVOFwOOedYL5KcVtUUeUQciMmal0ERHu3EhF7DHmSx17ggiBEeaKk3NyRK4NEyoLYn6QqCqKQY2XFBkZKUWLk90Qrx8i5pjtvuZQTuQqORcr3GOmNlMlkOe9MFDmGdCaBrQBVVDmCGIanp6fx+PHjqK615KIvLS1FXV0dysvL0z5dWZbFwsICRkZGMD09HaVEeJ5HXl4e6uvrUVFRIckb6Ha7MTY2hqmpqSh7E7GhNTQ0oLq6OqVni8jiOA4jIyMYHx+Hx+NJWLK3oaFBkpGdrFgWFhYwPDyM+fn5qLkQg3ZtbS2qq6ujVjiJWFpawuPHj8VE5kg5+fn5opxksW5kTHa7HcPDw5idnY06HzzPw2w2o6amBjU1NQmTmAVBwMTEBEZHR7G0tITi4mLk5eXldEWlVCrR1taG5eXlr4QXkSqqHEFu4KdPn6Knpwejo6NxN8ru3buh1WolVThgWRY2mw1Xr17F9evXo1YmpKojy7IoKSmR5A30eDy4ffs2ent74fF4ouSp1Wq89tprKCoqgtFoTKuowuEwhoaGcO7cOczOzkYpKq1Wi87OTpSUlEhSVMDqjW2z2XDlyhUMDg5GJS/zPI9t27bhlVdeSdkgIVLhXb16FXfu3ImqAcXzPGpra/HKK6+kbRYhCAKWlpZw7do1fP7552JcGpFTXV2NY8eOobKyEnK5PG6rR6pTnD17FuPj42hoaMC+ffvSbu8zQa/X46233hK9plsd6vXLkkRJyaRky8LCAvx+f9yNoNfrYTabU7q5CUS5OJ1OuN3uqNeI4dZsNsNoNMbdLIlk+f1+OBwOuN3uuCoGLMvCYrHAZDJJ9gYuLS3B5XLB7/dH3XxyuRx6vR4WiwVKpVLSjUkqQ9jtdiwvL8dtWXU6HfLy8pCXl5d2XJFyYmOitFqtKCfVuKTIMZlMyMvLS1qH3ul0wul0wufzQa/Xg+M49Pb2wu/35yQp+avG1lfFzxG5XJ7yhsrEsyUIq6VgSPeUREhtWkC8geXl5UlXc5l6A4uKilBSUhL1N/JZmXrwWJZN6flMZS+KHZdOp0vZMkqKB3WtchiGgcViQWFhoXi8zWbLKOqexJmlej32M7cyVFHlkHQ3VKaL11TeqGxlAdK9dKlI5cHLZpGeq7luFDmR54fYL6VCUo2Spe4Qhw35PuVyueQGspsVqqhyTLpViZScOCl/y1ZWsr/nUlY6eelCNTKVl+i4jSInE+XI8zw4jsPExATGxsZQX1+P0tLSqO1hKBTCwsIC+vr68OjRI6hUKrS0tGDXrl0oLi7esvaqrTmrDU6sITedJytTWcDaKhGsdWyRgY65mmcuZSSSs5Z5xsZZZTM+nucRCAQwOjqKX//61xgaGsJ3vvMdMVqfvMfj8eDMmTO4ePEilpaWwDAMhoaGYLfb8frrr2/Ztu5UUT0nGIaB0+mEzWaD3W6PCx7U6/UoKiqC2WxO27WYYRisrKyIsmJTZUinZYvFEte5ORE8z2Nubg6Li4tR3Y+JrPz8fJSWlsal/ySC4zg4nU7Mzs7GORRYloXBYBA9glJTZTweDxYWFrCwsBD1GrG9kRzKVI4AkqpE5MQa7NVqNQoLC2GxWKBWq9PKWVxcxMLCQpyhXaVSiXKknHuC3+/H1NQUzp8/j08//RTLy8tiYjOB4zhMTk7iZz/7GY4ePYq/+Zu/weLiIn7yk5/ggw8+wP79+6HRaKiiomQHw6yWQ5mbm8PFixdx586dqMqfPM/DarWiu7sb7e3tkqskXL9+HTdv3sTKyooY9EeSj48ePYoDBw5Aq9WmlMWyLAKBAAYHB9HX14eFhYWoAEKVSoU9e/bg2LFjYhv5VPA8j7GxMfT09ODp06fieEnA5fbt23H06FHJoQsymQxOpxNXr17FtWvXRDnksywWCw4dOoR9+/alVDAymUw8Z319faINiMgxm82inFQKhmVZeDwe3LhxA319fQgGg1FyTCYTurq6sH///rTnniAIArxeL6anp1FXV4eTJ0/iww8/jHNIuFwuPHz4EF6vF9u3b0dFRQUKCgrQ3NyMDz74AJOTkygpKYFCoYiSzXEcpqamYLPZAKx6n4mThlw7RqMRLpcLy8vLMBgMsFgsCIVCmJ6ehlKphMViQUFBAeRy+boY7qmieg4Qw2xxcTEOHz6MHTt2xH3ZOp0OJSUlSbugxMozmUzYu3cv6urqEAwG40IESktLU964BNLFpqWlBcXFxfB6vXGySCJzuvQXYPVGrqmpwWuvvQa/3x+XnGs0GsVcOCmEw2GYTCYcOHAAtbW1ca+r1WoUFxenDasIh8MwGo3o7OxEVVVV3HtVKhWKiorSnjOe52EwGNDR0QGr1RpnJFcqlSguLpaspIAvvYy7du2CSqXC0tJSwtAOl8uF2dlZlJaWoqCgABqNRszt5HkeTqcTgUBA7JRMlNTi4iJ++tOf4uLFi2AYBrW1tXjxxRehUCjQ19eHwsJCdHR04MaNG7h79y5qa2vxta99DU+fPsVPf/pTmM1mnDx5EqdOnUrphX6WUEX1nBAEAXl5eTCbzQDijbGx6RvpZGm1WtTV1aG+vj6hK5vIkXKzsCwLq9WKysrKlLKkIJfLUVRUFJfITORmIoscZzAYYDQaUV9fn/Q96eSS7bXBYEBdXd2a5Oh0Ouj1+oSKU6qcWNRqNVQqFYDkTSbC4TA4joNGoxGN5gyzWkef4zg8efIEbW1tYikhQVgNgP3xj38Mm82GY8eOQaFQwO12Q6fTobKyEmfPnsWNGzfEWLXGxkZ8+umncLvd2LNnD/bv34+pqSmMjIzA6/VKXgnnGqqockyqfLlIMnnaSpGTCwNz7OelMzZn6tlLN8ZsPY8bSU6i719KQ9fI1zNdsZDvJrYl2cLCAnp7e3H37l28/vrreOuttyCTyTA/P4+8vDyoVCro9XpMTk6isLAQO3bswMzMDD788EP4/X60tLRALpfj4sWL6273oorqOZHNaiL22FhyrZwiVz2R8hN58YitKJHyynaesZ8RSa7mmguvI5GTSejCWjyC6eST74LUOyOMj4/jwoUL2L17N1588UVUVlYCWC0mGA6HMT8/D7/fLzZLLSgowNTUFMrKytDd3Y0dO3ZgaGgI4XAY5eXlkpwpzwqqqHJIOByG3W7H3NwcvF5v3A2fl5cHi8WSNhUE+NJgvrS0lNBLqNPpUFBQgBcrl/EAACAASURBVLy8vLRewnSfAwCTk5NwOBwIhUKi8bSyslJsVLq4uAiLxQKz2QyGYRAIBERPYeRqgNSdInYjqSk0xIvpdrvjPHLEuBtbxjmRHK/XK8qJ9ciR1B6LxZJyXETOwsJCXDE9Iic/Px8WiyWqSoTX64Xdbsfi4mJUtQTiKSRNaCON3ZlAVmakKCIZD8dxkMlkKC8vF+1TALC4uIjp6Wl873vfExO6iRyfz4fHjx9DLpdj//79qK+vx+TkJCYmJnDw4EHs2bMHWq0Wdrsdfr8fNTU1kosaPgsyVlSCsJoHtbS0BL/fj+LiYuh0OtFTxHEcPB4PpqenEQwGoVQqYbVaJVWo3MyQ6OOxsTGcO3cOExMT4mvEmN7S0oLDhw/DYrGkLQNMlugXL17E7du340oUV1RUoLu7G3v27EnrJUwGy7Lwer149OgRPvvsM0xNTQEAPB4Pdu7ciR/84AdgWRaDg4P4zW9+g+7ubrz++uuip/CTTz7B7du3owy/JKv/2LFjUSk2qebKMAxmZ2dx/vx5PHjwIGouHMeJxl+iYFJtuebn53Hu3Dncv38/SsFwHIeqqiq8+OKL2L9/f9LqCQzDiJUrzp8/j8HBwajvipz7Q4cO4cCBA5DL5WIZZLfbjf7+fvT19SEQCESVIgZWE7bLy8uh0WikfD1xJWn0ej3y8vIwOjoKm80Gv9+PQCAAm80GhUKBwsJCqNVq8f2BQAAejwcmkwkajQYcx4kPPUEQMD4+DqVSiaKiIsjlcjidToyPj6O1tRUWi0W0cTkcDtGbuCkUFWkFPjQ0hA8//BB2ux3f+c530NraKno5fD4f+vr68P/+3/+D0+mE0WjEj370I3R1dUGn023ZnCSybbJarTh27Bg8Hk/cysBisaC0tFRSOgXP8ygoKMDBgwexffv2uM8yGAwoLS2V5CVMBsMwuHXrFv7xH/8R27Ztw9GjR1FdXY0PPvgAAwMDKC0txeHDh8HzPOx2O3w+n3hTKpVKHDlyBE1NTXFlXiwWi+glTGfbIFuooqIiHDp0CK2trXErGJPJJCq9ZHMlcgoKCtDV1YXm5uaEckhN9lRySNjDCy+8gMbGxihFRc59SUkJWJYVP4Pneej1erS1taGkpCRuReX1ejE0NJQ0gZykzQQCAaysrIDjOIRCIQSDQYRCITGPdNu2bZDJZHj48CGePn0Kl8uFJ0+eoKamBmVlZVElX1QqFXQ6HTwej5jg3tfXB47jcODAAczPz4sxcmSlNj8/j0OHDkGn04m/k5CEXG2/syEjReVyudDf34/33nsP/f39KCkpwalTp8QyGMFgEJcuXcLPf/5zsCyLzs5ODA4O4he/+AV4nsfLL7+8bnEYzwO5XI7i4mIUFRUlfY/UJGJBEGA2m5Gfn5/0fGXjXQJWbxyFQoHBwUH09PRgZmYGP/rRj3DkyBFYLBbY7XYsLS3hk08+QUdHBwoKCtDS0hLVIUatVqO5uRnNzc1xsmPHKKX2VqoyxZFzTSeHVDVId87SyTEajWkTwmPl6nQ60RMbK29hYQGLi4tJSxH7fD5cu3YNZ86cQX9/P548eYKf/OQnuH37Nk6fPo3du3dDqVSivr4eX//61zE4OIi/+qu/AsMwKC0txde//nUUFRVF7Vqqq6vR3t6O//zP/8TPf/5zFBQUYNu2bTh48CAEQcCDBw+wc+dOMVF9YWEBs7OzqKiogE6nw/DwMIaHh0VbFwlIXg/DekaKSi6Xw2g0oqamBiMjI3GGRY/Hg5s3b2J8fBx//Md/jMOHD+P69ev42c9+ht7eXuzcuRMlJSVbNh9JisE0mydTrp9kgiAgFArh2rVrePToEV599VXs3r0bOp0OHMchLy8PJpMJ4+PjEAQBFRUVOHLkiLiKSDQP8rvD4cDQ0BDu378PlUqF+vp67NixA2q1Ou3qL5fzfNbG93SrstjfYx0TschkMhgMBpSXl+PIkSPo6uqCSqVCeXk5dDqduPUvKCjAW2+9hfLycjx58gRKpRK7du3C/v37oVaro+RbrVacOnUKarUaKysryM/PR2dnJ1pbWxEIBPDSSy9h27ZtKC4uBsuyqK+vx9e+9jXU1tZCqVQiPz8fR48excLCAsrLy9d1kZGRxtDpdNizZw+Ki4vhcDjwxRdfiLYBnucxOTmJ6elpmM1mtLe3w2q1QqPR4Le//S1GR0cxPDyMwsLC56qokjWpjCWdApHJZFHR5InIdIWTSFaii1wqUuQxzGphN5fLJRape+edd8QKlGQLIgiraSUkLiqRAyBWNsdx+OKLL/DBBx+gp6cHOp0OL7zwAhiGQWtrq7gdTDavXJ23jSZHSgkdYttraWmJep9MJhNtQwzDQKVSYdu2bSgrK8Pk5CQ4jkNdXZ2ozCIxGo1ob29HS0tL1JZdLpdDq9XiG9/4higfANra2tDa2io6QaxWK9555x3wPA+ZTLaulUQz0hgsy0YFmkV+QeFwGPfv38fTp09RUFCAyspKsbuHRqMRo2pzXeA+FYIgYGVlRfTexJY54TgOKysr0Ov1aZ/2hYWFsFqtUcdnAzHWptpSZLqdS1cHPFJJE0X15MkT0Uja1tYmKieZTAaHwwGv14vq6mpJhfSIXL/fj9///ve4dOkS3G43lpeXcenSJYRCIfz1X/+1mJaRzVzTnbfYeaaSQ2RtBDkE4g2M9eDGxlYRR4vf78d7770Hp9OJv/3bv01YjJEEg8Z2s47cvkf+TsrFRJ7jSOP8eppsMl7aJAtcEwQBs7OzcDgcyM/Pj2s+QBJyn7eimpubEytxRuZl+Xw+OJ1OBINBaLVamM3mpCsmjuNw4sQJfOtb31rzapD0kEuUdCqTyWA2m8VuulIucrI6cjgcUSVzBWG1FrpGo0FeXp64LWCY1ZLJ4+PjkMlksFqtkMlkUfWTZmZm4HQ6ceTIEcmJtUQBTkxMiH3teJ6Hw+FAf38/7t+/LxqIBWE1eddkMkGv10sKrwgGg3C73XC73XFJ2AzDiL330qXAEDkejycu9ShSTmQ8UiJCoZAoJ7bnIcMwMBqN4nik3uCZBHyS7XsgEEjrQU4mL/bvqeK/1puc7cHIiSORsbFLaHJSn6fngGFWKy12dXVh27Zt4gXOsizu37+P3/zmNxgaGsKhQ4dw8uRJsbtuou1XVVXVmo2IpH372bNncf36daysrES5sE0mE06ePImuri7RPZxufsFgEJ9//jk++ugjzM/PR42Z2C9OnjyJhoYG8bVwOIy5uTnIZDIUFBRErWw8Hg9mZmYQDAaxY8cOaDQayT0FSQ13rVYrNlMl3qR/+7d/Q15entg2qqSkBC+//DIOHjwIs9mc8mYjXZHPnz+Py5cvw263R503hUKBY8eO4aWXXoLVak3asoxlWSwvL+PixYu4dOkSFhcX4+QcOXIEx44dQ1VVVVo5ly9fxqVLlzA/Px91bchkMnR3d+Pll19GTU3NM3s4SzFHbBVypqhYlkVBQQGMRqPoqieQJ1VBQcFz9RgwDCN2y21sbBQvOhJPYrfbEQgEEAqF0NnZifLy8qT7cJlMlnLrIQXi2ib2mtgnulqtRm1treTtFtmqVVRU4MUXX4TH44l7rby8XAzSJOdEEASx1jn5LJZlEQwGcfv2bSwsLKC6uhrNzc2SEpvJ56nVapw4cUK8iTUaDVpbW9Hd3R1lTBcEAUajEdXV1VAqlWlvZEFYrRHf0NAAmUwWlzjNsiwaGhqg0+lSbrfISq6+vh4Ms1o5IFZOfX29ZDkkZzC2WQbDMKivr0/b0YcinawVVaJlY2lpKUwmEwKBAAKBADiOQyAQQDAYhMlkQllZ2XN3bZItKDEYEqP/3bt3xbpE09PTGBgYwPHjx59p4TFBWE1M7ujoQHt7e0JbBHlCSl15KhQK1NXViR1aYmUSm0bkGEh1hTt37mBychLAanDg48eP8atf/Qosy+Lw4cMwmUxJVxWJ5iaTydDR0QGFQoHGxkYolUo0NTVh7969cVugyB57UsI1tFotWltb0dzcnPC8EVmpFANReC0tLXFxVkSWVDkkPKOxsTGtnPXOk9sKZKSoImNiIo2z5IlcXV2NoqIiPH78GGNjY9BqtXj06BFcLpfYN249o9MFYTXdYGBgADabDU1NTRgbG0NlZSWuX7+Ourq6qLSITCGKIVEsESGyYWSy9yXy1CWaC3lNJpMldB0nkkcU1a5du9DX14cHDx7g8uXL8Hg8GBwcxNTUFI4fPy62d5Ky/Yz8f2FhIV566SUcPXo06pzEvjfR2NLNkzxskr0vVQhANnISvSdSTqRjKZWc52nu2KpkpKjC4TCWl5cxMTGB+fl5OJ1OTE5Oor6+HhqNBrW1tdizZw/u37+PDz74QEyL4HkeHR0d666owuEwPB4Pnj59ih07duDYsWN499138c4772BsbAxOp1NsZ5TNFo8ojUSrhEgvkNQLOJWni8iJfHBIuSFI/andu3fj1KlT+PDDD/H3f//3EITV6PAf/vCH2L9/v6QWXMnGFhkOIsXdL9Vrme68pZMT64lLJkfqeaeK6PmRkaIKBoMYGxvDRx99hNnZWTAMg0uXLsFsNqOwsBAajQbHjh2Dz+fDp59+ivHxcYRCIbz99ts4evQoVCrVui6Dg8EgRkdH0dbWhtLSUjx9+lQsHbtv3z54PB7Y7fasUn1ICV6S9pDI+2YymST3uiM2FI/Hg+Xl5bhjlEoljEYjdDpdWqWSSDbP82IROdI3UK/Xo6qqSvR4pZIZCATgcrngcrmiVk0ymUzseyclN4zneSwvL4vnLnb1SbyDGo0mpSyS2Ew8ubGrIiInXWIt6THocrkQDAajtnWRcmJL/iZbTUe+RsmejCPTy8rK8Prrr+PIkSMAVg3AVqsVSqVSNOy+/fbbaGpqgtfrhVqtxs6dO1FYWLjue3WWZVFUVIT6+nrI5XI8ffpUNIw2NDTA5XJlZTAnMUT9/f0YHByEzWYTZfA8D41Gg/b2drz88stJi63FypPL5ZiYmEBPTw8GBgaixsXzPCorK3Hs2DHs27cv4+oJZAtcUFCAoqKiKM8X8cqlG9/Kygp++ctfYmBgIEr5qtVqdHR04NVXX0VZWVnasXAch3v37uHjjz/G1NSUGCJBbF6NjY04ceIEWltbU7rZw+EwHjx4gE8++QTj4+NRcoix/fjx49i1a1fSVT2R8+jRI3zyyScYHR0VW2YRB1F9fT1OnDiBtra2qPMZ+WCKVZKRNi+6+sqOjBSVQqFAUVER8vPz42wk5Msn+W6R7nWFQrHuSgpYXYVUVFSIZS5iLyhSvTCbpx85NzqdLqqzMXF7V1ZWSuqQTI7heR55eXlobm4Wn96RiookOGe6mooktjdfJnJUKhV27Nghrugigwarq6sldwAmD489e/agpqZG/HtkuEOqfEfyXoZZTS9pa2tDZWVllKJiGAYlJSUoKChIK4d0jW5ra0N5eXmcnKKioig55LWpqSn09vbi3r17USE6PM+joqICtbW1cV5einQyUlSxSikZUt4jBfJFh8Nh8ckW6U2JXFKTm47cNJFNHIndKJUNA0heAlbKOBUKBbZv346ioqI41zYZdybnJBwOizfFwYMHE441mT0sm/Fn+n61Wo3Dhw+jq6sr6rXIucaGqSRCJpOhqqoK5eXlcWMh36+UINtIOYlWNeTaTTceUpa5tLRUkhwyx8jtfWSVTVJVgZg9qKLKjg2bHUyUlMvlwqNHj8QAQtINY3l5GSsrKygsLIQgCFhcXMTKygrKy8tRWFiIqakpLCwswGQyobKyEhaL5Zka8kl6UbIASanG7kiSefOIvMh/nzdEGSWKO8tkruQmT1ZMTqqsSAUpxZuXSg6xRUmVIwgCSktL8frrryf87mUyGZaWlvDZZ58hEAhs6bpsz4oNraiWl5dx9epV/Ou//itmZ2cRCoXQ3t6Ol156CePj47h27Rq6u7uhUqlw/fp1jIyM4ODBgzhx4gTOnj2Ly5cvo76+Ht/4xjdw/Phx6HS6Zz7myJ9cytyI5GpsuZQT+e9aZWWibIEvvY6xx0UqT7qiyo4NqagEYTWZuK+vD++++y5aW1vxgx/8AJOTk2JrJ4PBgJs3b+Lx48fYs2cPXnnlFRQXF6O3txeCIODo0aMoKCjA3Nzcc80xJBd4Ki9QtsoslzKflyxAWg0uqbKkji1XcgCk3LJFhojEKiPy+alWehRppFVUxNYT66rNBST4LtZlz/M8hoaG0NPTA7VajdOnT+PAgQNwu93gOA5arVZMBGVZFrt27UJRURE8Hg8uX76MyspKdHV1iUmw61HrOV1kczZPWHLDxwZORv4uRV6slyrWmJ7p2CI9WqmOkSIvtipnsrmmkxUbY5bKY5hODslDzERO7Dkm3tSNujre6KRVVMFgELdu3cL//M//xGWJrwXytDl+/DhOnjwZVe6UuIgnJibw5ptvYvv27ZDL5TCbzRAEAYFAAAsLC9BqtTh8+DBaWlowPz+PlZUV7Nu3D93d3TAajWJ96Orq6udaA4tlWUxNTaG/vx/37t0T8+oIer0eXV1d2LVrF/Ly8iStDlZWVvDFF1+gt7cXDocj6iYgNYq6urpQWVmZ8jsi9c5HR0dx5coVPHnyJEoWz/Oor6/Hvn370NbWlvLmIval0dFR9Pf349atW3EOjqKiIuzbtw+7du2C0WhMqcBZlsXS0hIGBgZw+/ZtOJ3OqNAJuVyOAwcOYO/evSgpKUk6NpZlYbfbRTmkqQJBJpOhs7MTnZ2dYvPORHIYZrXBxs2bN3Hr1i0sLS1FjYekDO3btw8VFRVRD5JQKITR0VH09vZicnIS4XBYLEa3nnWdNitp795Yo2kuFRXJwYuVyfM8FhcX4fV60draKoYNkAvB7XZjamoKZrMZO3fuhEajwdzcHOx2u3jxEWXBsizq6uqee1VRUpAsUbkQEnNGthRStx9yuRwqlSouaZmsSqV4lYgLnhRRU6vVUcqDeE6lGHzJqoHMNTafTxAEca5Srxui/MjYIo8jzoXYpgmJINeWSqVas5xU41EoFOK5ilT4kedYqVQiHA7T7d8aSHv3krywurq6Z7Js1Wq1cV+gIKzWXyddbIjNan5+Hmq1Gj6fDzabTayMwDAMFhYWMD8/jxMnTsBgMIDjOMzMzKCsrAwmk+m5xnGRlcSrr76K48ePx22vIsM8pJZQUalUaGtrw86dO6O+ByJPavgDuYnq6+tRXV0dJwv48uEkZavCcRxKS0tx6tQpnDx5EgDi5kqUQrq58jwPk8mE7u5uHDp0KCrGi0AUfKqyMDy/2nb90KFDOHjwYNZyBGG1NdbBgwdx4MCBjOREnmOGYbC4uIizZ8/Gxe9RpCFpRaVSqbJuyZSORAZPlmWRn58Pg8GAoaEh+P1+OBwOXL9+Hc3Nzairq8PKygpqamqg1+shCKu1uknRPoZhMDw8jJWVFfA8D4/HA7Va/VyVFVndJPvMVIbeZO9PtWLKRB55X7KI9liblRR5qVZhmY6N3PxrkbXeciLPMbHFboSg582KpP1QpjfVWiAX/e7duzE2NoZf/vKX0Gg0KC0txcGDB7Fr1y7YbDYEg0FUV1dDr9eLbYbMZjOsVqu4wmIYBk+fPsW9e/fw4osvilHcqTw4ZAzZkMy7E7kl2GheuWxlkf/Hko3BOFfj24hygGivId36ZceGDE8guVlf//rX8fDhQ/A8j/z8fOzevRt5eXnQaDT49re/jYqKCmg0GoRCIRw7dgxtbW1iE4Jt27bh+9//PgCItc7D4bDYIy12y0O2mwzDZGXsJIZoUg44Uj6xQ0m9SMmxybZKmV7skWkgyeRJHR+ZZzrbWjZzjZWZ6PdUciIfNGuRk248mX6fuYI8BGJXZmTuZMxbceWWc0UVG0eUDQzDQK/Xo6mpCdu2bQPwpVGTYVZrHpG6UWRrSgqYkfeQNAjgy5Se5eVlPHjwAEajUTyejDEYDGJkZAQqlQq1tbWSv2wyT6/Xi2vXromt0SOVjFqtxvbt20XvUCpYloXf78fw8DCuXbuGqampOKVaX1+Pzs5OsWNJKgUkk8kwMjKCGzduiF2DImWVlJRg7969aG1tTVuRkmVX+9MRWbGVLRUKBQ4cOID29nYUFhamtP8QQqEQhoaG0NfXB5vNFnWMXC5HVVUVDhw4IFblTCVneHgYfX19mJubi0pjkclkqKysxIEDB8QGnsngOA6jo6Po6+vDzMxMnJzy8nIcOHBA9EQTUm0RyWtrxeFwwGazoaqqKu479/v9mJqaStoxaLOT05rpfr8fDx48wMTEBJqbm1FZWSk5OTWW2MqcscR+8bFevUT5huQi6u/vR2lpKXw+HziOg8vlwtmzZ8HzPJqamjIaZ+RTPPIJHGnnyWRLGfvEjFUsUr2EkcSuAGJlSh1bIrmp7DOZyohdEWUyz2Rzitx2SxlbsmNiv8fYz1tcXMTQ0JBYAYLA87xYojtS6WUD+Zzh4WFYrVZxPLOzs+IDuKCgYE2fsVHJmaIKh8OYnJzEL37xC1y7dg0//OEPYTabs1ZUzwKNRoPm5macP38ed+/ehdFohMvlEkvyvvbaaygtLc146SwIQlR5k9jKmGQ5nkzpxsoi5U3q6+sT2nyI4VpKrXGO41BRUSF65mIhK1Up8nieh9lsxtGjR9Hd3R03rkijupTtIZlLc3Mztm3blnDLHLmSTiensbFR9E5nK0cmk6GhoQG1tbUJk8tjDeNkjg6HAzdu3MD169ejugGFw2HU1dVh165dYmJ9thBF9P7772P79u2Ym5sTMzhmZ2fxve99D3q9Pmv5G5mcKCpStOy3v/0tLl26JFY72GiwLAu1Wo1du3bhvffew/vvvw+v1wufz4ejR4+irq4uqo9ZJpCbVKVSJbzAI/+VIovE4KTyykmFrE4TxZJlOjaicFP1n4usUpGudx95f6JifZFjkrISyqUcYqdMJ4e8XlNTg+9///v47ne/G1dsT6FQwO124/z58/B6vVlvA+VyOSwWCxobG/H73/8et2/fBsuuNuU4fvw48vPzt2wX8pzMyu12i91LpAbSrRcymQy7d+/GnTt30NPTI1aDfOGFF9ZUKpk8bXOVGZ9LQ22ujb6p5AWDQfj9fvh8PjDMahUCnU6XMtgxV+NbLznke0/Ww49hGHE1tZYxMgwDg8GA7u5uXL16VWygolKp0NnZmVVl2s3CmhSVIAhij7ienh6UlJSgsbERQ0NDuRpfziGF2tra2tDc3IwHDx5g586d2LlzJ/R6fdZfdKS3aCMq6OcBz/OYmJhAf38/7ty5A4VCgebmZnR3d6OkpERyG7DNCPG6JSIyIHQt8yeKv6amBu3t7bh16xZ8Ph/a29tRXV0tqfTzZmVNiorneczOzuLSpUsIBoPYuXMnFhYW8PDhw1yNLyfEXhwymQw7duzAm2++CZVKhVdffVXMB0x3ISV7Ynq9Xjx69AgzMzNb9mZMRzAYRE9PD65cuSJ2Yv78888xPj6OgwcPIj8//yvb5444brJRJLHbT41GgyNHjuDx48dYXl7GsWPHxN6NqbbYm5msFVU4HIbT6cTt27cxMTGBrq4uVFVVxbUQWo94E4IgCLDZbKInMhQKidtSkpjrdrsxODgoblUSwfM8mpubsW/fvrjqjgQib7NfENlCyjv39vZibGxMTMQm/9dqtSguLt6QtsvnAdl9SPXakvePjY3h4cOHUXX4GYaB0+mEzWaD3+/H5cuXMTg4GHevCYIgrsCamppgsVie2fyeNWtSVGNjY+jp6YFGo4FSqcTMzIxYxWB6ehqzs7PIz89ftyUpUVSk9bbf74+yn5Gfy5cvo7e3N6kcjuPw9ttvo6OjI8oGRRJO/X6/6GH7qsIwqxUDlEplVMVOkhhMgm2/qooK+NKOSa6bdPdEOBzGyMgIfve73+H+/ftRcX+RQZ6//vWvE3qqBWG1M/fRo0fFPgabFUbIcp9CNPk//MM/iEZ0EufhdDpRXV2NN954A3/2Z3+GoqKidSu/GggEsLKysuZkUJ1Oh7y8PPFC4XkeDx8+xN27d8XWYV9liMF4YmIC9+/fx9TUlNiReefOnQltVMTDFrsK2MrKjNhI29vbUVtbmzILQhAEeL1erKysIBgMZv15Go0GOp1uU5eXyVpRcRyHhYUF3L9/HysrK+A4Dj6fD7/73e9w8+ZNvPHGG3jjjTfQ0dER1wPteRIbvJctiYL8PB4PXC4XvF7vmmRvJfx+P1wuFzweD1iWhU6ng9lsFmOPYr8H8hDhOA5yuRxqtXrLxgIBX4bIkBjDdPdFpoGvicg0BGUjkvXWjzwtSZoKz/Nwu90YGRnB6OgoduzYgebm5mdepzwdz+pLYpjV9lqkVhYlMziOg9frxYcffoibN2/C7XZDo9Ggs7MT3/zmN2m1gf+ftYY0bBVyGh3G8zwCgQD8fj8CgcCWXsJTskcQBIyPj+PnP/85JicnYTQaUVlZidu3b2NqagqVlZXYs2fPlsxZo2RHzhQVifFob28Hy7LYvn07NBpNrsRTthBzc3M4e/Ys/uu//gt/8id/gjfffBOFhYX47LPP8L//+7947733UFZWRhUVRSSnikqj0eDkyZM4evQoNBpNwjK8lK82PM/j888/x8WLF1FXV4dXXnkFDQ0NYmmfqqoq9Pb2wuVyrfdQKRuInG79iPGUdH2he2tKJDzPIxgM4tq1a5iZmcFf/uVfoqqqKsoWRbsJUxKR8wxGqqAoyQiHw5iZmcHMzAyMRiO6u7vFkA/iRfV6vSgrK8s6OZyyNdmaqdaUDQnHcRgbG4PP50N1dTUKCwujVlM2mw2Li4tobW2FwWBYx5FSNhrU/0t5bnAch8nJSbAsK5aHBr5M6J2amoLdbkd7eztMJtM6jpSy0aArKspzQxAELC8vQxCEqKDOUCgkbgnz8vLEShYUCoEqKspzg4SwhMNhMZuBYVa7EZ87dw6Li4vo7OxEZbEU/QAAAP5JREFUTU2NpGqolK8OdOtHeW6Q+lQcx6G/vx+Tk5MYHR1FT08P/vu//xtmsxlvvPHGlq6rRMmOrHP9KJRMCYfDcLlceP/99/Hxxx+jqKgI4XAYwWAQzc3NOHnyJJqamtY97Yqy8aCKivLcGRsbw+eff44nT54AACwWC1588UVUVlZu6gx/yrODKirKc4WUceE4TswFJQ0jIptCUCiRUEVFoVA2PPTxRaFQNjxUUVEolA0PVVQUCmXDQxUVhULZ8FBFRaFQNjxUUVEolA0PVVQUCmXDQxUVhULZ8FBFRaFQNjxUUVEolA0PVVQUCmXDQxUVhULZ8FBFRaFQNjz/H5XpQjB2z+GHAAAAAElFTkSuQmCC)
