Physics-
General
Easy
Question
A point object O is placed in front of a concave mirror of focal length 10 cm. A glass slab of refractive index m = 3/ 2 and thicikness 6 cm is inserted between the object and mirror. Find the position of the final image when the distance x shown in figure is 20cm
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)
- 17 cm, virtual
- 17 cm, real
- 12 cm, virtual
- 15 cm, virtual
The correct answer is: 17 cm, virtual
Related Questions to study
physics-
A point object O is placed in front of a concave mirror of focal length 10 cm. A glass slab of refractive index m = 3/ 2 and thicikness 6 cm is inserted between the object and mirror. Find the position and nature of the final image when the distance x shown in figure, is 5 cm
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)
A point object O is placed in front of a concave mirror of focal length 10 cm. A glass slab of refractive index m = 3/ 2 and thicikness 6 cm is inserted between the object and mirror. Find the position and nature of the final image when the distance x shown in figure, is 5 cm
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)
physics-General
physics-
A ray of light incident normally on an isosceles right angled prism travels as shown in the figure. The refractive index of the prism must be greater than
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)
A ray of light incident normally on an isosceles right angled prism travels as shown in the figure. The refractive index of the prism must be greater than
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAIoAAAB7CAYAAACrSRjYAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsMAAA7DAcdvqGQAABdzSURBVHhe7Z13eFTFGod/yaZssiG9hxSqXq/IRZByBUIPJXQQpAiCgggKCChdelGKAoqCioiICNJDSIBAQGwUlV5Cetv0vjV77sxkALkCaZvNbva8z8OzuzPzB2fz7sycOd98YyEQICJSDpb8VUTkiYiiiFQIURSRClGuKDoyhVn0Ww57FTFfyhXlcFwJFp/PQ5f9aSjVibKYK+WK4iotaxKdqsTYE5miLGZKhecoS9u4YNedIow+ngGtKIvZUWFRXmosw+4QT+yJKcaIyAxoSkVZzIkKi0IZ3NgBe3t54UBsMYZHyKEWZTEbKiUKpX9DGfYRWY7El2DoMTlUoixmQaVFoYQ2kOFAH29EJJRg8FE5lFodrxGpKdRxsSg+c5p/MjxVEoXSK9Aeh0K9cTJZgYFEFoUoS41Qmp+HzOWLkdC7K7I/XsNLDU+VRaH0CLBHWF9vRKco0T9MjhKNKIu+EDQa5O34GvHdOyJ/zy64TZ2B+jv38lrDUy1RKF3q2yG8nzd+TlOi75F0FIuyVJvi6FNI6BeCzKUL4dAtBEHHz8D1jSmwlEp5C8NTbVEowX52KJwYhA6+Ujh8Ho9l53N5jUhFKfn1ZyT074k7TQNQeGg//L76Fk1uJ8JrxYew8vDkrWoPvYhCsbCwYENRPWsLRCQqUKgWe5aKUpqTg6KIo1Dfuglr/0A49OwDK28fXmsc6E0Uyn99pDje3wdXstUIOZSGfJUoy5MQ1GrkfrUF8d06oPDgfrjPmouA8BNw6B7CfnjGhF5FobTxluIEkeVGjgY9DqYhT1XKa0TuQYMKi05EsDuZrNXLUa/vAASeOAOX8RNgaWPLWxkXeheF0srLFicH+CAmX4NuB9KQoxRluYfqxnWkvDIcaW++zoaZgMOR8Fy8HFaubryFcVIjolCe97RF1EAfxBdqmSzZCvOWRZuZAfm8d5FIJqzaDDl8t3wN3692wLbpU7yFcVNjolCau9vi1ABfJBdp0YXIkmmGsuhUSuR8tomthxRFhsNj/mIEHjkOWacuRjcPeRI1KgqlmbsNTg/yhbykFF32pyKDvJoDdB5SGH4ECT27IPvjtXAaMhxBx8/C+ZVXYWFtzVuZDjUuCuUZVyqLD7KVOnQisqQXa3lN3UR55S8kjxiC9KlvwrbJUwgMO0F6kkWQODvzFqaHQUShPO1ig2jSsxSoqSxpSCXDUV1Dm56O9HenI2lwX+gK8uG3bSeZi2yDTcNGvIXpYjBRKE2crZksJdqynoXOXeoCOoUC2RvXI75HR5REnyJ3MSsQcPAY7F/swFuYPgYVhdLIqUwWunAbvC8VieSuyFQRdDoUHNyHhB7BbMLqPGosWw9xenkULKyseKu6gcFFoTRwtMZpcutMd4BQWeILNLzGdFBcuoCkl/pDPmsapM1bIDD8JNzfnQtJPUfeom5RK6JQgogstGeRkDvE4H1piM03DVk0KclImzYZycMHkQ9a+H37A3w2fQ6bgCDeom5Sa6JQ/OtZMVlsJWU9S0ye8cqiKypC1roPyDDTCYrff4XXyjXw3x8G+9ZteYu6Ta2KQvFzKJPFwdoSwWSCeztXzWuMA6G0FPl7d5OJajDyvtoK59cnsvgQx8EvwcKy1r8+g2EUV+ojs8IpMmdxtqGypOGmkchS8tsvSBzUBxlzZ8GubTsERp6G+7RZsJTJeAvzwWh+Et5MFl+4Sy3RicxZrmXXnizqxHikTn4dKaOHwcLGBvV374fPuk2w9vXjLcwPo+o7Pe0lTBZv8tqZDEOXs1S8Rn9okpP4u39SWliAzNXL2LK76spleK3dAP/dB2DXoiVvYb4Y3SDrbidhT53pRJc+SPwzU3+y6JRKpE4aj9KCfF5ShqDVIm/XDhZAlL/zG7hOnorAiNNw7DvArOYhT8IovwVXqYQFPzVwLJPlUoZ+ZMlcsoCFGyov/8VLgOKfopHYrycy358HWaeuCIo8AzciiqWdHW8hQjHan4sLkYWGVTZ1tkZXIst5uZLXVI2CfXtQQO5eKMXHI9hmqriQzkgdNxqWTk7w//EwvFevg5W3N2sj8jDlJvs7m6pARzK5vDWyPpq62PBSw0EfIvY6lIarZHIbQcRp6135LQuq27eQNDgUgor3TDQOhF62rS08Fi2H06ChJhUbUhsY/QDsSG6Zj/XzYUFQNAb3XFrleha6UJb21sQHklCIJBIPTzT4+SKc6XqIKEm5mMRMrR6RhW4ya+lpixAiy5kUBa95MrSzlM9/D5q4WF7ygNLMDOR98TlrI1I+JjOll1lbIizUmww9tuh1OB2nk8uXJfujtSg6eph/+ie5mzcig0xidWr934bXNYx+jvL/0M3wA8Lk5P+lxGEiTlf/f96daHOykbFwLoojw3kJIHH3gJWvL6x9/Mgr/cff+/nBpkEjWNrb85Yij8LkRKHQNBs0g8LpFCUO9vFiOxQptGfI374NOZ9uYLEi9QYOhsuosbAKCDDa/TKmgskMPX9HamXJ8rN0I71JvyPpCIsrRlFEOBJ6dUXW2lVMkAanfoYXuaOxadxElEQPmKQoFFuJBX7s5YXurloMPJyCneu+JkNIQwQciYTnwqWQuLryliL6wGRFoZuocufNxOpFIegq/wtT+q7A+bmbYdu4KW8hok9MThT6vIbOQdiGqqjj8J2/CAcXDsCgxg4YGi7HjzFFvKWIPjEZUeicu/DIISSEdEL2po/gNHwUCyByHjUGNrbW2NnDE0MbyzAsIgM/3BFl0TcmIYryzz+QPGwg0t+ZAttnnkXg0ZPwmLMAEqcHG6qsLC2wo7snRjR1wMtElu9uibLoE6MWRZOWivQZb7Nod52iBH7bd8F38xewCWrAWzyMhMiyrasHxvzLgWXY/uZmIa8RqS5GKYqupITt16X7ZUrOnYXnstUIOBAO+3Yv8haPh8ryRRcPjHumHsvdv+26KIs+MCpR2IaqfXtYIHPuls1wHjO+bEPVSy/DQiLhrcrH0sICn3d2x8Rn62FcVCa2XivgNSJVxWhEUVz4HUlD+kE+ewbsnm+FwGNRcJ85GxKHerxF5aCyfBrsjinNHDHhVBY+uyLKUh1qXRRNUiLS3p7Edv/Tx//1d+6Bz4bNsPYP4C2qDg0f2NDRDdOaO2JSdBY2XX44BFKk4tSaKKVFhchas4oFMtPtmV6r17EoM7sX2vAW+oHKsq69G2a2cMJbZ7Kx/s88XiNSGQwuCttQtfs7JHTriLztX8JlwiQERUbDceCQGgtkprJ88F9XzH7eGe/8lIM1l0RZKotBRSn55RwSB/RCxoLZLCVEIBGEpu42xCN+KsuKdi6Y38oZs37OwaqLoiyVwSCiqOPjkDrpNaSMeRmWdvbw/+EgvNdugLWPL29hGKgsS9u6YlFrF8z5JUfMsF0JalQUdjLEiiUsn6rq+lV4r9vEdt1J/9OCt6gd3ieiLGvjggW/5bITWMsJyTEraK9P8/DTjA1/p0ZEYRuqvt1edjLE7p1we2s621BVL7Qf+1UbA/NecMGqdq7sBFYqjLnLwnr9N8bf7/VdJz4sCv2CnsiZlBIBG+8Kt3JUvOTJFEWfEuJ7dhFuN/EX0mfPEDTydF5jnKy5lMuu771zWYJOp+Ol5oM2L1fIWL5YuP2vBkJscFuh4MjBR34PehNFdee2kDx+NBMkacQQQXH1Mq8xfj76I49d44yz5iOLTqMRcnd8LcS80Ey40/wpIXvzRqFUoeC1/6TaomizswX5onnC7acChdguLwqFx46a5Je96a8yWaaeyazzstBeP65n50r1+lUWRadSCTlfbRFinv+3EPOffwk5Wz8TSlVKXmuafHYln13rm6cyhdI6KIvyzi0hedyosl5/5FBBce0KrymfSotCf22FJyKEuG4dhNtNAwT5gjmCJiuT1dUFvriWL1iQ650YlVFnZPl7rx/Xpb1QGHms0r1mpURR3rguJI0exoxMHjNCUN68wVvVLbZdL2CyjD9h2rLos9cvV5TopGImyk/zl7IeJK5HsFAUdaLOj+M7bhYIluS6xx6XC9pS07pW1usfP/ag1184V9BkZ/HaqlGuKKdjcpgoxzt1F3K//lLQqdW8pu7z3a1CQbLprjAqQi5oTEQW5fVrD3r9sSMF5a2bvKZ6lLvgZmlXlmaCZgOw7xBskidDVJWXmzpgV4gndt0pYqGVWp3xLsppszLZhnx2HpA8Xe/nAVV4ZVbi6Qn53FksCs2cGNrYAT/09MLemGKMiMyAptS4ZGHnAW35tGz7yrGjNXYeUIVFcZ/+HpSXLiD/ux28xHwY1EiGvb28cCC2GMMi5FAbgSxkNHhwHtD6D+E0eBiCTtTceUAVFkX63HNwenk0stasZGm+zY3+DWXYR2QJiy/B0GNyqGpRFuXVywY/D6hSDwXdZs2GxNEJGQvnMKPNjdAGMhzs442IhBIMOprOsioYEjr3SJ89A0mDQqHLz2dzEEOdB1QpUWigs+eSlSg5G43Cg/t4qXnRM9Ce5WWJSlay1Bs0X0tNQreuKK9eQdqsaYjr2h7Fp0jvsXg5Ag4dg6x9MG9V81QpP0r6zKkojo5CYHgUrNw9WJm5EZWsQOjhdLT3leJAby/YW1fqN3cfGjusvnMb2tQU8i8VmjT+mprMXulJYveoN+QleMxewHp1Q1MlUUpzc8kkqjPs2rRjEfPmSnSKAn2ILG28bHGI9DI0fVhlKVUqkLVk4f3Upo/Dfd4iuIwZxz8Znir9DCQuLvB4fym5HQtDUeQxXmp+BPvZsYyVv2eomDBF9FizSiKR2sFrxYdwHj+Bl/wTp5Gv1KoklKr1lwSHXqGQde2BjEXzWMijuUKHnkgiy6VMFUtCWFgFWShOr05giZH/H9tmz8FjzkL+qfaosih0Mcdz0TIISiWyVi7lpeZJOx8py7J9JVuNkENpyFdVXBZdaSk7YT2hY2t2J0O+WF5D/jhkLuLz8WZ2wkdtU2VRKFZe3nCfs4DtFy4+d4aXmidtvKUsf/+NHA1LnJynKv8g8Lyd3yC2xTMo2PM9rHx8UX/3ATiE9ue1gNeH62Fd359/ql2qJQrFccgw2LV7ERnz3oOuuJiXmietyKSWngwSk69BtwNpyFE+WhbF+d8Q16E1MhfPJ38B0jMv/4AlJ7Rr8TzqhfRmbVxeewMOnbux98ZAtUWhQ5DX0lUozclG1voPeKn50sKjTJaEQi2TJVvxQBaNPB1JQ/sjeeRQaDMz4DRqLBpdug6nocN5i7I5ibRVa7i98y4vMRLo7fGTqGhwdc62rezRdsmF33mJeXMlSyV4bI0TnvsuSUjPVwhpM6ey2BAWhvjKcEGbm8tbPoxOqxU06Wn8k/FQ7R7lHs6jX2Xn/9KJGX2iae4862aD04N80en0TmS1fZatZFv7B8L/wFHU377rsc9laB4YOvczNvQmCr1Az5UfQkM3Ek19sHmIbkrP+WQD/2Q+FP90BtLQdphy6hOoLa2xZuD7kB6MgvSZZ3kL00JvolBojlf74M5QRB1nGRwpmauWIe978wlN0KQkIXFAb6SOG4XS3By2kOZw9i+EPd0NnfanIbVIy1uaFnrPhU8fYsW2ac6eLtOzgQt2fcvKG168WmePo6fQ/Lfy96az4CFy8ewH471+IyQOZdd8l9wJ0QM1pRILMtklt8IOVqzcVNBrj0KxkErhOGoMoFbfl4RCH3zVVbLJ0Hq35b9RFB4G6waNEBB2An5bt9+XhNLIyZodBE4Xbump8YnkrsiU0JsoRSePQ75gDuK7tkf+l1t46QPUMXf4u7oDzZx9l/SeOR+vYTlefDZ+hqBjUbBt8ug06w0ciSzk1pn24VSW+AINrzF+9CaKXZu2dD0a2sdEv9WlHkUdF4eE0O5Ie2M8dIWFcHnzbTT8/TIc+GLZkwikspCexYp888FkSI8lQ5IpoDdRaFCT1/IP4PvlDlh5+/DSB9QFUejKMz03OSEkGOrbtyDrFoKGF67AfdpMtvBYUeiZzqfJPEVqZcF6lpg845dF73MUWYdgBBw9wZb2/47q1g3+zvSgE/OsdR/g7gvNUEyGWJunnkZAZDR8P90Kib2Mt6ocfmQye5oMQw7Wlggmk9zbuWpeY5zoXRQK611WfAjfL76BxNOLlZVmZ0FrguEIhWSCGksEyf1sEySOjvDZsg2BhyNh+5g065XBR0ZkGeQDZxsqSxpuGrEsNSLKPWQdOyEw/CTsXuzAPuc9YpJrrNCzkuN7dkb61Ens1tdt+iw0+OUPOHTqylvoBy97KosvPOwkbBi6lm2cstSoKBS6dlJ/204WNpm3/Sv2MMyYKS0sQMr40Ugkk1V6DK5D775odOEqXCe9Val5SGWgkkQN8IEv6WE6kWHocpbxnZpa46LcgwbgWEqlyFxS+9Faj4LOQzJXLkFs6+Zsl4Htv5sh6OQ5+Hz0Cft/1zTuRJaTRJYAMtHtciANf2YalywGE4We8cfibCOOsoMijYmCgz+yBbO8bV+Q/6cbfEkPGLA/DNb16/MWhsFVKmHBTw3JLTSV5VKG8chiMFEoxhZnq01PR9LYEZDPmg5oNHCfPR8Nz12AjM+pagMXIgsNq3zK2RpdiSzn5cbxJN6gotyPs1WpajXOVqdQIHvjesT36Aj19WssgKjhpetwGff4SHhD4mRriQgiyzOu1iz46df02pfFoKJQHoqz/SmalxoGmomh4OA+dmBUDrnddSaCBJ08C8+FS2BpZOk8HMktM90K0tzdlsXgnkurXVkMLgrlfpzt/NkGi7OlJ3jQI+fks6axAKug8Ci4vzvXqJ9o1yOyhPfzRitPW4QQWc6kKHiN4akVUR6Ks123mpfWDDTzQtr0yUgePoh80KL+t3vgs+lzWAcE8hbGDd19eCTUG+28pWzf0Onk2pGlVkSh0D8UDSDO3/E1FBfP81L9oSsqYsvuCSGdofjtV3itXAN/cidj11q/5wEZArqv+VCoF9r7SNGbyHIyyfCylBu4dDwmC32mLMBL/hZwtn38uX5BDYIw4513KrUoRcMk6S+9tCCf7c63tK3+egWbh+zfi+y1q6ErKIDzaxPg+vqbsJRV7ZmMMUHTbAwOl7NMCnRjfEhgzR9fc49yRTl6PRWDRo7FczIVi856FBcvXmSvWZkZsLOzY+8riirmNhL794LL+Ilwr+YWhZLff0XW8sVQ3bgGh9B+cJ85B9a+fry2bkAT+NAT4yMTS7Cvtzd6BxlIFirKk6jIdo3vv98t2MschJKSEl5SObI2fcSS5VYmk/LfUSXECSmTX2dbIRKG9BVKLl3gNXUTlVYnDDiSJth8clc4FFvES2uWWpuj/B3X1yfBpklTyOfMhKCpeGwGfS6TuXoZEnp1heryX/BauwH+uw/ArkVL3qJuYkN6dpqAsG8DGRuKaG65msYoRKGbsGlYgvrmDeR++TkvfTzsPKBdO9i5hPk7v4Hrm2+z84Ac+w6osXMJjQ1rIsuuHp4Y1FDGhqK9MUW8pmYwmm9V2qw5m6fkbPwI6rsxvPSf0M3wNJdq5vvzYN+pC4Iiz8Bt8lRYVnJuVBegsnxLZBnWxAHDIzKw+07NyWJUPz/Xt9+BlY8P2234//ls1bF3kTrhVaS+Ooqlg6BH33qvXgcrb+PbVWdIrCwtsL2bB0Y2dcAIIst3t2pGFqMShT7OpyeX0l2HNMGu4o9LSB49DHeaBiBz6fssK2WT24nw3/Uj64FEypBQWbp7IvO1QKz9Mw9uW+Pxh57DFIxuQKdzDJvGTVmAU8nZ0+RW9zosZDLYtfuvyaym1hbOtpZo6WGLXJVO76JUeKfgkEYyNHV+9IOzm1EHcWzl25gSdgtWNtVfNNOp1Xhu2SS0TLiE28ED8cfgyVA6ufFakSdB0/Wv4geA0yHplafrsffVpVxRkgq16B+WjixlKawes+qqK84jdyy/QNqyFy+pPm65qbDVqpHqEcRLRCoK/YPGk7/birYumNPKpaywmpQriogIxTwWHUSqjSiKSIUQRRGpEKIoIhVCFEWkQoiiiFQIURSRCiGKIlIBgP8B9YkvQk8ux3oAAAAASUVORK5CYII=)
physics-General
physics-
A bi-convex lens is formed with two thin planoconvex lenses as shown in the figure. Refractive index ‘n’ of the first lens is 1.5 and that of the second lens is 1.2. Both the curved surface are of the same radius of curvature R=14 cm. For this bi-convex lens, for an object distance of 40 cm, the image distance will be
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)
A bi-convex lens is formed with two thin planoconvex lenses as shown in the figure. Refractive index ‘n’ of the first lens is 1.5 and that of the second lens is 1.2. Both the curved surface are of the same radius of curvature R=14 cm. For this bi-convex lens, for an object distance of 40 cm, the image distance will be
![](data:image/png;base64,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)
physics-General
physics-
The effective focal length of the lens combination shown in figure is - 60 cm. The radii of curvature of the curved surfaces of the plano-convex lenses are 12 cm each and refractive index of the material of the lens is 1.5. The refractive index of the liquid is
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)
The effective focal length of the lens combination shown in figure is - 60 cm. The radii of curvature of the curved surfaces of the plano-convex lenses are 12 cm each and refractive index of the material of the lens is 1.5. The refractive index of the liquid is
![](data:image/png;base64,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)
physics-General
physics-
A transparent thin film of uniform thickness and refractive index
is coated on the convex spherical surface of radius R at one end of a long solid glass cylinder of refractive index
, as shown in figure. Rays of light parallel to the axis of the cylinder traversing through the film from air to glass get focused at distance f1 from the film, while rays of light traversing from glass to air get focused at distacnce f2 from the film. Then
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)
A transparent thin film of uniform thickness and refractive index
is coated on the convex spherical surface of radius R at one end of a long solid glass cylinder of refractive index
, as shown in figure. Rays of light parallel to the axis of the cylinder traversing through the film from air to glass get focused at distance f1 from the film, while rays of light traversing from glass to air get focused at distacnce f2 from the film. Then
![](data:image/png;base64,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)
physics-General
physics-
A ray of light travelling in air is incident at a grazing angle on a large transparent slab of thickness
. The point of incidence is the origin. The medium has a variable refractive index(y) given by
Where y is in m and ![k equals 0.25 m to the power of negative 1 end exponent](data:image/png;base64,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)
