Maths-
General
Easy
Question
- 2
- 1
- 0
- log x
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: 2
![Lt subscript x not stretchy rightwards arrow 0 end subscript 2 over x log space left parenthesis 1 plus x right parenthesis](data:image/png;base64,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)
We first try substitution:
= ![Lt subscript x not stretchy rightwards arrow 0 end subscript fraction numerator 2 log space left parenthesis 1 plus 0 right parenthesis over denominator 0 end fraction space equals space 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.
= 2 x
( L'Hopital's Rule for zero over zero;
)
Differentiate the above form
![space 2 cross times Lt subscript x not stretchy rightwards arrow 0 end subscript fraction numerator 1 over denominator left parenthesis 1 plus x right parenthesis end fraction](data:image/png;base64,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)
On substituting, We get
= 2
We can only apply the L’Hospital’s rule if the direct substitution returns an indeterminate form, that means
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physics-
A medium shows relation between i and r as shown. If speed of light in the medium is nc then value of n is
![](data:image/png;base64,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)
A medium shows relation between i and r as shown. If speed of light in the medium is nc then value of n is
![](data:image/png;base64,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)
physics-General
physics-
The graph between sine of angle of refraction (sin r) in medium 2 and sine of angle of incidence (sin i) in medium 1 indicates that ![open parentheses t a n invisible function application 36 to the power of ring operator end exponent almost equal to fraction numerator 3 over denominator 4 end fraction close parentheses](data:image/png;base64,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)
![](data:image/png;base64,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)