Consider the situation shown in figure. Water
is filled in a breaker upto a height of 10 cm. A plane mirror fixed at a height of 5 cm from the surface of water. Distance of image from the mirror after reflection from it of an object O at the bottom of the beaker is
![](data:image/png;base64,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)
One side of a glass slab is silvered as shown. A ray of light is incident on the other side at angle of incidence
. Refractive index of glass is given as 1.5. The deviation of the ray of light from its initial path when it comes out of the slab is
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAQwAAAC6CAYAAABbaHNPAAAevklEQVR4nO3de3CU1f3H8ffekk12k02ygYSQG5sskSQgikRIILYg14mIBXRai5e22nEqah3HURhvFSudEamdtvyhrbeiFQFrkCDlLogiAhGCQIBIQsg9Ife9Zff5/cFvt1yCLJAlyeb7mnGcWcg+B8J+cp7v8z3nqBRFURBCCD+oe3sAQoj+QwJDCOE3CQwhhN8kMIQQfpPAEEL4TQJDCOE3CQwhhN8kMIQQfpPAEEL4TQJDCOE3CQwhhN8kMIQQfpPAEEL4TQJDCOE3CQwhhN8kMAKkq6uL4uJiDh06hGw5IoKFtrcHEKwcDgfr1q0jMjKSESNGoFKpentIQlwzmWEEiMPhoKioiK1bt8oMQwQNmWEEiNvt5vTp0xIWIqjIDCNAVCoVer2e0NDQ3h6KED1GZhgBoigKzc3NGAyG3h6KED1GAiNAdDod48ePZ9CgQVLwFEFDJccMBIbH46GxsRGNRkNMTExvD0eIHiGBEQCKolw0q+juNSH6Gyl6BoA3GFwuF11dXee9JkR/JoERIC6XSzo9RdCRomeAOBwO1q5di8lkYuTIkTLDEEFBZhgBYrfbWbVqFUVFRTLDEEFDAiOAbDYbdru9t4chRI+RwAggjUaDRqPp7WEI0WMkMAJEURTsdjsOh6O3hyJEj5GiZ4CEh4fz29/+FpPJJAVPETSkcSuAXC4XcLZNXIhgIIERANLVKYKV1DACQKVSoSgKbW1ttLe39/ZwhOgxEhgB4nK52LdvHyUlJdKHIYKGFD0DxGaz8fbbb2M2m8nJyZFbFBEUAhIYbW1tOBwOwsLC0Ov1A7IXwel0smXLFoYOHSozDBE0AhIYO3fu5OjRo4waNYrMzEzi4+MDcZk+zbtFX0hISG8PRYgeE5Aahk6no6amhuXLl7NmzRqam5sDcZk+TVEUbDabNG6JoBKQwBg+fDiJiYls2LCBf//73+zatYumpqZAXKrPUqvVxMTEYDKZensoQvQYzYsvvvhiT7+p0WjEbDYTHx9PaWkpa9asIT4+nmHDhg2YXbQ1Gg2JiYnk5+eTnp4uRU8RFAISGGq1GrPZTGpqKvX19ezbt4/29nYURSEpKYmwsLCevmSfo9VqSU9Px2KxDMiirwhOAe/0rKioYPPmzTz//PNERETw2muvkZubS1RUVCAvK4QIgIDMMM5lMpmIiYlBURQaGhrYtm0bISEhWK3WoL498Xg8nDlzBofDgV6v7+3hCNEjAh4YAFFRUWRkZNDZ2cnq1atxOBxERkYyePBgwsPDA335XuHtw6ivr8disUgNQwSF67r4rKysjA0bNvDmm2/S0tLCa6+9xuTJk4mMjLxeQ7humpqauOuuu4iLi+PDDz+UOoYICtd1LYnFYuGOO+5g6tSpmEwm3n77bVauXBmUfRput5sTJ05QXl7e20MRosdc97UkiYmJPProo6SkpPDMM8/Q1NTE0KFDufXWW/vkCWGKouDxeICzT3/8vbVQqVQYDIagveUSA1OvrFZNTExk2rRpLFy4EI1Gw1NPPcW6detobW297mO53B1ZY2Mja9asYdu2bZw8edJ3MJE/79ve3k5HR0dPDFOIPqHXVqtaLBbmz59PW1sb77zzDmvXrkWtVjNz5kyio6N79FqKonDo0CFsNhtpaWlERkai1Z79o3v3rqisrKSmpob29nbfTlmhoaF8++23bN26lZkzZ5Kamur3NXU6HWPGjJHDmEVQ6dXl7QkJCTz00ENYLBZeeuklDh48SExMDLm5uT3aUt3c3MwLL7xARUUFr7zyCmPHjj0vlBRFYfXq1axYsYKjR4/S0dHhu/3whkdBQcEVPe0IDw/n97//PXq9XgJDBI1e3w8jJSWFyZMnc+LECXbs2MGSJUu47777mDdvXo88PSkvL6ewsJADBw6g0+mw2+2+msS5GhsbcTgcZGVlYbVasVgseDweurq6MBgM5ObmXtEHX6fTccstt1xR3UOIvq7XAwPOhsbvfvc7TCYTL7/8MpGRkcTGxjJhwgTMZvM1vfexY8fYsmWL7zqXWm6uUqlISEggPz+f2bNnk5mZ+aPv63K5OHPmDDabDUVRMBqNGAwG34xCpVIRERFxTWMXoq/pM1v0JSQkMGfOHF599VWqq6t56qmn2L59+1UXQt1uN5WVlXR0dJCenk5qaioxMTG+msWFvK+7XC6/lqSXl5ezaNEifvKTnzBx4kRefPFFdu/e7ftaj8dDfX09jY2NVzV+IfqiPhMYAGlpacyePZvJkycTHh7O+++/z6pVq2hpabni92pra2P9+vVUVVUxYcIEUlNT0el0lwwMj8eDoiio1erLHgvwww8/sHv3brq6ukhLSyMrK4vS0lL++9//+o5GtNvtfPDBB3z66afd3gIJ0R/1qcCAs49cFyxYwCOPPMKWLVv4xz/+wVdffcWZM2f8fg9FUTh9+jSbN2+mqamJiRMnYjabfbcP3Tm3yOnd6VtRFNxu90Vfs3//fnbu3ElBQQHvvvsuH330EfHx8Xz55Ze+GUZnZyd//etfeffdd2WLPhE0+kQN40KJiYlMmTKFxsZGNm7cyNNPP83TTz/NnXfe6Vdd4LvvvuOrr74iKyuL3NxcIiIiqKmpoby8HI/H0+3yepPJhMPhYP369Xz++eeEh4cTEhLCuHHjmDNnDhkZGb5FZI2NjdTV1ZGWlsbQoUMBGDx4MO3t7ajVZzPYe3vjb9+GEP1BnwwMOHt78uCDD2K323nrrbdYu3YtGo2G6dOn/2ifhsvl4uDBg5SWljJr1izy8/PRaDQ0NjbS0NCATqejvr6elpYWBg8e7LtNyczMpL6+nmPHjnHq1ClOnz5NZ2cnHR0dKIrCnDlzGD16NHC2PuJwOHC73b7rhoSEnPcIVaVSodVqZQ2JCCp9NjDgbCH0V7/6FSkpKSxevJiDBw8SHR3N+PHju+3TsNlsHD9+nB9++AGn08mIESN8H1i73U5XVxchISHs3LmTkydP8utf/5qEhARUKhWTJk1iwoQJuN1uNBoNra2t7N27l3/9618sW7YMo9GIxWIhMjISo9FISEgIhw4dIj4+HrPZTGtrKy0tLefdfrjd7vNCRYj+7rosb78W0dHRmM1mHA4HDQ0NfP31177drC7cT6O6upo1a9bw2WefsWfPHsrKyti9ezerV69m586dNDc3U1NTw6effsrRo0cpKChg0KBBwNkt9byzhJCQECIiIkhJSaG0tJSNGzcyePBg0tPTSUhIQKPRYLfb+eabb1i/fj07duygo6ODm2++mfHjxxMaGorb7aaqqors7Gxuu+026cUQQaFPzzC8UlJSePTRR4mOjuall14iPDycwYMHk5eXd96CNYfDQVVVFZ2dnbS2trJq1Srfr3kbtrxPMkaOHHnZ6+r1eiwWCwB1dXWUl5czatQosrOzfYGxY8cOdDod8+fPZ/r06b46h16v5xe/+AWhoaESFiJo9KvDmI8fP05RURHvv/8+LS0tLFmyhClTpvgKoTabjdraWt9BSt4CZ1tbG4899hjl5eUsXLiQkSNHMmTIENLS0i67G9aKFSv45S9/ycyZM3n44YeZNm0aer2ezs5OTp8+TWtrKyqVisGDB2M2m311DEVRsNvtvvNJhAgG/WKG4ZWens7PfvYzKisrKSoqYsWKFbS2tnLXXXdhMpkICwu75AKx2NhYampqGDt2LBMmTPC97nA4aG5u5sCBA6hUKvLy8nxPUex2OydPngTO1lOSkpJ8T0HCw8OxWq3dXst7evu5T2PkRHcRDPpVYMD/+jQsFgvPPPMMVVVVJCQkkJOTc8mNhZ1OJ06nE5fLRUVFBTU1Nb7T2Ox2O0eOHGHp0qU4HA5ee+01xowZg91uZ8uWLb4FcdnZ2QwfPvyyTV1w/unt3hZxCQsRDPp80bM7JpOJqKgoDAYDFRUVFBUVYTabuz33pKysjPfee49PPvmEuro6jhw5QnJysq+G4fF4aGtr4/vvv+fQoUNs2bKFFStWsHLlSl99Ytq0acyYMYOUlBS/P/jt7e0sWrSIffv2SdFTBI1+GRgAMTExWK1W6urq2Lp1K06nE51OR0JCwnm3AhUVFXz77be43W5CQ0PRarWMGzeOG2+8EcD3QVar1Xg8HsrKyqiqqsJms/ke4c6ZM4cbbrjBr9mFV2trKwsWLKC2tpbf/OY3vlsZIfqzflX07E5ZWRmbNm3iT3/6E6GhoSxdupS8vDzf0niXy0VnZ6ev69J7i3Du1nneRiyHw4HT6cTj8aBSqdBoNISGhhIWFoZWq72iWUJDQwO5ubkkJCSwefNmaeASQaHf1TAuZLFYmDp1KsePH2fnzp0sW7aMmpoa5s6dS0REBDqdrtsmr3OLkBqNhvDw8B7df1NRFF8ACREs+n1gAKSmpvLYY48RGxvLiy++iE6nIy4ujvHjx1+yjTzQNQXvYcxywpsIJv22hnEh78FIiYmJ7Nmzh8LCQtLS0khMTOyVE9a8M4xRo0YxZswYKXqKoBA0gQFgNptJTEykurqa0tJS6uvrURSF1NTU6948FRISQkxMDBaLBbPZLIEhgkK/L3p2p7y8nPXr1/Pss88yfPhwFi9eTE5OTo9uLCzEQBSUgQFn28jfe+89tm/fTmdnJ48//jizZ8/GaDT2+LUaGxs5ceIEJ0+epKGhgfLychRF4a677mLUqFEYDIYev6YQvSEoip7dSU9P5+GHH0ZRFJYvX87atWvR6/VMnjy5R8496erqoqWlhZMnT3L48GFOnTpFbW0tTU1NVFVV0dXV5TvM6Pbbb5dbEhEUgnaG4XXixAk2btzI0qVL0Wq1LFu2jLy8vGve0fvUqVP85z//Yf369Rw4cIAbb7yRm266iUGDBpGeno7L5eLZZ58lKyuLjz76SPowRFAI2hmGV1paGhqNxten8Ze//IWamhrmzJlzxaGhKArl5eVs3bqVL7/8EqfTSXx8PDfccANZWVmkpaURFRVFeno69fX1tLa2cvr06QD9yYS4/oI+MOBsn8bjjz9OXFwczz//PADx8fGMGzfuivokampq2LRpE++88w7FxcXMmzePe+65h6lTp150y+F0OjEajb3ySFeIQBkQgQGQlJTEnXfeiaIorFmzhieffJLFixczdepUvwqhp0+fpqioiL///e8MGzaM5cuXM3r0aFJTU7utT3j3w/DnjBMh+osBExgAw4cP5+c//zm1tbUUFhaycuVKbDYbBQUFl3zk6vF4aGhooLCwkC1bthAZGcntt9/OPffcc8lT1OBsp2dmZqZvC0AhgsGACgw4O9NYsGABVquVRYsWUVZWRlxcHDk5Od2e5VpfX8+OHTt4++236ejoYMmSJeTl5f1oWMDZLfrmzp2L0WiUlaoiaARVp6e/oqKiiIqKQqvVUl1dzaZNmzCZTFgslouCoKSkhDfffBOHw8HEiROZM2cOcXFxl72GWq0mNjaWlJQUaRgTQWPA/uhLT0/nkUceIT8/n8OHD7N27Vo2bdpEc3Pzeb+vtLSU/fv3c+ONNzJv3jzfTl0/RlEUNBoNKSkpJCYm+l4Tor8bsIEBZ7f