![](https://mycourses.turito.com/tokenpluginfile.php/c161933dbfaab094c54655ab71e9b8f0/1/question/questiontext/472699/1/943357/Picture17.png)
a) Express a relation between the angle of incidence and the slope of the trajectory m, in terms of the refractive index at that point m ( y)</span
A ray of light travelling in air is incident at a grazing angle on a large transparent slab of thickness
. The point of incidence is the origin. The medium has a variable refractive index(y) given by
Where y is in m and ![k equals 0.25 m to the power of negative 1 end exponent](data:image/png;base64,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)
![](https://mycourses.turito.com/tokenpluginfile.php/c161933dbfaab094c54655ab71e9b8f0/1/question/questiontext/472699/1/943357/Picture17.png)
a) Express a relation between the angle of incidence and the slope of the trajectory m, in terms of the refractive index at that point m ( y)</span
physics-General
physics-
A ray of ligth enters into a glass slab from air as shown .If refractive of glass slab is given by
where A and B are constants and ‘t’ is the thickness of slab measured from the top surface. Find the maximum depth travelled by ray in the slab. Assume thickness of slab to be sufficiently large
![](data:image/png;base64,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)
A ray of ligth enters into a glass slab from air as shown .If refractive of glass slab is given by
where A and B are constants and ‘t’ is the thickness of slab measured from the top surface. Find the maximum depth travelled by ray in the slab. Assume thickness of slab to be sufficiently large
![](data:image/png;base64,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)
physics-General
physics-
The refraction index of an anisotropic medium varies as
. A ray of light is incident at the origin just along y-axis (shown in figure). Find the equation of ray in the medium
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)
The refraction index of an anisotropic medium varies as
. A ray of light is incident at the origin just along y-axis (shown in figure). Find the equation of ray in the medium
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)
physics-General
physics-
Due to a vertical temperature gradient in the atmosphere, the index of refraction varies. Suppose index of refraction varies as
, where n0 is the index of refraction at the surface and
. A person of height h = 2.0 m stands on a level surface. Beyond what distance will he not see the runway?