The graph between sine of angle of refraction (sin r) in medium 2 and sine of angle of incidence (sin i) in medium 1 indicates that ![open parentheses t a n invisible function application 36 to the power of ring operator end exponent almost equal to fraction numerator 3 over denominator 4 end fraction close parentheses](data:image/png;base64,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)
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAOIAAAChCAYAAADa3GMVAAAgAElEQVR4nO3dWVSUZ4L/8W+tFMVeVVDsILIINLJowF2juAJBWk00GSdzznRmeqYvZs5czDlz5sztzN1c90Um092ZNjpGI0pENEYFFYMoRkEoQWSVVYodan3/F5l6/xowbigFPJ9zuIFa3rd4f/W8z66QJElCEIR5pZzvAxAEQQRRELyCCKIgeAERREHwAiKIguAFRBAFwQuIIAqCF1DP9wG8TZIk4Xa7AVAqlSgUink+IkGY3aIO4tTUFD09Peh0OkJDQ9FqtfN9SIIwq0V7aypJEj09PfzhD3+gvLyc0dFRxCAiwVstyhJRkiSmpqaoqanh4sWLhIWFkZCQwIYNG0SpKHilRVkiut1uhoaGuHr1KhaLhZqaGm7dusXExIQoFQWvtOiCKEkSNpuN27dvY7FYmJiYYGJigsbGRiwWi9x4IwjeZNEF0eVyYbVauXTpEjExMWRmZrJt2zYCAgK4fv06TqdTlIqC11l0dUSbzcbjx4+JjY1l3bp12O12UlJSyM7OZnR0lL6+PiIiItBoNPN9qIIge60gOp1O4Ke+OaXy3RaqLpcLt9stv/fP+wYdDgdTU1Ps37+f8fFxvvvuO3x9fcnJyUGpVDI4OIjZbH6nxywIL/LKQXS5XDx+/BhJkjAYDPj7+7/TjvKxsTG6u7uJjIwkKChoxnsHBASQk5ODTqejo6MDSZKQJAkfHx8MBgOhoaGoVKp3dryC8DJeqTjzNIQcOXKEP//5zzx48ACXy/W2jm3GezudTu7du8fnn3/OnTt3mJ6enlHfUyqV6PV6VCrVjJAqlUrUarUYYSN4nReWiJ4L/emL1+FwyLeI74rL5aK/v5+KigoqKysBiI2NJS4uDrX6/5+GQqEQQRMWnOcG0e12PxM2hUKBSqVCq9Xy0UcfARAaGopCocDpdMr1Ns9zJUlCrVbPWo/zlG6SJMl/95SsGo1m1iA5HA5aW1u5cOGC3C1RVFREZGTkM0EUhIVo1ivY5XJx//59zp8/T01NDTabjfT0dAoLC1EqlRw5coSYmBiKiopwOBycOXOGW7dusWnTJtxuN9XV1YyNjbF//342bNgwoy5ns9n4/e9/T319PVu3bsVsNvP5558TGRnJP//zP2MymZ6px7lcLgYGBqisrKS/vx+FQsH09DTXr18nOjqapKQkUQoKC9qMOqJneNjZs2epr69n+fLlxMXFMTAwwPDwMHq9Xu4iePLkCVqtFq1Wy+PHjzl37hzj4+OEhobS1dXFlStXaG9vn/UWVq/X09/fz7Fjx6itrcXf35/e3l7sdvuMep/D4aC7u5uenh7y8/NJTk7mgw8+wGq10tnZKbfiCsJCNaNE9DTI1NfXo9Pp+Pjjj9HpdDx8+JDo6GgSEhJYt24dAwMDuFwu/Pz8yMrKorW1FYvFwsqVK9m8eTPT09P09PTQ19dHWlraMyWcWq1m1apV1NXV0dzcTFxcHPn5+fT29hIQEDCjS8RqtWK1WsnMzMRkMjE5OcmuXbsYGRlBkiRGR0cxGAyiVBQWrBlBVCgU6PV6cnNzaWhooKysjJUrV5Kenk5YWBgKhQK1Wj2jCyA4OJjVq1eTkJCAw+EgODiYkZGRWfsZ3W43nZ2d2Gw29uzZQ2FhIVqtlpUrV6JSqZ55jiRJTE9PYzKZWLt2LQ0NDSiVSnx8fNi5cyfDw8NMTExgMBjewscjCO/GrEHUarUUFxcTExNDdXU1J0+epL29nV27dhERETFry6RSqUSr1T7TODNbCSVJEi6Xi8bGRsLDw8nKysLHx+e5I10UCgVmsxmj0Yi/v7/8BaBQKNDpdERHRyNJkigNhQVt1jqiy+WSS8VPP/2UpKQkLl++TEtLi/x3h8Mht3x6WljtdrvcYup2u+XW1J/X+VwuFxaLBUmSiIyMfOHoHL1eP+stq+dLw8fHZw4+CkGYPzMS4HA46Orq4ssvv6SyshKFQkF4eDi+vr5MTU1ht9sZGhqiq6uLgYEBnE4nU1NT9Pb20tnZycTEBE6nE5vNxvDwMOPj4zMaaxwOB729vfj6+hIeHv5Sw+REiScsZrPemqrVap48eUJ5eTkulwudTsfWrVtJT0/HarVSXV3No0ePUKlUrFixgsbGRq5evYpKpaK2thZfX1+ampq4f/8+d+7cYcOGDfj4+KBQKOQQGgwG4uPj8fPzEyETlrwZQVSpVBgMBvbs2UNKSgoTExMEBASQlZVFREQENpuNgwcPYrVaiYqKwmg0kpmZyd/+7d8CkJKSglqt5pNPPqG3t5fk5GR0Op38+kqlEpPJxG9+8xtiY2NFZ7wgMEsQlUol/v7+rFu3jnXr1s14gl6vp7i4+JnfRUVFkZOT88zv0tLSZn9DtZrQ0FC2bt36JsctCIvKopsYLAgLkQiiIHgBEURB8AIiiILgBUQQBcELiCAKghcQQRQELyCCKAheYEEHUQyNExaLBRdEjUaDXq8XCwQLi8qCC6LZbGbz5s1i0ShhUVlwV7LJZKKgoAAfH593vsq4ILwtCy6Ivr6++Pr6zvdhCMKcEkWKIHiBBVciCouPZ/kVSZJmLB62VIggCvPKs/RKR0cHU1NTpKWlYTKZllzXlAiiMC88C455Fqa+ePEiCoWCf/zHf8RoNIogCsLbJkkS4+Pj3Lt3j2+++YYLFy7Q399PXl7erKv+LQUiiMI746kLdnR08MMPP1BaWkpNTQ1+fn4UFRVRWFjI8uXLl1xpCCKIwjvicrmw2Wx0dnby7bffcvLkSSwWC7GxsezZs4dDhw4RHx+/ZPuHRRCFt86zP8n9+/f5/PPPuXz5MjabjbVr13L48GE2btwo7wC2FEtDEEEU3iJJkrDb7XR1dXH58mX++Mc/0traSlBQEMXFxRw4cIAVK1YQGBi45IcrLu2zF94ah8PB8PAwTU1NnDlzhu+//56+vj7i4+P58MMPyc/PZ/ny5Wi12iVbCj5NBFGYU559TwYGBjh//jxHjhzh3r17+Pj4kJ+fz0cffcSqVauWZF/hLxFBFOaM2+1mYmKCuro6zpw5w6VLl2hra2P58uXPlII6nU6E8GdEEIU35qkL9vb2cvPmTU6dOkVNTQ2SJLF161YKCgrYtGkTUVFRaDQaEcJZiCAKb8TtdmOz2Xj48CEVFRWUl5dTV1dHeHg427dvZ9++fWRnZ6PX65dkt8TLEkEU3sjo6Cg//vgjx44d49y5c4yMjJCens5HH33Erl275I2GRCn4y0QQhVcmSRJOp5PW1lauXbvGqVOnuHPnDkFBQWzcuJEPP/yQnJwcDAaDWNLkJYkgCi/NE8CJiQna29v55ptv+Oabb+jv7ycqKori4mL2799PQkICGo1G3Iq+AhFE4aW53W4GBweprKzk6NGj1NTUoFKpWL9+Pb/97W/JyMggNDRUBPA1iCAKL+R2u5menubRo0ccOXKEc+fO0dnZSUpKCkVFReTn55OYmIherxd1wdckgij8IofDweDgILW1tZSVlXHt2jUmJyfJy8tj7969bN68mdjYWNEt8YZEEIVZeeqD/f39lJaWcurUKWprazGbzRQXF1NcXExGRgYhISHiVnQOiCAKM3gm7jY1NXHy5EnKysro6ekhIyODkpISdu3axbJly1Cr1SKEc0QEUZB5SkHPxN2ysjKqq6vR6/UUFBRQVFTEmjVrCAsLQ6vVzvfhLioiiALw08Tdqakp2tra+Pbbbzl9+rQ8cXfHjh0cPnyYZcuW4ePjg0qlmu/DXXREEAXcbjdDQ0P8+OOPfPHFF1y9ehVJkti8eTOHDh1izZo1mM1mMULmLRJBXMIkScLhcNDZ2Ul5eTknT56kubmZ0NBQ8vPzOXDgAMuXLycgIECE8C0TQVyiXC4XIyMjNDc3c/ToUSorKxkYGCA1NZV9+/axZcsWEhISRADfERHEJUaSJCRJYmRkhEuXLvHFF19QW1uLRqNhx44dfPLJJ2RlZYluiXdMBHEJcbvdTE1N0dLSwsmTJzl37hwPHz4kLi6OAwcOsGfPHnnirgjhuyWCuAQ8PXG3urqac+fOcfPmTZxOJ/n5+ezevVtM3J1nIoiLnGc90aamJi5dukRpaSl3794lNjaWgoICiouLyc7OxtfXVwRwHokgLmKSJGG1Wrl79y5/+tOfqKysZHJyktWrV3PgwAF2795NRESEaJDxAiKIi5CnW+Lhw4dcuXKF8vJyamtrCQkJYfv27ezdu5fs7GwxcdeLiCAuMp6Juw8fPuTkyZOcPn2avr4+wsLCOHjwIHv37iUxMVFM3PUyIoiLiNvtZnh4mOrqar744gtu3LiBJElkZmbyD//wD6xatYqwsDARQC8kgrgIeCbudnR0cOzYMcrKyujs7CQsLIySkhI++OADkpKSxMRdLyaCuIB56oL9/f3cvHmTixcvUlVVxfj4OGvXrmXv3r3k5uaSkJAglrb3ciKIC5Tb7cbhcNDd3c3p06c5ffo09+7dIzo6mpKSEgoLC3nvvffw8/Ob70MVXoII4gLk2ebszp07lJaWUlFRweDgIL/61a84cOAA27dvl5evEBYGEcQF5Okdd6uqqigtLeX27dsEBgZSUlLC9u3bycvLw2w2i4m7C4wI4gLhdDqx2Wx0dXVx5swZjh8/TktLCzExMRQVFXHo0CF54q5oFV14RBAXAM/E3bt37/Lll1/y/fff43K5yMvL46/+6q/YsGEDZrMZpVIpGmQWKBFELyZJktwtUV5ezqlTp2hpacFkMvH+++9z8OBBEhMTCQwMFMtXLHAiiF7K6XRitVqxWCwcPXqUa9euYbVaycjI4IMPPmDjxo0kJyeL2RKLhAiil/FM3B0aGqKiooLjx4/zww8/oNfr2b17Nx9//DFpaWli4u4iI4LoRSRJYmpqitbWVr766isqKipob28nPT2dvXv3smPHDpYtW4ZWqxUhXGREEL2AZz3RwcFBecfd69evyxN3i4uLWbduHeHh4aJbYpESQZxnnom7HR0dXL58mW+++YYbN24QGRlJUVERH374IStXrsTX11eUgouYCOI88tQF7969y6lTp6ioqGBsbIzc3FxKSkooKCggMjJSTNxdAkQQ54Fn3/mWlhauXr3K119/TWtrK0ajke3bt1NcXExmZiYhISFimNoSIYL4jjmdTkZHR7FYLBw7dowrV64wMDBAQkIC+/btY9euXcTHx4uJu0uMCOI7IkkSbrebgYEBrl+/ztGjR6mqqkKn07Ft2zYOHTpETk4OJpNJBHAJEkF8B57ecdczcffx48eYzWYOHDhAUVERCQkJokFmCRNBfIs83RJDQ0PcunWL06dPc/XqVSYmJsjNzeXAgQPk5uYSHx8vJu4ucSKIb4ln4m5PTw9nz57l9OnT1NbWYjQa2bNnD/v37ycvLw+9Xj/fhyp4ARHEt0CSJIaHh/nxxx8pLy/n7NmzDAwMsGrVKgoLC9m6dau8kpoggAjinHK73bhcLtra2rhy5Qrffvst9fX1BAYGUlxcTFFREe+99x4hISH4+PjM9+EKXkQEcY44nU4mJyd59OgR3377LcePH6erq4tly5ZRUlJCcXGxvIiTaJARfk4EcQ54RsjU1NTwxz/+kWvXrqFWq9m4cSOffvopeXl5hIaGiom7wnOJIL4BSZKw2Wz09PRQWlrKiRMnePDgAeHh4ezcuZMPP/xQ3nFXTNwVfokI4mtyOBxYrVaam5s5ceIEly9fZnBwkPT0dPbv38/WrVtJSEgQE3eFlyKC+Io8I2SGhoY4e/YsX3/9NbW1tfj6+pKfn89f/MVfsHLlSgwGg6gLCi9NBPEVuN1uxsbGaGhokEvB7u5u0tPTKSgoYNu2baSkpIgGGeGViSC+BM/S9h0dHdy4cYOzZ89SU1ODRqNh9+7dFBQUsHr1asLDw9FoNNhsNpxOJ5Ik4ePjg0ajeeM6otvtxul04nK55NdTKBTy+ygUCvl3Tz/Hbrdjt9sB0Gq1c3IswtwTQXwBz8Td1tZWysrKKCsro6GhgYSEBHbu