7u++++/jjH/9IcXExCxcu5Ouvv/adj7pv3z6OHj1KXFwckyZNIjc3V/opxIA24GoYF7Jareh0Ol+fxt/+9jfa2toYP348RUVFVFRUkJubS0ZGht/vqVKpsNvtfPLJJ4SHhzNr1izp9BRBYcAHBpzt03jiiScYMmQIzz//PHq9HpfLxRdffIHZbGbq1Kl+3Yqcq6Ojg1dffZUhQ4ZQUFAgMxMRFCQw/l9ycjKzZs3C7XazYcMGFi5ciNVqJT8/n7y8vCvejUtRFGw2GzabLUAjFuL6k8A4R0ZGBvfeey9NTU0cO3aMuro6mpubr/qxqMfjkWKnCCoDuujZnaSkJB555BEWLVrEqVOnWLVqFV9++SWtra1X/F5qtVp6MERQGZB9GJcTHR1NdHQ0Op2Ouro6Nm/eTERERLd9GpfidDrZu3cvqampzJw5U4qeIihIYFyC99yT+vp6CgsL8Xg8REREEBcX59d2f94ahtVqJTs7WwJDBIWg3w/jWpWWlrJhwwaWL18OwNKlS5k4ceJlF6wpikJLSwtqtbrblnMh+iOZYVyG2WwmLi6O+vp6qqqqOH78OCqVCovFcsml694zT/R6ve/3yGHMIhjIUxI/pKam8uSTT5KUlMRzzz1HZ2cn8fHxl9xY2HsYs9PpRKVSERISImEhgoLMMPxkMpkwm83ExsZSUlLCunXrSEpKIiUlpdtCaEdHB4sXL6a4uJjx48dLYIigIM/8rkBGRgbz589n3LhxnDlzhk8++YR169Z1+8jV4XDw2WefsXnzZunFEEFDbkmuUHJyMo8++ihWq5UXXniBI0eOYDabycnJOW+PUO8ticvl6sXRCtGzZIZxFSwWC7fffjv3338/YWFhvPzyyxQWFtLe3u77PbJFnwhGMsO4SlarlQULFhAWFsbrr79OXFwcUVFRTJgwAZPJhEajISoq6pqPMxCiL5EZxjVITk7m3nvv5ZVXXuHQoUM8/fTT7Nq1CwCDwUBOTg4jR46UgqcIGjLDuEYZGRnExsZSV1fH9u3b+fDDD7HZbNx2223cc889mEwmWU8igoYvMDwej6yuvAoajQaTycQDDzxAZGQkzz33HFVVVURFRXHLLbdgMpmk8Cl6nUqlQq1Wo1KprmnGq1IURbHb7Wzfvp1Nmzbx1Vdf4XK50Ol0PTjc4OX9JjgcDiorK30nnWVnZ5OSkoJaraapqUk6PUWv8BbfR44cyd13383YsWOv6egL3wzD6XTS3t5Oc3MzTqdTAuMKaTQa4uPjsVgsdHR0UFtbS0lJCTqdDqvVikajwe129/YwxQDU2dlJa2srDocDj8dzTe+lUs7C5XJJ38A18E711Go1tbW17Nmzh2XLlpGRkcGf//xnjEYjnZ2dvT1MMUBpNBr0ej1arfaaampawLfewd+9HsSPi4iIQKVS4Xa7cTqdmM1mADlnVfR78pQkQGJiYmhra6Ompga32y2bAAexzs5OPB4PISEh1/wTvK+TwAgQj8eD2+2WukUf508x+nK/p6ioCLvdTmZmJunp6UG9/4kERoCoVCri4uLkMOY+pqamhoaGBgCGDBniu138MSqViqqqKkpKSqitraWjo8M3o2hsbGTdunVkZWUxcuRItNrg/kgF95+uF+l0OsaMGUN0dLQ8Tu0jnE4nW7dupaSkBIPBwPTp0/0KDICDBw+yZMkS9u7dS1tb20W/npKSQmpq6hUfR9HfSGAESFhYGA899BA6nU4Cow/4+uuvWblyJZs3b0an0zFz5swrmg04HA66urq4+eabycjIICcnh7CwMN9TxYyMjMtu2xgMJDACQFEUtFoto0aNOu81CY7rz+l08sMPP3Dw4EHKy8s5efIkMTExaLXaKy5Eh4WFkZGRQUFBAdOmTQvQiPs2CYzrZCCGxaVC8nqGZ1NTE++++y6JiYksXLiQmJgYKioqUKvVV1WQdrlctLe3D9huaAmMAPC2im/btg29Xk9+fv6ADAyVSkV9fT2rVq0iMjKS0aNHY7FYCAsLA2DXrl2cOHECs9nMiBEjGDZs2FVf61IhFB4eTm5urq/GYDabqampueLvh6IoeDwe1Go1YWFhAzIsQAIjYOx2OytWrMBsNjNx4sQBGRgAJ06c4PXXXyczM5NBgwaRlJREWFgYHo+HwsJCtm/fztSpUxk0aJAvMNxuN3a7HZvNhsvluuTfnUajITQ0FKPR2G3vg6IoREZGUlBQAJy9Penq6sLlcl3xIkuNRoNGo8Fms1FdXU1FRQVGoxGPx0N4eDihoaEDotdGAiNAurq6KCkpIT4+fsCuAG5paaGsrAyn00lGRgb5+fm+Q6AaGhrYt28f1dXVzJo1izFjxvi+rrq6ms8//5w1a9bw3XffERoael5ouN1u1Go1Q4cOZdKkSTz++OPExMRcdP0Lg8b7fbia8DYYDERERFBcXMyOHTt45ZVXUKvVWK1WHnzwQfLz84mPj7/i9+1vJDACxOPx0NTU5Jt+D0SnTp2iurqaIUOGYLFYfGHR2dlJZWUlDocDs9lMWlraeV+n1WqJiooiKSmJjo6Oi45p8Hg8vj6X2NhYv3+yX0twJyUlMWPGDI4dO0ZlZSWNjY00NDRQX1/Pxx9/jM1mY+7cuRgMhqu+Rn8ggREgKpWK0NDQAb0+p7y8nPr6erKzsxk6dKjv9ebmZo4dO0ZCQgIGg+GiFZTx8fHMnTuXOXPm+HWd63G7l56e7gs27/VKS0spLCzkD3/4A2fOnOGWW27BarUG9fc8eJvee5larSY+Pp7Y2NjeHkqv2bNnD9999x033XQT6enpvtdra2vZuXMnMTExjBs37rwP2LmzAO8K4Mv9d+HXBcqFm88MHz6cvLw89Ho9J0+eZP/+/Zw5cybg4+hNMsMIkJCQECZNmoTJZBqQBc+Ojg6OHj1KXV0do0aNIjU11fdrlZWV7Nq1izvuuIO8vLzzuiO9T5iamppoaGigo6Pjog+qNxxCQ0OJiooiMTGx11qyhw0bRmRkJHa7nerqamw2W6+M43qRwAgQg8HAE088gVqtDurVi93p6Ojg8OHDtLa2Eh0djdVqPa+WU1ZWRnFxMQ899BAjRoy46Otramr49NNP+eCDD9izZw96vb7bGkZycjLTp09n0aJFfs/kejq8vdta6nQ6IiIiZC2JuHLenoBzz10dSJ2era2tHDt2zBcYcXFxvl974403+Pjjj0lJScFkMtHe3s7+/fsZMmSI77bFaDSSlZXFrFmzGDVqFFqtttvAMJvNZGdn+4qpF7rw71yv1+N2u+nq6kKv119UoPR4PJSVlXHgwAG+//57pkyZwq233kpjYyN79+6ltLSUqVOnMnz4cN/7FxcX09bWRkpKClarNeiPlZDACADvYcx2u913ivtACQs4+zj12LFjNDc3ExoayvHjx7FarRw9epS33nqLkpISJk+eTFNTE9u3b+fw4cPk5OT4AsNsNjN58mQmT57s9zW7C2Tv98HhcKDT6airq6Ouro6mpiYaGxupra0lOTkZtVqNRqPB4/Fw6NAh/vnPf7Ju3Tq0Wi233norTU1NbNiwgVWrVtHV1UV4eDgGg4GDBw/yxRdfYDAYyM7OJjMzM6iXtoMERsDY7XY++OADjEYjd99994ALjG+//Zbjx49TUlLCjBkz0Gq16HQ6srKyiIqKYvPmzZw+fZqCggLuv/9+30/tq3Wpv9+WlhbWrl3L7t27KSkp4ZtvvsFms3HkyBG2bdvGT3/6U+644w5uuukmdDodHo8Hu90O4Pt/ZGQkw4YNIy4ujjfeeINly5ah1+sJCQkhLi6Ou+++mylTpjBo0KCg/z5LYASIw+Hg888/JzY2lnnz5gX9PyT43w7VTU1NREdHM23aNFwuFx0dHXR2dhIbG8vs2bNpa2vznQqXlpbGDTfcELB7f28rt9FoJC4ujilTpuByuXC73ZjNZoxGIzqdzjdDSUlJYdq0aRiNRkaPHg2cDYyxY8ficDjYvXs3lZWVaDQaYmNjyc7OZsaMGWRlZQV9/QL+fxPg3h5EMGpoaGDixIkMGTKEjRs3Doi2Ybvdzs6dOzl16hShoaGMGzcOi8WC2+32PdnwFoC9vRfXoyjsLUx290/93PM64H9rRhRFOW9s575+4ddf+Ig3mAV/JPaigXYYs9PpZPXq1Wg0Gh544AGSk5MBug3LC0MikEXhKwkklUp13ni947rw9YFqYD3vu87Cw8MHVGt4Q0MDxcXF1NbWXnFvRF/96dxXx9VbJDACRKPR+NY6DAQNDQ0cPnwYo9FISkqK7GUapOSWJED0ej0PPvggBoNhQDRu6XQ6kpOTmT9/PomJiTJ9D1JS9BRC+C34f/QJIXqMBIYQwm8SGEIIv0lgCCH8JoEhhPCbBIYQwm8SGEIIv0lgCCH8JoEhhPCbBIYQwm8SGEIIv0lgCCH8JoEhhPCbBIYQwm8SGEIIv0lgCCH8JoEhhPCbBIYQwm8SGEIIv0lgCCH8JoEhhPCbBIYQwm8SGEIIv0lgCCH8JoEhhPCbBIYQwm8SGEIIv0lgCCH8JoEhhPCbBIYQwm8SGEIIv0lgCCH8pi0vL+fEiROo1WpUKlVvj0cI0cO6urqIj48nMzPzmj/j2jNnzlBWVoZarUatlgmHEMHG6XSiUqkYMWLEtQeGwWBg8ODBMsMQIki5XC5MJlOPfL61ISEhREZGolKpZIYhRJBRFIWuri7CwsJ65P20ISEhGI1GVCqVzDCECEJdXV2Ehob2yHtpdTod4eHhEhhCBCm32x2YwBBCBB+Px9NzgaHVan33NxIaQgQfj8dDSEhIzxQ9NRpNj6WPEKLvURQFrVbbI++l1Wg06HQ6mV0IEaR6NDDUajU6na5H3kwI0Tf1VMuEVnovhAh+PXUHoZWGLSGEv7QgT0eEEP6RqYUQwm8SGEIIv0lgCCH8JoEhhPCbBIYQwm8SGEIIv0lgCCH8JoEhhPDb/wHrvm4DOXpDFwAAAABJRU5ErkJggg==)
One side of a glass slab is silvered as shown. A ray of light is incident on the other side at angle of incidence
. Refractive index of glass is given as 1.5. The deviation of the ray of light from its initial path when it comes out of the slab is
![](data:image/png;base64,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)
A plane mirror is placed at the bottom of the tank containing a liquid of refractive index
. P is a small object at a height h above the mirror. An observer O-vertically above P outside the liquid see P and its image in the mirror. The apparent distance between these two will be
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)
A plane mirror is placed at the bottom of the tank containing a liquid of refractive index
. P is a small object at a height h above the mirror. An observer O-vertically above P outside the liquid see P and its image in the mirror. The apparent distance between these two will be
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)
If an object moves towards a plane mirror with a speed v at an angle
to the perpendicular to the plane of the mirror, find the relative velocity between the object and the image
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)
If an object moves towards a plane mirror with a speed v at an angle
to the perpendicular to the plane of the mirror, find the relative velocity between the object and the image