3Mm+fftITU3Fx8cHp9PJ48ePaWxspKurC4VCwYoVK0hJSSEkJOSN6oo2m43GxkZGRkZIS0vDaDTidDrp7e3FarUSGxuLwWCQHy9JEhMTEzQ2NtLY2AhAUlISycnJGI1GUW/1MiKIv8AzQubOnTt8/fXXXLhwgbGxMfLy8jh48CDbtm0jIiIClUqF3W6nqamJc+fO0dPTQ0dHB6Ojo4SGhvLpp5+yefNmdDrdawXA5XLJe1xMT08THh6Oj48PDQ0NnD17lunpaQ4fPkxwcDAqlUouwe/evcv//u//0tzcjEKhwGw2U1BQQGFhoRjb6mVEEGfx9I67VVVVHD9+nMbGRkwmE9u3b2f//v1kZGQQHByMWv3/P8K+vj5GR0cpLi7GYDDw6NEj/vM//5MbN26wYsUKYmNjX/nid7vdTExMUFlZyfj4ODt37iQoKIiWlhaqq6u5du0ay5Ytw+VyIUkS8NPggq6uLi5fvgzAP/3TP6FQKPjDH/7AxYsXSUlJISkpSYzu8SIiiD/jdDoZGxvj4cOHfPXVV3z33XcMDAwQFRXFwYMH2bdvHxERETMm7qpUKtasWSMvdajVajGZTISHhzM5OcnExIT8WE/dbWBggMnJSVwul/w3pVKJj48PoaGh+Pr64na76enp4datW0RHR5Obm0tPTw/d3d0kJyeTm5vL5OSkHEJA/hK5c+cOO3fuJCsrC4CMjAxu377NgwcPiIuLE0H0IiKI/8ezwcvg4CBXrlzhv//7v6mrq0Or1bJp0yYOHz7Me++999yJu2q1msDAQAIDAwHkcLndbgICAuRZFpIkYbfbaW1t5fe//z23b99mampKfqxGoyE9PZ2/+Zu/ITMzE4fDwblz5zCbzWzYsIGAgADUajVGo5HJyUmampro7e19Joie8xgcHMRoNOLv74/L5SI6OhqLxYLVan0m/ML8E0HkpwBMTk7S2NjIiRMnuHjxIu3t7fLyFZ71RPV6/Ut1S3jqlrdu3UKlUpGZmUlkZCQKhQJJknj06BGlpaVkZWURHBxMWloaXV1djI+Pk5SURHZ2NpGRkUiSRFdXFxcuXODjjz8mOzsbhUKBr68vWq0Wh8OB2+2WW02ffn/PF4tCoZB/AHp6eujs7MThcLy1z1N4dUs6iE/vuFtTU8Pp06f54YcfGBkZITExkb/+679m8+bN8l6DL1u/m5ycxGKxUFlZSX5+PhkZGfJtoCRJBAQEkJqaitFoxM/Pj1/96ld0dXWRkpLC9u3b5RbWtrY2KioqSE9PZ8WKFfj5+cmheroEfN65Pe/3L3qu8O4tiCB6vt1tNhsACoUCtVqNWq1+7Y5zz8Tdzs5OysrKKC0tpb6+HoPBQGpqKiaTiS1bthAXF/dMg8yLjtPtdtPe3k51dbXcuBMdHS0/RqlUEhYWRk5ODj/88AORkZFMTk4yNjaGyWSSN5TxdJlUV1fz29/+lqSkpFdu6PGUlJ7wKZVKDAYDBoNB9CV6mQURRLvdjsViobS0FIfDQWBgIFlZWaxevZrAwMDXCuP4+Dj37t3jxIkTlJeXY7VaWbNmDXv27EGj0XD+/Hl5XRl/f/+Xek2n00l3dzdXrlxBkiR+/etfExkZOeOid7vdjI6O0tLSQlRUFE1NTcTFxZGQkCCHvq2tjdraWhISEkhMTMTX13fG+z0vmAqFAq1Wi0qlYmxsDIfDgSRJTE5O4uvrS1hYmAiil/HqILrdboaHh6mpqaGqqorBwUF8fX3p6OigoaEBjUZDTk4OAQEBL/16LpeLzs5Orl69ypkzZ6itrZV33P3ggw/IycnhyZMntLW1cf36dYxGI2lpaS98bZfLxfDwMLW1tQwNDfH+++8TFhbG2NgYfX19BAYGEhUVhdvtpq+vj6qqKuLj45EkiZs3b7J+/XqGh4dpbm4mLi4Oi8VCV1cXv/71rzGZTM8Ex3OH4Blt4yntPPVFtVqN2WwmNDSUBw8eMDAwgEqlorm5GaVSKa+RI3gPrw6i3W6nrq6O//mf/2F6epp/+7d/w2QycefOHf793/+d6upqYmNj8ff3f+Ftm8vlYmxsjPb2dr777juOHj1KW1sbUVFRlJSUsH//fpYvX45Go0Gr1bJu3TqOHDlCRkYGSUlJL1zWwul00tzcTGVlJSaTicnJSe7fv09nZyfd3d2sWbOGyMhIxsfHqauro66ujn/5l3/hyZMnPHz4kIiICOx2O2FhYQDU1dURGxtLSkrKjIEA09PTDA0N8eDBA9rb2xkfH6e1tRWz2YzBYECtVhMfH09OTg5NTU1UV1ejVCrp6+uT+xDFMh3exWuD6Ll9O3HiBHa7nb/8y78kNTUVtVqN1WolJiaG3t5eBgcHiYuL+8UgSpLEkydPaG5u5ssvv6SmpgaFQsHatWv57LPPyM3NxWg0yqVOQEAAGRkZqFQqHj58SHZ2trwj7/M4nU56enq4efMmTqeTs2fPyuM/d+7cidFoBKC2tpZ79+6Rn59PaGgodrudyMhIysrK+N3vfkdmZiZnz57FYrHwu9/9DrPZPOM20tPFUlFRIY+aOX78OCMjI2zbto2YmBgiIyMpKCjAZrPxX//1X6hUKgoLCyksLBRD3LyQ1wZxYmKCO3fuYLFYWLNmDbm5uc+0XHpa/n7pglIoFLjdbh49eiR3zre1tRETE0NhYSG7du0iOTkZf3//Z0Lm6SJYvnw5drsdq9Uql1TP4+Pjw5YtW0hOTn6mZVKpVBISEiJf/KtWrSI1NRWdTodOpyM6Opp//dd/ZWxsjJCQENrb27FYLKxfv57ly5fPWpcLCwtjx44d5Obmyg1YWq2W4OBggoKC5HNJTEzks88+48CBAwAYjcY3HvO6lDidTmw2GxqN5o0aBl+G1wbRc2un1+tZsWIFQUFBcgugJxyJiYno9fpZLyxPC6bL5aKqqgr46YNdvXo1hw4dIjc3l5iYmFnHXCoUCjQaDREREQwMDDA8PPzCJn9PJ7un5Hue4OBggoODn3men58fkiTR0dEh7wz82WefYTAYZj03Hx8fwsLCXvjloNfr0ev1REVF/eLjhNk5HA7a29txOp0YDAb8/f1fu3HwRbw2iFNTU7S0tBAYGEhsbKzcmuhwOBgcHGRkZISoqKjnXqyedWRGRkbo6uqSb9U++ugjMjIynqlXzhYylUpFaGgoHR0djIyMyA0hb4vD4eDixYvU1dWxdu1aDAYDGo1G9PnNI6VSSXBwMBUVFXR1dZGVlcX777+PTqdDqVTOaSC9MoiepvbBwUECAwMJDg6WT3p8fJyuri6USiXR0dHP7VpQKpX4+/uj0+nIzMzkk08+ketlCoWC6enpXzwGt9tNREQE09PTjI2NMT09jdPpnPNz9ZAkiVWrVpGYmCh3Y3iGvgnzQ5Ik/P39ycvLo7e3l88//5zy8nK2bNnC1q1b5UJgLm71vTKI8FMJ4XA45I57+Ckc/f393L59m5SUlBc2w/v5+REcHIzb7eb+/ftYrdaX/tDcbjeDg4Pcu3ePrq4umpub5+S8nsdTr1QoFFy9ehW32y3qcl7AU8Wpr6/nxo0bSJJEU1MTzc3N7N+/X95K/U15ZRAVCgU6nQ5/f39GR0exWq2Mj48zOTnJhQsX6OzsZN++fcTExPziqBc/Pz/Wr1+P3W5ndHSUkZGRVz6O2NhY3G63PLn2bfr5eFHBe/T09GCz2VAoFDx58oTW1laGh4fnbPC8QvLS//jg4CDHjx/n9OnTpKWlsXr1anp7e7l27RrZ2dkcPnxY3k33eTyNNZ5Ob0F4VZIk0dbWRnl5Od9//z0RERHk5+ezZcsWwsLC5mytWq8Nome+3ldffcWPP/6IRqMhICCAtWvXyp3jYqlC4W3ybCp77do1mpubiY2NJTMzE6PRSEBAwJwOivDaIMJPH8STJ0+YmJjA6XSi0WjkGQtirOT8GxkZYXp6Go1GQ1BQ0Gv/T2w2mzwmNigoyGt2yHI4HLS1tTE6OorZbCYoKAg/P7+30n3h1UEUvJckSVy6dImqqiqSk5MpLCx8qaGGs2lra+P8+fN0d3dz8OBBUlNT38IRvzrPBrOeVRPe5t2XVzbWCAuDw+FgeHiYycnJN3qdqakpBgYGCAkJmXWWyXxRKpXy8bztKpAIovCLXC4XU1NTTE1N4XQ6UalU8vC8qKgodu/eLc8OmZqaklsWVSqVPERMp9Oh1+tnNPN7lnxUq9XyRj1PLwk5FzwrEajV6tcK07tqgxBBFJ7LE5Rbt25RXV3NyMgIer2evLw80tPTsVgs9PX1ERQUBEBzczOXL18mJCSEuLg42tvbaWpqIjk5mW3bthEVFfVM/crTJ1dWVoa/vz+HDh3Cz89vTs/hyZMnTE1NYTKZ8PHxeetjRl+XCKLwXC6Xi/r6ek6ePMnk5CSBgYHcv38fhUJBfHw83d3d8kyWlJQUbDYb9+7do6Ojg02bNqHVamlpaeHWrVsEBgZiNBrx9fV9ppSx2Ww0NDTQ3d3Nnj17MJvNc3oOCoWC5uZmvv/+e9LT00lJSSE4ONjrWttFEIXnkiSJ/v5+2tra2LNnD1u3bsVisaDVagkLCyM7O5vJyUm5hImNjWX9+vWMjIxgNBrZuHEjcXFx/OlPf+Lx48fY7fYZdcCwsDByc3Opr6+XB/Z7uN1u+ed1+fv7YzabuXv3LkePHiU+Pp6srCzS09MJCgrymi4wEUThuZRKJSaTiaioKPr6+ujp6SEjI4OQkBACAgLw9/fH399f3nNDq9USGBhIUlISGRkZREZGMjw8LE+98iyC/PSF71nXdbYJ0J7VDYaGhl77HDxD1AwGA3/+85/5+uuvycvLo6ioiPXr1xMTE4NOp3ujz2kuiCAKz6VUKsnOzkaSJMrKyviP//gPMjMzKSkpITc3d9bnKBQKuWFGqVTKwXve4Gir1crExIS8SNfTj3nw4AEnTpzgypUrr11qeXrnpqenaWtrYzi0iAEAAAKKSURBVHx8nPPnz9PQ0MDf//3fU1JSQkxMzGu99lwSQRRm5SlJHA4HSUlJ/OY3v8FiscgTrNPT0wFm3Dp6nvd0AH/pPR739DA4OMjmzZtntKquWLGCv/u7v+OTTz55o/MYHx+noaGB48eP09nZSWJiIvv27WPz5s2Ehoa+9mvPJRFE4bmmpqaoq6vj0aNHpKam4u/vj1arZXp6Wh5I393djUajYXx8XJ6x0tbWRn9/P1FRUUxMTDA6OiqPkAoKCgJJQnI6cY6N0dXayujwMEaTaUaJGBAQ8NILg83GM52uqamJoaEhVqxYwcGDB0lLSyMpKYmgoKCXXirzbfOOoxC8jqdk6+3tpbS0lGPHjsl7cqxevRqNRkN9fT2XL19Gp9OxadMm9Ho9169fp6qqisjISPR6PY2NjTQ1NSFJEu+///5Pa/AoFEijo9jr63E2NuKj0Tx3pYU3OX6n00lbWxs9PT2kpqayY8cOEhIS5O4WbyKGuAmz8izZ2NnZSUNDA4ODgwAkJCTI+z3W19fT2NiIWq0mJycHrVbL/fv36e7uJiUlhYiICIaHh2loaCAwMJDVq1f/tM6rUgmShNvhYHR0FJRK9P83iHouw+jZA8RutxMYGIhOp5uxeZC3EEEUnstTqjgcDnkq2dO7Dv98Z2RAfvzTjTUOhwOlUolWq505wsVz+b2FLgRPqQ7M2XSlt0UEUZhfbzGIC4n3ldHCkiI5HEjT07DEt4kTJaIwvyTppx+FYkmXiiKIguAFxK2pIHgBEURB8AIiiILgBUQQBcELiCAKghcQQRQELyCCKAheQARRELyACKIgeAERREHwAiKIguAFRBAFwQuIIAqCFxBBFAQvIIIoCF7g/wFtMZOzW8ERYAAAAABJRU5ErkJggg==)
physics-General
physics-
For a small angled prism, angle of prism A, the angle of minimum deviation
varies with the refractive index of the prism as shown in the graph
![](data:image/png;base64,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)
For a small angled prism, angle of prism A, the angle of minimum deviation
varies with the refractive index of the prism as shown in the graph
![](data:image/png;base64,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)
physics-General