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q2MPKLuCQAKmbiJ+2cx73ojJJO0kBF+oUvfKGez/2Kr2233bb+1puOOrNawSas0si9Oo880PJ3E2HxIn6lkfxD8ORLeVi6i3N523NLa+dlEHz729+uYZzHvSgjnsd5iIjK9qyzzqoi6zruwTMRfPfMzf3Rj35U01I6ys/iZ6+99qri6XnkKeXswgsvrOf0nWsog/KM/KI3XNyqfNybtCVW++yzT70nZUA6am4Thz5Lgze96U312eWXdr/aOOUL96ij17X83g5lvaVz+yy9XKeloTzuf8J5ppe85CU1HeVR/+ln5mt5SkSR59VnES3RWZ5f/epXy9e+9rXyhje8oSaeCBeJMr/XZiERBLWRBJNBCJtOpve+973l3e9+d80gMqXrDLY81YTN8pTRCQARZr0QGW6EmrCJkTDNYoHvWBESX+F1XoWhWZ5wn70WiwzJYiSy3kNhJCIsH+H9V4FTI8swriODOE+v5elZFW7n8QwyjIJA+OCZCaf4EbcKa7M8xRvBUhgUGpWKQqeguU6v5alACtMsFt9rSvFMMmizRliO0lE8NMtT3Lk/aexanqllCemqIHh+BdN5CITRFcI6B8uCQLoPhdSzExO4NmGVRr2WpwIlfoWFexCmWZ7yiR0JVAzCKHTuRfyrTH2nQpDW7gsKbYt/6ShdmoXr+VreFUZlSDzFKcvTMwsj7qSjczic02/OI2+JO/fXLE/ncR1x3yw55/Gc8pt09Gye2f06ei1P4iudmuUpjVo6wrVUuCxYadIsT+lIFD2T/KANkni6tjSSH6SHfEqMPadKWyeP+3ENZc39trR2Dffimv4njIr7K1/5So0rC5sLIw7dO8SLfL7uuuvWOBE/8qxXwqsS3WGHHer9+Q4tHd3HhBVPX0uclvFaMBnMZ26aGpkIqk0UEhHvdxHKupDxFAoi53cZxPdHH310edvb3lZrVaLifDKha7XrKCDtAFGV4IRX4XrNa15TM5YMrnBh8P26l3aOFmbwdSARhRHe934Xrp2jnUe49p3M0BvG+du1fNfO03svwjhH7704Whjft/N49V1vmN57cXjv+/a7A/7b0sL7dg6Hc7Yw4l4Y+G/v/cI12nng/577nHPOqRYza6SJFbEg2gqzZ2z/ac/TCopzu46j0X4XFu1eXA/O1Z5ZGOfovd8WxjmE8b5dx+8O3/Wep4XxPH73voVp50HvdVoY99Du13e915pXmHaeFt73LUy7l5ZGwqL3HML4voURvoWRRl7Rew7PxoNSyTA2GD0qj94wzuPcntd5Gu5V+dUlQmSJp8qReCqLrRJ1ju23375W1M5J+BlStIE1/oEPfKBa+40W/+2Z+plHY3wIWoQSJwVC7ehQ6/heTaP2ELFqxFbj+E1NpVY2bOG4446riUdQtbUQvuaWNloG6L2O67aMhZZ5JHbLRC0h/Db4fh3eC68mdX+sFJ97wzha5nMOr0TF9+7Dq2duItLCDQ7Te7/C9N5Lb5je+xW+N4zrOG8L0+LF94Pvpd2HsP7TwrTz+F4YtDDtOi1MO0c7T++9OHzuDdPul2XOfZTuvkOvCPlPu16733aO9lu7RrtOe2ZHu5f2u/MMjhfX7X1mYYZKxxam9156w/Q+cwvT0rH3XnrD9N6vcwwnTLvfFsZ799d7L71p3cL4XwvjfC1ee8P4XfzL44StlQ1hpUcvzuOcg+9XWL+1QxiHcuq+eCYsaOLIytbEw4Noz+maBNf1Wa3C8kh4Lc7fDtdp8dLvzFM854fE4rKphURUcwcVHpEnQrnc9jMipEx/7gPXXYEjutwj5xkuMoEEcoj4lqHmhfuR4Iccckh51ateVS1V+ymdeeaZNZMNzlRh+DSR7I3DwZ/D4oFgaQo4+eSTy2tf+9ranviOd7yjzJ49u35PHIkfw0HYkUDoNLfwGlvzEkOIcGoKMMZTU4CyrFzKF8qdpgVh25bEE5XO4qndgtusDVHjsle1kkQSkSJUx5FZRdpniKc2SxaodjLu3khqHwnDgnQuNZgMMRQKsHvQ7qOJgLCzkmUA7XTulYC7x9AN6SaeJ4L10K+If2LIkzNdUjs+oWLQaPckcjw9MGaUHcI2EgivsqptVtswT1InnPMr/5ptiCsLtVm+2lp5Jq5n5EVr35+IjFg8FRhmtwZztY7Pemj1CBMnjfxqJQImUg11Eckal0W+xFZjaSMZieVJ7JyXQMsgEnaowsvy5VZol9Pgrbf9S1/6Ujn00ENrm4/7kvgSOoR+hXjKx+edd15tQiFShx12WDniiCOqBarsEU/lRlnRDqlsDBdlS5OA8ksole1vfOMbtZ1Tp53vueWMGRaue2mTJRguPFNjv3X4TlQ6WZ4iVm1maAPrkiVoqBFxZNkx8bnzREwPotqIUEpQNZLPEnO4bl6rZZsws2p1TgwWXxmFOBNy92D3TtNFia3E1Fzgf87VXM/QncTf2CDvMiIYLTplWHg6bXTaaaPUp8AKlT6EzneEVNnpAhFVbpRbB8H0yqvjceo8Mu7bSBhCTjAZVm1kxESl89z2VjO1xCFcah9iaYgOq4/5bngGDHnRDqodRWQTX9anzwtCJiC2xNn59e7rxW+N3C2MRmqDetWS3AlWp4wkjPvj2shAalLDYtx/+38YHuJZQVFJ8ih0DEoHcSlNvVdJKjQLapcOI0f8Ey+dNfK6+DYMqXly8nkzXliG8ro8b+ynoVPG1A4H1+GdSWeH80pv1yHcyqHrax7gVRoJ476UcUaLsHRhJN5lv7FQ4ili1HAiVEKx6LgGEksvvAJFvCSY4QpqI9+pMXXmKGysQa/zK2TaU9ScXBTnlzjGi/X+R21MvE899dTaYK2XT2KasUHAJba2IedijRLP4Qh3+G8inmOL+OcmszgZA6xNNMOFy6xd0jAjrjXBFJ54GqZkrKZ0WpComX1FFDV/tX4Kna7GKStXBFQYnqTzMaKMG95ll13qNQjnRLY60XlJusGIUJYfcfNeTaUQteEXRFZBYu6bSXHkkUdWsf3whz9cI31evXJuz3+4BNpTiKaB+TqcenFd1u7HPvaxmqlcV0HuzSTCmD1ywAEHVPGc6Im7KFBJfeITn6ize4zVNQBaZ5ymERUW905hEv/iN+I5uigzrDzlRies/C2ft7iWPtr1lalPfepTVch4egcddFAVOIYHN19azQvXUDnqVWcE8RrN3lL2lMfWftqav1plqfnOeRckzBOFzpbnYESYyFN4FCQ1j4hUsHzfElfjNWtU4VI7mmrmOwkjE/QWNglFhA1x0unjvIYdtdkfDQnoXBLcq8Q2ZMOcXxmlTTtzTZlKx5F7SsEeOdIklufY0AwJzWKtacq0VhUYb8oMIeVN/BNNzVv6B+R1xolZW9oohVM+Mbi8sSgZKaaS6j+Qxm2abqsQnc91lG9l0rl9lgcmi3Bi1MRTIszv6A1DLAkazBhSk0kALogCKEwTTpmE66BtxbAn7n+zYiGcQ+2q04owawPaaaed6tx3Mytci+uhR5J4GikgI7RzhOEjriOeY4O4J34MDnGrk2i33XarBgLx1A/AGiRurY9BWZMuypZ2Ular8sMKZehIn1beWKzKEeF0HS6/JeiUn1ZeFnRMJsakmhDJEk6Hzn777VdrOJYlt9t7iWiQraEPFqIwPpS7LSFbgvci4dXI2kXVtA4Ip41TAzoXR21rbOpgCzeEfkH7pTZ8ll5reiKkvC8GAqtRnmd5CiOfO7w3hImoWizFgigEUlMbI0XbJQ/vpJNOquWI0dGmXTavMfw3Y2ZjS3CdRTqRJJIa0mICOnX04pk7ffDBB9eaUK2qzUUNOJRbQDxZrwTUeVqmkSlkEEuKqWnVpG2loRD6DfmcW23IHgOAkSCfE04TP+Rzn5UTote8OIfwvreXGANCOdNurf+BoWJkjH4F4sxi1bTFVedR+H/4X8a0gUKimP2jfVKiqgXViJZyY4X6zFXnhkvwoazOhgzEZdFZJZP5rEffLCM1KoE2OD+ZIfQ7jIKWzx1Gt3DlNafoDWeQaIscnM+588rAq1/96iquDAvD/xgqpi0bpWJkjOUXCW3KyvwZtTbPrrAkJZI2GVajnnJTwYiqXnW9gwuqAWUgQsk9l6m4GdwQNbEZETLS7rvvXt0c10uG6I64Tpvn2MG7MhyJYIpbh8ko3HVWKQ/NEnFDNU35LG00X2n3lz6GIxk6qNzoDzAryJCmZrWGeTPm4gmJyKrkxhNQ49WIoQ4fjeDNDR+K9r1XGYob0lx/liuXnwCn7WZ0iHiOLeKU0LE05XMemrJCDK30rq1zfh6a73X+CGMMNK9MehmZQniVk4xEGR7jQjwhsSRoG8ak40iN6r0CuqDecYVXLyKIraFPamDDLKxDKNMhmWLhiHiOHeJS/LbRJuKcwaGNkqFhUPyChE/6GdxuuJM01LmkfVM5MRvJ+ZNmw2PUBsmPFtoqNWCbI3vggQdWy9OiyVwK7sa8EtZjaPPkrntVcGUEBTqFePSQPhkkP7bI30aksEDFr7hucT4/lBH/M2RJO6cx0YRXnwNjY0H/D//NmHYYDQWh04towZEPfehDtR2HcaxdZn6LibRMpFb2f4VZLZwCHCYaLHuVlHzOoPB+uMKpP8FQJa6+Ji0dqRmB0o1xJ54goDp3jOs0vlMGsRyWwbtcDtbPvCCUvUcIE5GR5HPCaTqlzlhliGdnlpF2Tp2xcdW7MS7FExKTFfm6172uuu1WiTGMSUO59tB5WaAhhP+gnFgdyYQTs/nacCQTVAxHinB2Z9yKJ1igrE7tarYh1p5p104uvNrTeLcQwtA04dSjbgIKV90MI01ihiNx9SOc3RnX4gkCagwoF96QI5/t12KfckOTYoGGMDQ6lIz/NADe+FCdQxnHOXqMe/GETh8Cqv3TTCQdR9YnNKaTgM6vDTSEyQaDQrkw1tlYUK66mUWGI5mBZIhThHPh6QvxBAE1po31acUkA3ztDa1mjQUawqMoB5q3tHEajmSxEJ1DjA7jOOOqjx59I54wnEIv/BZbbFE7kvC5z32utoGaTRQLNExmWhunwe9WImvrcfLYTGZgcYbRo6/EE9o8rctpcQMiKrOceOKJdVA9AQ1hMtKE08wh29XYlsNiOspI1q9dNPSdeIILb4Aw933fffetK2TrhZdx9MLHAg2TCcJpHKeFww3n08ZparK57lx1HluEc/TpS/GEzGCNTnN63//+99dZFp/85CfrtsNx4cNkoQmnnRYMR2quumXlTLmMcC46+lY8G/Zjb+uBQluPNQptXCVjhdDvyMfmsw9lEDThNPKEcOoc0quecZyLnr4WTxlDG6h57OboWrPTRvx2/WsD6VuGkwHNk9cuFFEN/YSVj0xLNje95V2vPCx7ElkB3hqfVlUyjtNwpIzjXPT0veWJ5sJbWss+LTKZufA2hGsCajaSjNY254+Ahn5BhW+N2zYt2dEW+Zg9e3b1stoK8NbjzJTLxcMiE08JTLRaYi9qdCKtsMIKdSaS2te19cLPmTOn1tDcHtsOaFSf3+pMIYw3WJ2EUg+6fN2GIxkA7zvCaZthnUMWEw+Lh0Uiniw7tSGxWpyLeHDhDaTfYYcdahuoAcJ6H7UHEUyHNQztDmggcQQ0jHfkUZuyGUlCKAmnrTMs8qF8mave9hxKG+fiZZGIJ5fCcAljL7nOhKpZoYsaGchq9DLUHnvsUcXymGOOqbsDEnSLI8h83ocwnlFeNDeZl25/LpW+mUMMArtlEk7DkUZzrrprOnhqjCDlNgzNIhFPw4ZsfWE2kES3gyULFItDQNtA+u222668/vWvryszHXLIIbW2timcKZ2L0yIOoSuanExFJpwWwznnnHOqG2+IHuHs3WJ4NCDWyoaNExk/jA2krPwvI97DSE3E/dW7x5UgjhqzfW6HtTcltt9sUCUh2n4rhJW4LSrUmHrVuToymTYgtbT2TxlBB5LhHbb1sBDsoryXiYhClD2MFg+ETNk699xz6+gRbjsvziI5Zg8ZpkdcxbH4dowGyodyzMpVnmyvohylrPw3I97DqEXs0UcfXY477rgauYOX8G8FxhALLrxIZ4nus88+dQ92CbEoCpVHkZm0BbEwbSCnjYiLzlW3riHxNF1t//33r22j89uZM/wvKs/sYbR4UNZ4bUcccUQVT3HP0jQkiWelHBFQK8IbntQ2hpsfyogy69xe5wWDwzUZP85tLQnGTyrE/zBi8VQbsur0/hEoCTq4RmqRy/xvUyathsTNsKGbgrUo8ChtTNwdd9xRa2oCqga16ZV7Ia6aE/bcc8+aIVpDexgeEc/Fh4r/y1/+cjn44INr2704nT59eo1z7Z1mEE2bNq0aJobqsfrnh/LBmFEWrPHJM8TgNFKeheOpaTIwFdq2xHvvvXf1NGKBPsoi2T2zCSzXjsCKfEOIbDQloRZHgfJYatdrr722Wp3Gd7KYZQYCK/PtvPPOtdbOPtXDJ+K5eBDPRovo7LRhmzglkATT2pwOVqi4H+64TmWCIJuR5Jw8Md/1/td7hzLMCGGAuIYO2Pe85z11OFTE81EWiXhKIGKlg4apr9ZSQy7uwuTR1KDaiby6L+2xal7toto9NbxnbNzwiXguHlTwLEOuMy/q+c9/fhVOrnlrgySaI41j6Sfv8waVicHi2dDDr5xYUFlvvlXMWL3SNmn6KItEPFl82hnVWnq61ZDjoa2kian2HO47i5i4D26zDfMm4rl4YPlZ5JsHB1anuBWnixLpy+K0UhkLlXCycrnr0jT8h0Vif6sRjbXkGq+yyirjQjjhHvQKq8G1vWr7jHCG8QiRVLkzPBwszkUtnGBgOFi2yu6MGTPq9VNO/pdFIp5EimC2YzxZH+3eZESvIYxXesvR4ipDrkWorQdqe2Ku+uK8fj8R9QghzIVIsjI1EWiKGW5n1GQk4hlCGJKI5vyJeIYQQgciniGE0IHO4qlHzrAGh2EVXtv3Dt+1730OIYSJRGfxNC/WlhcWLbDSi2mQxlASSwPRbQ1gPyGD5Q34DSGEiURn8WRVmgFx1FFHlc985jPlrLPOqoN6iacpmQcccED59Kc/XRciJp6xPkMYfyiXDCGTWkxdNpuprb/re599b6qoyS8px/+hs3gazmDbizXXXLMummrpLJEOQxx8b4yYIQ/ptQthfEIkLTFpyUarnpk5Zs4744igmltvTvtBBx1URTTi+R86i6eBs5bFmjlzZn1lXYpwkes3U/VsgbrRRhvVBLJMnEU6HFZkYrWaeua3EMLYwLBRXq37oOntvPPOq2Wz1/K075eDcaR8R0AfpbN4inRzXc1GMJcZIlWkawu1qIB5saZ4mStrO44LL7xw7grV2kolSFz6EMYO5VgZtniPXReUac1vyqQpmoyfXXbZpS4pabqo7/VtENbJXm4XSjzNE7caO7edQLI8dRZpG5EYhNMiHIRTzWY5K5aqFWKsNG/FGP8NIYwNyrFDU5v1KIhn8waVY3t/eSWeFoA5+eSTy0c+8pFqHE12r7GzeEKkW23lU5/6VG3fJJA//OEPa9uI/YO4823PILUW0WSNCivitak0Vz+EMHYwhKxrSyh5gyzL1qxmAR2rOnmvb4N7b1m7WJ6jAAvTVkgi81dXXln+PpAAlu5/aCCybxlw4bnx9l2xPN0D1tV84IG5WwhobwkhjB2MIOWR+67ziDDyDC+77LJq8Oi7MMedO28JR648K9X/JjOjplzaPa3797599inbb799Ea1/H0iI+wbceT3uajU8MGCd3n7bbbWme+aKK2bNxxDGAcphM2aIpN0X9FEweOz5pYzalkM4234Q2ojnKKNdc8YLX1imDLjjD/7yl2XKb35THjsglFMtpDpgiVpOdcY665Q377FHmbX11rVGG0iFR/8cQhgTlEBtmoyaK6+6qvx6wDVfZUAk257w/xzwKn974421aa5tPlfFcxK77iMXz2FE1hRrZQ6I5xMHInuzgQR48047ldUsqDogoE8ZMPdXGvjuydOmleWe9KSyJMtzkredhDAmKHcPPlge/t3vBlzCB8rjl122vGLbbctGG25Y1h8wgN6wyy7luQNldQn9ErffXh68776y1IAHSTyXGbBQfffwH/844GL+/d8nnFx024bDX0bLWtTbbpXqtH32BToNsg3HBGGgHD8yIIiP3HVXmbriimUg0f79wzBp0jFJ07ibYo1mZHHbI5whLH4GyvGUJz6xTB3wCkcsnKADk7hyjGqFEEIHIp4hhEd5+OHyyIMPlkesUTHwXpMal/6hG28sD//+9+XhW28tj5h9pKmtQ2vfRCPiGUJ4lKlTy5THPrZMMaxQU5r9i6ZNK0vYAfdZzypTn/GMMmXZZcuUjJCpjI54DlUL+U7t5bUdIYQwQRgd8RyqFvKd2qs1KqemCiFMIOK2hxBCByKeIYTQgYhnCCF0IOIZQggdiHiGEEIHIp4hhDHHEhu9x7y+G09EPEMIC4XFYqxA33VLHbtJWOrOyvW287GKvXNa0d7izNYXtfmccOOJiGcIoTMEjejZEdcCygSU8I3EUvT/s88+u25vfNhhh5XrrruuiqbzHXXUUeWzn/1sOeecc2q48WSBRjxDCJ0hZqxOWxTbLO7888+vQnrXXXcN290muLbqIaBf+cpX6saQhPK2224rRx99dDn++OPLDTfcUK8T8Qx9Tdt3akFrdWYtz4lP275jxowZdXX5z3/+8/WwvfhNN91U7rnnngWKnv/vuOOOZddddy0rrrhi3TTyxhtvrJtG2izSHkqzZs0q06ZNG1d5qttiyGGhadHOxXH0C+714IMPLocffvh8F0Necskla8EaqQsX+hPpbNdc1uOZZ55Z2ynXXHPNuq/Zi1/84ro9jy13iN9QAiiPXHLJJeXUU08t11xzTc1Pa621Vt1ozusaa6wxdx+08ULEc4yQ2exQePXVV5ebb765ui7j3VJzf0Tx9NNPrzsrvv3tby+bbLLJkOJJOG1T++Mf/7h2BvgcJi4t77I07e1+7bXXVrFceeWVy2abbVatx5kzZ5YVVlih7jIwFNo5L7744rL//vuX++67r+y2227ljW98Y92xk7cz3nbajXiOEcRzzpw55ZRTTqntRDLLeBeYZjXYRZGL9s53vrNuQzuUeArHdfv4xz9eCxTRDRMbac4IuPPOO2vvuDzOWpQvVLLve9/7ygYbbFA3mRuMsHrXtZvKV1z2/fbbr6y33no1fzVxHk9EPMcI0X733XeXP/3pTzWzjbdhGEOh5lcYjjzyyHLWWWdVy3PTTTcdUjxZHbfffnu5/vrra5vXeLMawujQRM2rQ0eRHvILLrig5gHi99KXvrQ276yzzjpztzfuRVmQR771rW/VDiLnsWvnxhtvXLcxZ61GPMNcWrSrcfspCdyroSOOBbV5Ovrt+cLIkb7SmRFw3nnn1YqVt2F/dx1J3PWVVlppyDZP/yW43HWeGGNC+6imLOf4yEc+UlZfffX/+d94IOIZRgQL+YADDsjumWEuBrUTunPPPbfMnj27tnNutdVWta1TvmBpDpUPCO7f/va32i7+5S9/uay22mrVm+H6f+5znytnnHFGOfDAA2tPOzd+vHkv8aXCiIgYhl7YXto3DUvSpKO98s1vfnNt4yR486tAiaf/cdeNDTVWVKeRfeHXXnvtWgGrpA2QH4/NWhHPEMJCwSJkYRpOpFed8D31qU8dVkVLcNddd92y0047lc0337x+Jpra0vfaa6/aIenc49FBjtseRgRr4ROf+ETc9jAXeaJZhtq5h5vm/sflN5RNT7t8oydevvE9l548+Y6oxm0PIUwoiJrK0jGSytL/dCItt9xyZfnll6+Vr8/Ek5DqmTerSIU83oQTEc8QQuhAxDOEEDoQ8QwhhA5EPEMIoQMRzxBC6EDEM4QQOhDxDCGEDkQ8QwihAxHPEELoQMQzhBA6EPEMIYQORDxDCKEDEc8QQuhAxDOEEDoQ8QwhhA5EPEMIoQMRzxBC6EDEM4QQOhDxDCGEDkQ8QwihAxHPEELoQMQzhBA6EPEMIYQORDxDJ9r+3I888kh99Xkke3aH0O9EPMOIWXrppcsTnvCEMnXq1PLwww9X0VxyySXraxPTECY6Ec8wYlZZZZUyc+bMsvzyy5cllliiPPTQQ+X+++8v//rXv2KBhknDlAFLIaZCGDayy0033VQP4rnsssuWq666qlx44YVl1qxZZcMNNyxLLbVUtUodIUxUkrvDiJk+fXq1PFdbbbUqoH/+85/LueeeW2655ZZqdbJGI5xhopMcHkYEcXzMYx5TlllmmWphEkrWqLZPeB+3PUwGIp5hVIhghslGxDOMGhHQMJmIeIYQQgciniGE0IGIZwghdCDiGUIIHYh4hhBCByKeIYTQgYhnCCF0IHPbQwihA7E8QwihAxHPEELoQMQzhBA6EPEMIYQORDxDCKEDEc8QQuhAxDOEEEZMKf8PTbTyKFufLzYAAAAASUVORK5CYII=)
Figure shows a cubical room ABCD with the wall CD as a plane mirror. Each side of the room is 3m. We place a camera at the midpoint of the wall AB. At what distance should the camera be focussed to photograph an object placed at A
![](data:image/png;base64,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)
Figure shows a cubical room ABCD with the wall CD as a plane mirror. Each side of the room is 3m. We place a camera at the midpoint of the wall AB. At what distance should the camera be focussed to photograph an object placed at A
![](data:image/png;base64,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)
Two point white dots are 1mm apart on a black paper. They are viewed by eye of pupil diameter 3 mm. Approximately, what is the maximum distance at which dots can be resolved by the eye ? [Take wavelength of light = 500 nm]
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAQUAAADRCAYAAADFTqccAAAgAElEQVR4nO3deXDU92H//+feqz21uiV0I4EASSCQDIhDGJDBxi4+cOo2juvWbjytPe00E8809UziupM4bZJp49SuTd3YIRMbc9gYY3EYc59CnBIgIRBCCB3olna1935+f/i3ny9rwAgk2BV6P2Y8HlZ7vPd67ft+KyRJkhAEQfj/KcNdAEEQIosIBUEQQohQEAQhhAgFQRBCiFAQBCGECAVBEEKIUBAEIYQIBUEQQohQEAQhhAgFQRBCiFAQBCGECAVBEEKow12A2xEIBBgcHMTtduP3+/H5fACo1WpUKhUajQaj0YhKpQpzSQVh9BpVodDf38+aNWs4evQoLS0tNDQ04PP5yMrKIiUlhfz8fL73ve+Rmpoa7qIKwqgV8aHg9/vp7e2lurqaI0eOcPLkSTo6OvD5fJhMJuCbGkR7ezsulwuHw8GMGTOYPn06cXFxqNUR/xQFIaIoIn0/hZ6eHvbv38/777/Pnj17eOCBBygsLCQnJ4fMzEx0Oh3t7e00NDRQU1PD119/TU5ODi+//DILFiwgKSkp3E9BEEaVG/6MSpKEQqG412W5oYsXL/L222/T1NRESUkJixYtIjc3F4vFQnR0NFqtFqPRSGpqKjk5OWg0Gk6fPs1///d/Y7FYeOSRR8L9FARhVLlhKCgUCgKBAJ2dnXR0dNDd3U0gEECpvPlghVqtRqFQ4PP5CAQC14WKz+fDaDQyceJELBbLLUNHkiQ6OjqoqqqipqaG7OxslixZwvTp04mJicHv96NUKlEoFFitVkwmE6mpqURFRaFSqdi6dSvHjx+noKCAlJQU0fkoCEN00wa3y+Vi+/btrF27li1btuDxeNBqtTe9I51Oh1KpxOVy3TAUXC4XEydO5L333mPu3Lm3/JIGAgE2bdrErl27KCwspLS0lJKSErRaLV6vVx5xUKlUKJVKPB4PKpWKkpISlEolSqWS2tpa1qxZww9/+EPMZvNtvjSCMDbdNBQ0Gg0TJ05k2bJlZGdn4/f7b/hFVqvV+Hw+Nm7cSEdHB3/zN39DbGwsdrs95HpOp5OUlBTGjRs3pKaJJEmcO3eOlpYWpk+fzvjx4zGbzXKNRaVSoVar5XBQKpWo1WpMJhNZWVkUFxezZcsWzp49i9frvYOXRhDGpu8MhRkzZjBjxoxb3sng4CCdnZ3U1tbyz//8zyM2JNjW1sbAwADjx48nPj6eQCAg1w6CgRAMheD/vV4vVquVKVOmUFFRwZUrV+T5DIIg3NqwZzR2d3fz+eefc/r0aS5evMgnn3zC+fPnh10wSZJobm6ms7OT9PR0EhISbhkIKpUKSZKIjo4mOzubgYEBLly4IEJBEG7DsAfxGxoaWL9+PefPn2dgYID169eTnJxMTk7O8AunVqPVakOaCN9uNny7byHYxAk2d7RabcSMpAjCaDDsmkJDQwO7d++mr6+PQCDAwYMHOXv27LALplAoSE9PJzExkY6ODux2OxqNBo1Gc10gXBsaGo2GgYEBLl68iMViYfz48WICkyDchjsOBZ/PR1VVFYcPH2ZwcFC+XKfTce7cOb766iv6+vqGVbjExESMRiN1dXX09vZisVjQarXX1RAUCgUKhQKVSoVer2dwcJDTp0+jVqvJzMzEYDAMqxyCMJbccSi43W527NhBY2Mj8+fPJzY2FoPBQHl5ORqNhk2bNnH16tU7L5hSydSpU8nOzubEiRNUV1fT09ODUqlEr9dfV2PQ6XSoVCoGBgaoqalh//796HQ6srKy6O7uvuNyCMJYc8eh0N/fz4EDB9DpdPz85z+nuLiY6OhofvrTnzJ//nxOnTpFf3//HRdMoVCwbNkyysrKOHXqFF9++SX79+/H4/FgNBpRq9XyfIRgDUGSJPbv38+6dev46quvsFqtZGdnc+jQoRHp/BSEsUD1+uuvv367N2ptbaWmpgaAefPm8eCDD7Jx40auXLnCq6++Snp6OgqFArPZjE6nw2w233Znn0KhQKPRoFQqaW1t5fLly5w7dw6tVisHgdVqRafT0dfXR1NTEwcPHuSPf/wjDQ0NFBQUsGjRIrRaLatXr+bw4cN0dXVhs9mIjo6+3acsCGPGHfXAtbW10dbWxhNPPMHkyZOBb3r7/X4/TqeTrKwsXnzxRQ4fPkxDQwPJycl3PAKQnp7OCy+8wPvvv8/u3bvZuXMnvb29TJo0iczMTDQaDS0tLZw7d46TJ09y4sQJJk2axAsvvMCECROoq6ujpaWF8+fPU1tbi81mw2azDWmqtSCMRXe0SrKrq4uenh6SkpLk5ctPPPEEhw8fZv/+/WRlZQHIHY3D+QJKksTg4CCXL1+mpqaGnTt30tjYiN1up729Hb/fT1JSEmazmeTkZMrKypg2bRoZGRlERUXhdDq5cuUK+/bto7q6mqSkJGbOnMnChQu/cy2HIIxVd1RTiI6OxmKxoNFovvN6Vqv1jgp1LYVCgdFoJC8vT26W1NTUcPXqVcxmMz6fT57clJubyyOPPEJcXJx8e61Wi9VqJTY2lrS0NAYGBjCZTHJI2e12rly5QkxMDPHx8cMuryCMdiO2n8KNagp3Q7C43y528Ev+XTWS4G2C1wkEApw/f55169ZRWFjIo48+ejeKLAijyqib1TOUL/+tbhvkdrvp7e3l8uXLnDx5kj179jBr1iyKioruarAJQiQbdaEw0vR6PdnZ2XR2dnLkyBGcTidqtZpx48Z951JxQbhfjelQ0Ov1TJo0iezsbJ588klqa2vZtGkTx48fp7S0NKRvQhDGijEdCsG5EBqNBpPJhNVqRZIkNBoNer0e+GZzmNraWmJiYkhPTw9ziQXh7hvTofBtcXFx13U2OhwO9u7di81mY/78+dhsNqKiosQiK+G+JQbqbyEQCNDb28vKlSt5+OGH+bd/+zcOHjwY7mIJwl0jQuEW9Ho9+fn55ObmolQq5fMn2tvbw100QbgrRB34FsxmM0888QRlZWXU1tayfv16WlpauHTpEnq9fkQmaAlCJBGhMEQxMTFMnToVnU6H1+slIyMDk8mE2+3m1KlT8vb1Yit5YbQToXAbjEbjdRvZOhwO6uvrsdvtNDU1kZWVJa/FEGsrhNFIhMIwqVQqTCYTmzZtYvfu3ZSWlvL444/z6KOPiqaFMCqJUBgmrVZLXl6evBCrs7OTY8eOER0dTVFRESkpKeEuoiDcFlG/HSaNRsOECRN49tlneeutt1i6dCmBQICzZ8+GjFD4fD68Xu91C7kEIdKImsIIW7JkCbNmzUKr1coH2LS2ttLS0oLT6aS4uFhsJCtENBEKIyR4UndiYiKJiYny5V6vF4fDQU1NDVVVVdTV1TFz5kxyc3OJiooKY4kF4cZE82GE3Gwpt1KpJCoqiqtXr/LFF1/w05/+lH//93+noaEBv99/j0spCLcmagp3mVKpJCYmhocffpiEhAQqKyvp7u7m97//PcuXL2f+/PnhLqIghBChcJcFt5MrLCyksLCQadOmsWPHDmpqaujq6pKv53a7cbvdGI1GMQFKCCsRCvfY5MmTyczMxO12YzabgW/6HRoaGqirq2P27NkhfRKCcK+JULjHdDodOp1O/ncgEMDlctHc3Mz+/fs5c+YMEyZMYNKkSaSlpWGxWMJYWmEsEqEQAfx+P16vl76+Pnbv3k1UVBSPPPIIS5cuZerUqeEunjDGiFAIs2Cfw8yZM0lPT6e2tpbKyko2bNiAyWQSoSDccyIUwiy4JVxsbCyxsbGMHz+emJgYent7iYmJka/ndDrp7e0lLi7uludtCMJwiFCIMHq9nrKyMubMmRMyCtHW1saBAweYPXs22dnZYSyhcL8bsVCw2+309vYSCARG6i7HJIVCgUqlum5Ysr+/n0OHDvHZZ5+RnJzMQw89RHFxMcnJyWEqqXC/GrFQyMnJweFwhPSsCyNHq9USFRXFyZMn2bdvH5IkYTAYRHNCGHEjdmxca2srbrebcePGiQ/pXeD1eunp6aGhoYETJ05w8OBBcnJyePjhh8nLy5MP+hWE4Rp2TSG4EOjaamzwMmFkBM+iSEhIICEhgZSUFCwWC0ajEavVikajwePx0NnZidlslidFCcKdGLGaghBeHR0d1NTUoNfrSUxMJCkpSSzRFu6IGH24TygUCvr7+3n77be5ePEiTzzxBMuXL6egoAAQtTdh6EQo3Cd0Oh2JiYnExcVx7tw5KisriY6OxmQyicNyhdsimg/3CUmSCAQCqFQqzp8/z1tvvUVXVxf5+fk888wzZGVlhbuIwighQuE+tW/fPnp7e4mOjqagoACr1Upvby/t7e1IkkReXl64iyhEKNF8uM8E+w7mzp0bcrnb7aavr48jR47Q0dEBQGZmJlqtVpxPIYS47VC43Q4r0cF1b93stVar1ahUKiorK/niiy/Yu3ev3BkplmcL17rtUFAoFDQ1NXH69GkuXrxIbGwsM2fOJDMzk76+PjZu3EhzczPR0dE89thjpKam3o1yC7dJqVRiNpuZPXs2LpeL3t5eDhw4gMPh4JFHHiE9PT3cRRQihXQHduzYIT377LOSVquVJkyYIH3wwQfS4OCgVF9fL6WmpkqAZDQapR07dtzJ3Qt32eDgoPTJJ59Izz//vFReXi7t27dP/lsgEJD8fn8YSyeE2x31KUyfPh2VSoXb7aaxsZG9e/dSVlZGTEwMaWlpGAwGHn74YVFLiFBRUVGUlZWRk5OD3W5n4sSJ8t+ampro6+ujsLAw5DaSaAaOGarXX3/99du5gSRJ6PV6MjIy0Gq1dHZ2cuTIERISEjCbzfT09DBv3jyeeuopuSNLiBzBL7fJZCI5OZmMjIyQmY/Hjh2jsrKS/v5+fD4f8M0pWGIz2bHjtkMh+GshSRJJSUm0tLSwevVqWltbASgpKWHBggXk5eWJFZMR6Lt+7QcHBzl8+DBbtmzh008/5fTp0+j1ehISEsSCqzHkjockFQoF0dHRFBYWkpmZicViwWq1UlhYSFZWlqhqjkIajYbi4mLUajVHjhzhwoULfPzxx8TFxYkdpseQYc1TcLlcuFwu8vPzMZlM8lRbEQijk0ajYdKkSUyaNInCwkI+/fRTdu3ahd1ul6/j8/nw+Xzo9fowllS4m257RuO1HU6vvPIKR48eZfz48Vy4cIH09HTeeecdYmNj70phhXvH7XbT29tLf38/CQkJWK1WAOrr6+no6KC0tDTMJRTuliGHwrVhcOnSJfbu3cuBAwcwmUwUFRXJc+0//fRT8vPz72qhhfDZu3cve/fuxWAwkJ2dTUFBAampqWJjnfvIkJsP1zYJVq9ezcqVK/nlL3/J008/DcDGjRs5c+YMx48fJz4+XrRB71Mej4f6+noqKirIzMzkpZdeory8nLS0tHAXTRghtzX60N3dzZo1a3j//fc5e/YsSUlJZGZmEh8fT3NzM+fOnWPr1q10dXWRnZ2N2WwWQ1n3GYvFQnZ2NpMmTUKr1VJTU0NfXx8ajYa4uDjxft8Hbquj0efz0dfXR2ZmJkajEZvNRn9/PwClpaW0t7dTUVGBx+PB6/WKnZ3vQ3FxccTFxTFt2jT27NnD1q1bgW86nYMGBwfRarWo1WK93Wh0Wx2NgUAAt9uNx+OR9w3UarVoNBq8Xi8ejwePx4NGo0Gv16NSqcRIxH1KkiT5PVepVGg0GtRqNVevXuXq1atYrVZiY2PFlnCj0B11NArCzTQ1NVFZWcnWrVvR6XQsXbqUefPmyaMX4nMU+e6oo1EQbkatVuN2u9m3bx89PT24XC4MBgNz585Fo9GIz9EoIHZeEkZUsN/p8uXLHDp0iJ07d+JyuZg+fTr/+I//SHR0dLiLKNyC6AkSRpRarZYPy42Pj0elUnH58mUSExPlkQmv18vg4CAajUb0OUQgUVMQ7imv10tfXx91dXVERUUxdepUMYwZYURNQbinPB4PjY2NrFy5ks7OThYtWkR5ebl8PoUQfiIUhHtKoVCgVCrR6XTY7XaOHj2Kz+eju7ubBx54gKioqHAXccy7K80HMewk3IwkSfj9fvx+P7W1tWzbto1169ZhMBhYtWqVmC4dAUaspvDxxx/T3NzMiy++iM1mG6m7Fe4zCoUCtVqNWq0mPz+fQCCA0WhEkqSQg3E7OzvRaDTy/Abh3hmxmsLSpUs5ePAgx44dY/z48SNxl8IY5fV62bdvHx6Ph6KiIiwWi9gS7h4asZpCcMqzaDYIw9XT08O6des4cOAAaWlpPP744yxdupSkpCRxcM09MGKvsFqtFjPWhBGh0WiYPHkyEyZMYHBwkK+++oqPP/6Yy5cvh7toY4KIXSHi2Gw2Xn75ZX73u9/xwgsv0NHRwZ/+9CcuXryIx+MJd/Hue2JIUohYCQkJlJWVER8fj8PhYOLEifIOTx0dHWg0muumTYuRr+EToSBEtJSUFFJSUkIuCwQCNDU10dHRQUxMDPHx8cTHx2MymUQgjADRfBBGHUmSaGxsZNWqVTz55JO88cYbVFVViabFCBE1BWHUUSgU5OXlsXjxYvR6PR0dHaxatYquri5KSkrEYbnDJEJBGHWUSiVTpkxhypQpPPTQQ7z77rvs3LmTxMRE4uPj5VAIBAIoFArRpLhNIhSEUS0pKYmXXnqJp556CrVaTXx8PAC9vb243W5MJhNGo1G+vuiIvDURCsKoplarSUtLIy0tDUmS5P/cbjdnz56lqqqKcePGUVxcTG5urgiEIRAdjcJ9I7gCE76ZAHXu3Dl++tOf8rOf/Yy1a9fS3t4e5hKODiIUhIjxXctwbmeJjkKhwGw2M3/+fH79619TXl7O2bNn+a//+i+2bNkyEkW9r4nmgxAxFAoFvb29NDU14fF4CAQCqFQqMjMzb/t8Uo1GQ15eHnl5eWzbto0//OEPfPTRR9jtdpYuXSpfLxAIiPUU3yJeDSHsrq0F7Nq1iz//8z9n4cKFlJaWsmDBAr744oth3X9aWho5OTlcuXKFxsZG+XK/309vb6+Y3/AtoqYghJ1CocDpdPI///M/nD9/noULF6JUKmltbaWuro7Gxkbq6urIyspCq9UO+X59Ph9nz55l+/bt1NXV8eijj4bUEs6ePcuaNWswGAzMmDGDGTNmEBMTczee4qgiQkGICCdPnuTNN9/kwQcfZOXKlURHR9PZ2cnatWtpbm5m+/bt/MVf/MVtfWkvXbrEhg0b2LNnDwqFgh//+MfMmzcP+GavyObmZjZv3izvG+nxeJgxYwaJiYljepRChIIQdm+//Tbbt2/ntddeo6ysTF7kpFKpiI+Pp7e3F7i9zsb6+nq2bNnC5s2bKSkp4ZlnnmHy5MnyHpBqtZqZM2eycuVKqqurqaqq4ic/+Qlz5szhl7/85Zje8UmEghBW3d3d1NTU0N/fz9NPP824cePkvykUCjkIbmdmYn9/P59//jl79uwhNTWVBx98kNmzZ4dcR6lUYrPZsNlspKWlodPpaG1tJSYmRn4cSZJwuVzo9foxVXMQoSCETXt7O/v378dkMjFnzpzrDoYZGBigpaUFh8Mx5GbD4OAgtbW1rFmzhp6eHt59911mzpz5nbeJjY3l6aef5qmnnkKhUMjbvrlcLhoaGrDZbNet1LyfiVAQwqatrY01a9ZQVVWFz+fj6NGjGAwGfD4fGo2G/v5+2traKCsrY/z48eh0ulve58WLF9m0aRPx8fHMnj2b/Px8TCbTd94mWAv59tBkV1cXq1atoq2tjaysLJ588kkKCgru+1qDCAUhbJqamjh48CBOpxOLxcLJkyfl5oLX66W7uxu/38+iRYuYNGnSkELh7Nmz7N27lzlz5rBs2TJ5LcSdCAQC2O12zpw5Q319PVFRUbhcLiZNmnRf790gQkG45wKBAO3t7dTX1wPw6quv8sILL+BwOIBvAuHq1ats2rSJ999/n4yMjJC+hhvx+Xw0NTVx6tQpWltbmTZt2nX9CLcrNTWVn//855w8eZJdu3bxySefsH//fn70ox8xbdq0+/awXBEKwj3n9/u5cOECXV1dZGVlUVhYSExMTEi/QV9fH3q9nuLiYjIzM295n263m+rqarq7u8nNzR32oTKSJKFUKomOjmbmzJkYDAZ0Oh16vZ6EhAR0Oh2SJNHb24vJZJK3ibsfiFAQ7rlAIMClS5dwOBw3bPM7nU62bt3KhQsXWLRo0ZDOEfF4PJw4cQKPx8OCBQtue1r0t13bNNDr9ZSUlFBSUnJdORsbG4mKiiI1NRWtVotKpRr151OIUBDuOUmSuHr1Kk6nk4yMjJCToYKBsWvXLlQqFcuXLycrK+uW9+nxeDh+/Dh6vZ7p06cTFxd3N58C8E3t5Ny5c2zZsoXGxkZWrFjBww8/THZ2NjB69264o1Do6elhYGCA1NRUucf22vHk4L/7+voAsFqto/LFEe4uj8dDf39/yGWHDh1iw4YNaLVaSkpKhvwFczgcNDU1MX78ePLy8u7J5CONRkN8fDxWqxW73c7u3btxu92UlZWRm5uLxWK562W4G+5oQVRDQwO7d++mq6vrptfp6+ujrq6Oixcv3tZMNOH+p1AoSElJQa1Wc/LkSdra2oBvquNr167lN7/5DUuWLOGf/umfrvuxuZne3l6cTicGg4Hk5OR78iNkNBpZuHAhP/vZz/jNb36D1+vlj3/8Ix988AFnzpy5649/t9xRTSE9PR2Hw8HKlSvJz89n+fLlmM1mFAoFWq2WS5cuUVFRQXZ2NhMnThyxN8jlcrFjxw5qa2vp7OykpaUFv99PcnIy8fHxZGdns3DhQnHAbYTTaDQsWrSIlpYWPvroI5qampg6dSoAcXFx/O53v2PZsmW3nF8Q5HK5GBgYICoqasi3GUk2m41p06bx93//9zQ3NxMVFSUPhXq9XgKBAGq1OqSvIZKbFncUCvHx8QQCAX71q19RV1fHtGnTGBgYkHuVm5qa2LdvHxMmTCA5OXlYBQxurdXR0cHp06epqKjgzJkzdHd3c+XKFQKBAOPGjSM2Nlauak6bNo2kpCQMBkPEvvBjmVKpJC4ujpKSEjIyMmhubqanpwer1cqPfvQj/vZv//a27s/hcDAwMIDZbA5LKABYLBbKy8uBbyY9GQwGJEnC4XDQ2NhIW1sbmZmZpKamRvwchzvuaDSZTMyaNYuqqir+4R/+QZ6E8t5772EwGIiNjSU5OXlIE06+i9PppLq6mg8//JDt27eTlZXFhAkTSE9PJzk5GY1GQ09PD83NzTQ0NPDaa69RUFDA3/3d3zF9+vT7diz5fjBjxgwqKirw+XzyjMI7Wbpst9sZGBjAZDKFdFqGS3R0NCqVCp/Ph91uZ/Xq1bzzzjssWrSI5557jieeeAKI3NrCHYeCTqfjoYceoquri3fffRen04lKpWLHjh2UlZWxePFiEhMTh13A5uZmVq1axaFDh9DpdEyZMoX8/HySkpJITk5Gq9XS19dHZmYmiYmJdHR0UF9fzx/+8AeioqKGPYFFuDskSSIqKmpIcxBuxefz4fF40Gg0ETFfINhMUCqVmEwm8vPzWbBgAR6Ph82bN3PlyhV5lmYkuuNQUKvVlJSU0NDQwDvvvAN8Mymlo6ODpKQkFi1aNOyxYp/PR3V1NRs2bCAhIYHHH3+cOXPmkJiYKG+jJUkSsbGxZGRkkJeXR2xsLJ999hkVFRUUFxdTVFSETqeLyEQey0by/VAqlSiVSgKBAIFAYMTud7iCk5/+8i//kgULFrBu3Tq2bdvGoUOHMJvN918oBGVmZlJeXs6uXbtwuVyUlJQwderUYQdCIBBg8+bN7Ny5k5ycHIqLiyktLSU6OhqFQiF33KjVajQaDZIkYTAYmDdvnrzNd01NDevXr+fxxx8P2ftfuL8YjUYsFgsDAwPXDXFGAqVSSUpKCitWrGD27Nl0dnaSl5cX7mLd1LBDIS8vj2effZaWlhYaGxtZtmwZpaWlwy6YJEkcPXqUuro6Jk+ezNSpU0lJScHv9wPIgaBWq+Uag1KpJDk5mRkzZtDZ2cmBAwc4fPgwTz755LDLE2mG0h4dapv1Xt/XSD+myWTCarXS29uL3W6/5fXDQalUkpqaSmpq6nV/O3/+PCdOnCApKYmMjAySkpLC2gwa9satVquVRx99lJycHGw2GwsWLGDChAnDLpgkSbS3tzMwMMD48eOJi4vD7/eHhEHwv+BlKpUKj8eD1WqloKAAgJaWFrxe77DLE2nudXNopB9vJO/PYDBgsVjkUYjRZvfu3bz66qu8+eabfP7551y+fDmsm8netKbg8XiorKzk4MGDnDhxAp/Pd8M53Wq1mkAgwK5du7h69SpvvPEGCQkJctsuOPlkcHCQjIwMXnrpJfLy8m65rbYkSTQ1NdHZ2UlGRgaJiYnyvPKbBYJKpUKSJGw2GxMmTEChULBlyxaeeeYZ/uqv/ooVK1agUqno6+ujurqar776itOnT6PRaHC73URHR/Piiy8ya9YslEolV69e5dixY3z++edcvXoVnU6H0+kkPz+fH/zgB2RnZ6NWq+np6WHbtm189tln+P1+ueZSXl7OkiVLGDduHCqVivb2dj788EMOHjyIwWDA7XZjs9n4sz/7M0pKSuTh27Nnz/LWW2/R1tZGVFQUHo+HrKwsFixYQHFxsdyB++WXX/LBBx+gVCrl3vuCggJmz54tL+Lxer383//9HwcPHsTn8+F2u7FarUydOpW5c+cyffp0FAqFfIrzxYsXcTqdBAIBEhMTKSws5KGHHiIjIwOAvXv3snnzZlpaWhgcHEStVhMTE0NxcTFPP/00RqMRl8vFF198QWVlpRzKOp2OmJgYHnnkEZYsWQLA5cuX2bp1K6dOnaKtrQ2lUolarSYlJYUXX3xR/nE5c+YMBw8e5NChQ/T09KDT6fB6vcycOZOXX34ZvV5PbGwsOTk5HDt2jO9///soFAo8Hg9+v5/nnnuO5cuXA9/s9FRdXc22bduora1Fp9PhcrmIjY3lhz/8IcXFxdEqpGoAAA4QSURBVCgUCtra2qiqqmLjxo10dXXJ731RURHPPvssGRkZKJVKuru72bx5Mxs3bpQ/uwqFgqVLl1JeXk5ycjIqlYqWlhZ+//vfU1VVhdFoxO12Exsby/Lly8nIyODVV1+lra2NmpoaDh48yDPPPMNjjz02hK/wyLtpKPj9flpbWzl+/Djbt2+Xe3dvRKFQYDAYyM7O5tSpU/h8vuuu09/fT35+Pt/73veGPMPR6XTi8/mwWCwYjUa8Xu9NAyHYjFAqlWi1WoxGIwqFAofDwfbt2ykpKZEf1+Px0NraSmVlJXv27CEqKgqHw0FiYiLLli2Tr+d0OmlqamL37t00NjZiNBrp7+/H4XDw2GOPEQgE5HkU9fX1bNu2DZ/PJ4dCSkoKpaWl8vkFTqeTY8eOUVFRgcViwel0kpSUREFBAZMnT5afd3d3N7t27aKhoQGz2YzL5WLq1KlkZWUxZcoU+XqNjY1s3bpV3i1IqVTi8XhIT0+X3wO/309NTQ1ff/01Ho+HwcFB4uPjUSgUTJw4MeT9OXLkCCdPnsRut+Pz+cjKykKlUoU0B1taWjh06BD19fX09fWh0+lISUnBaDTKj+nz+Th//jwHDhygvr4el8uF0WgkOTlZrsHBN0OJwf0PGhoaUKlUaDQacnNzWbFiRcjrcebMGXbt2kVra6sclFqtVn5Mm83G4sWL+fLLL9m6dSuBQAC/34/P52Pu3Lnyfbndbvk5HDp0iKioKOx2O2lpaSxfvlxusgQXO+3atYsrV64QFRUlz8UJvvdKpRKXy0VdXR1bt26VH0OpVJKZmcns2bNDfhSrqqqoqKjAarXicDhIS0tj2rRpPPnkkyxevJjjx4+zbt06jhw5QktLy5C+I3eDQrrJNzS4wUR/fz92u/0723fX7loT/KLc6P50Oh3JycnXbbt1Iz6fj7/+67+mrq6OH//4x+Tk5GAwGEJqBTcKBI1Gg8vlorGxkV/84he0t7fz5ptvUlRUJE9m8vl8DA4O0tPTw+DgIAqFQp51lpSUJM9Z93q92O12urq68Hg8cg+30WgkISFB3rvP5/PR09NDV1dXyHMP7gGo1WpRKBR4vV7a2toYGBiQgyP4S2s2m+XtywcHB2lpaZEfU5Ik9Ho9VqsVs9ksh3N3d7d8FFrwvTEajZjNZiwWi3zbtrY2+vv75Q5YlUqFyWTCYrHIk31cLhdXr17F5XLJ72EwXG02mzzfpK+vj56eHvlXWKFQoNFoMJlMxMXFoVKpCAQCdHd3MzAwgNvtlvt7gs81OOPU7XbT09ODw+HA4/HIOyBptVqSkpLkTVYHBwfp7+9nYGBAntMgSRJms5mUlBT5fent7WVgYACn0wn8v1pqQkKC3PHt8/lwOBz09PTgdDrl916j0ZCUlCTPc/B4PPJ7H3zMQCCAyWSSl04H39Pge3/t98FmsxEdHS2/9x6Ph7a2Nux2u1xejUZDbGwsVqsVlUqFy+WSn+e1r9O9dsNQiIRJFT6fj3/5l3/h2LFjLF68mJkzZ5Kbmyt/EG8UCMEPe3NzM3v27OHTTz/FZrPx3nvvhSzcCvdz+y5D7YCDW7fLR7rTbyiPOZQTl0a6/CP5mJEkXJ/VG76SkfDCKRQKsrOziY+Pp6amhqamJrkafrNACCZwc3OzvN/f+PHjQ3qkI+G5fZehlG+oOxsP9bmO5GMO5Qi2kS7/SD5mJAlXeSN2PwWlUsmyZcvw+/3853/+p9xBVlJSQnR0tNw7G2wyREVF4fV6OXbsGOvXr2fjxo08++yzPPXUU0NqrgiC8I2IDQWFQkFaWhrFxcWMGzeOCxcusHHjRtRqNXl5eRgMBsxmM2q1GqfTSX9/P5cvX2b9+vUcPnwYq9XKtGnTyM3NDfdTEYRRRfX666+/Hu5CfJeoqCgSExOpr69n586duN1uvF4vGo0Gi8UiD10eOXKEzZs3s3btWkwmEy+//DJz584dtRtdCEK43HT0IVL4/X46OzuprKyksrKSpqYm3G43Go1GbkLo9Xp5HkVycjJFRUXMmTMn7DPDBGE0ivhQuFZnZycfffSRPI577tw5fD4fOTk5jBs3jvz8fL7//e8PaU8/QRBubFSFQiAQkMe1vV6vPAau0+nkzkabzSZqB4IwDKMqFARBuPuGvSBKEIT7S0SHwrcrMaJSc2/d7PUW78PdF87XOOKbD263m87OTnnNvHBvSZLEqVOnuHLlClqtltzcXHnFpDCyOjo6CAQCxMfHD2mW5t0S0TUF+Oa48k8++YRTp06FuyhjUiAQ4Be/+AXLli2jvLycTz75JNxFui8FAgG2b9/Ol19+Gda9FGCUhMKaNWs4efJkuIsyJikUChYuXMi8efPkrfCEkSdJEl9//TUVFRVhD4WIneYc1NfXx+HDh5k/f364izImBdegmEwm1q5dS1JSUriLdF8K7ina0dFxw/1I7qWIrylcu4GIcHfdrHvp4sWL1NfXY7FYIuJchftVcPOgcAt/CW5hqKHQ0dFBd3e3vFGGCJGhC67bVygUnDlzhkOHDmG329HpdBgMBtra2nC73aSnpw97l+6xIhAI4HA4aGlpwWazkZCQcMvbBLcBCLeID4VbCe6iVFNTQ3NzM6WlpRgMhoh4cUeLa/sJNm7cyH/8x3/Q09ODXq8nNTWVSZMmMWXKFCZMmDAiB/yMBcGdoKqqqkhNTZW3wBvKhjDhNqpD4eTJk+zbt48jR44wZcoUFi9eTHx8vJjmfAcuXbrEb3/7WxobG1m+fDmzZ8/GZDLR1NTEmjVr6O7upry8XPQpDJFarSY2NpbS0lJ27tzJqlWr5M13r90zMhKNmlAI7iQ9MDBAS0uLfIjt6dOncTqdJCQkUFhYeMMdp4VbO3HiBH/605+YM2cOzz//PGVlZQAcPXqUjz/+mLa2NpKTk8VS9NtgMBjIysri3LlzdHd309raSm9vL16vl5SUFKxWqxyykTSqM2pCQaFQ4Pf72bZtGxs2bGDPnj3Y7XbmzJnDG2+8QVFRUcRXy+61oezxFwgEOH36NMePH0en01FaWioHgt1uZ3BwkJiYGOLj42/ZLo70/S/DZcmSJRQUFPDmm2+yevVq/vd//5cZM2awYsUKnn/++YjbGSziQyF4LNyGDRvo7Oykurqa2tpaOjs7ATh+/Di//e1viY6Oxu/3R9RZguHgcDjIzs7mlVdeIS4u7pbXlySJuro6Ojo6KCkpCTnf0OVy4Xa7SU1NxWg03vIEcYVCQUVFBevWrZP30BSQz6nYvXs3V65cAWD//v10d3dTWVnJihUrmDlzprzrdbhF/LsW3JS1pqaG7u5uent7GRwclP/e1tbGhg0b5E6csc5ut1NUVMTzzz8/5FBoamrC4XAwa9askGPNent7OX/+PHFxcfLhJ7dSXV3Nhx9+iFqtvmWIjDVerxeVSoXf78fr9XL27Flqa2uJiYmhoKAgYmpaER8KXq8Xj8fDiy++yCuvvMKWLVtYu3YtVVVVAMyePZs33niD5ORk+XyKsczn82EymeTTpm5FkiT5jAabzRZSlW1oaGDVqlXMmDGDSZMmDam/5rnnnuPBBx8clbsn3w3Bcyz6+/v56KOPqKiooLGxkby8PBYuXMgDDzzA/PnzSUhIkM/MCLeID4XgST/Z2dkUFhbKC6Py8vJoaWkhPj6eixcvkpOTE3LikTD0Nr7D4cDtdssHugCcOnWKL7/8kqamJsrLy8nIyLhlKEiSRHJy8pADaawYHBzk6NGjxMTEUFJSwqxZs+QtA/Pz87FardcdsxhOER8KwV+c4BHj2dnZvPTSS7z00kvs3LmT9evX86//+q9cvnyZn/zkJ2I48hpD/aXW6XSo1WoGBwflU5vee+89tm3bRlRUFEajcUj9A6JmcD2v18v27dtZv349ZrOZ8vJyHnzwQVJTU9Hr9fL1bnayWjhEfCgE3egFmzFjBrGxsZSXlyNJEocPHyY3N5fY2FjRyTVESqWSBx54gPb2dn71q1/x61//mpycHObPn09xcTGrV6/mrbfeoru7m9dee01Mc74NXq+X5uZmrFYry5cvJzk5mbS0NJKSkiL68xm5JfuWG/0KWSwWCgsLKSws5PLly5w7dw6v1xsxiTsaKBQKioqK6OjooLq6msbGRmw2G6WlpaSmplJfX4/H4wn7yr3RSJIk/H6/fJDsaNkPZNSEwq2kpKSEHFcvDI1SqSQ9PZ0f/OAHPPXUU/j9ftRqNWazmaKiIhYvXgyAVquVD6MVhkaj0cg7i4+mptV9EwoiDO6cSqXCYDDccBJN8OTnoEgZNhsNgov5Rpvwz5QYgkjqhBnrRCDcPZIkRcTnPOJDwefz4fP5cLlc4S6KINxVDocjIubaRHzzISkpiccff5yioqJwF0UQ7hqFQsFDDz1Ef39/2GeCRvxuzk6nk6tXr2KxWLDZbOEujiDcFZIk0d7ejt/vJzk5OaxrICI+FOD/zVEQ7VnhfhYpn/NREQqCINw7Ed/RKAjCvSVCQRCEECIUBEEIIUJBEIQQIhQEQQghQkEQhBAiFARBCCFCQRCEECIUBEEIIUJBEIQQIhQEQQghQkEQhBAiFARBCCFCQRCEECIUBEEIIUJBEIQQIhQEQQghQkEQhBAiFARBCCFCQRCEECIUBEEIIUJBEIQQIhQEQQghQkEQhBAiFARBCCFCQRCEECIUBEEIIUJBEIQQIhQEQQghQkEQhBAiFARBCCFCQRCEECIUBEEIIUJBEIQQIhQEQQghQkEQhBAiFARBCCFCQRCEECIUBEEIIUJBEIQQIhQEQQghQkEQhBAiFARBCCFCQRCEEP8fy5YgCm0VrFgAAAAASUVORK5CYII=)
Two point white dots are 1mm apart on a black paper. They are viewed by eye of pupil diameter 3 mm. Approximately, what is the maximum distance at which dots can be resolved by the eye ? [Take wavelength of light = 500 nm]
![](data:image/png;base64,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)
We can only apply the L’Hospital’s rule if the direct substitution returns an indeterminate form, that means
We can only apply the L’Hospital’s rule if the direct substitution returns an indeterminate form, that means
We can only apply the L’Hospital’s rule if the direct substitution returns an indeterminate form, that means
We can only apply the L’Hospital’s rule if the direct substitution returns an indeterminate form, that means
We can only apply the L’Hospital’s rule if the direct substitution returns an indeterminate form, that means
We can only apply the L’Hospital’s rule if the direct substitution returns an indeterminate form, that means