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)
Due to a vertical temperature gradient in the atmosphere, the index of refraction varies. Suppose index of refraction varies as
, where n0 is the index of refraction at the surface and
. A person of height h = 2.0 m stands on a level surface. Beyond what distance will he not see the runway?
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32o4fhulQMT201vC0t8Bv0KuKS76PSOEZN5CFBST3uiMhG9S31muBtbFTNkvZjh9VMm9wD3DA3Afqp8eiWvUvxY9XmcYbF82BaswqW3O2wnyqAu7pSpHA6lcKxuZJEG0rqcUFGRz6fEolMvXytLWqXANelUiUay56d4RRuyQK1Nq5rzAh0jhisLo4ptz4xpS+HNW8XnKVF8La1IGC1IOh2qUgJUkzi/weqh4kRE4kylNSjgBCD2itJDtmR7fep6EgKKWgxq7VtslgtL3Apa0SyF8m6KyeyYHe2ukKvFFLne4PV1VP082bBmL5CREo74Dh7Sl2519fSpGpTco2c+GWRX0z6gtS2HEH5v5Ma6mHygKCkYh0ZvQhxyCvwyuvEeW80qAtaypk0e8ExNatm25MLy46tMGevR++6dBhXpqgid8/i+UpScqjtTtamwSLk5TgjxFRdFV6GwobKj0VACMnpD6HXE0SPOwibNwgfHf9AoaRiBflfYLksREZILqfaLSDQrRNSugFXeRkc507Ddmg/zDu3oTdrDXpSE1XTpGwF+GAsnCPktFTIKB3mHVvU8c7zZ0V0dU2kf62qLhV0OtTvkHJSBW8ZnRFNyIjJ4Quh0eJDoc6DC10eXBf3XdJc5IFBSUUTKSIZGYm/UyUIIaXwmrde1ZfkbaiHu6JcXTtO7jxpFRGSjI5katYje5SWLoA+0qckLxMuL3hpXJGktjuRbQNyexO51a68EIHc4sSv1ynZSSmRB09A+N3gCuJUuwvp16xIE+Nspwt2hlIPFEoqSoSn/HvgbW4S6drVsIiOHVFXPOnNzlKzaaZVqTCtSIFxeZKSklFES1JCcm9vmapJGclub4uMkvLz4Dh5Aq6SIniqRKR0c98lWezmf8ijgnRRu92P3Ot2TLloVGN/kwNWkfKRBwcl9aCQYpARkkyjRHQk06qg1aou+e1tahQp22VVQ5KXXJLCkdP8csuSzveGoWPYQHQNHwzd+PfVTFtP4iI1E2fZuQP2E0fVEhN5sQHZ0ySL47JIHujtDbcERFI3+buZukUXKalWmx/b6+2YcN6oRl6jAxZK6oFCSd0vMkxRQ6ZtYsgIyWqBv6MjPOVfXKQu6W2VEdL6DLX6XzZEds+cDN3UCeF9u2dOgX72dOhlHWnZQrXmzbJpg5qRsx8+qJaiuOSulPX18HV1qi1QbtaS1OweiQlulVTcOaMaUlJmSuqBQkndA1VDcjnhl0tHVO9RldqgTU7dy+1vZS1IpmEqRVs0H4Y5M1U0JLfClXso6SaMRffUeLV1iSFxsYiQ0sVrtqp9ux3nz4an/9vaRCpoUpGXvCCBLJyrTm6/iMyYu8Usd4ukKKkHy+MvqZuRzy0FazWLJocUgceNkEzNpBxsIj2Ts2oilZIzYXLphyxAyyl/+5mTaluS3vXrVDomJdQ5fBDa+r2K1ldeQOvvX0T7O2+g6/1h0ItISS7GlWvcpMicpcWqKO5rb1eyk4XygPhdantc2SzJNO2RhJKKDo+1pJSIXC51BVy5Tk32BcmdIGXx2iP3RKqsgKu0CA4hINuxw7AeyFczapYd22DevCEcIamZtUSVlslFtnKXSdV7JFI1Ncs2b1a4Byl9pXjNRljz98Bx6oS62q5HiMmv16sZPPL4QUlFh0dTUjcjI1mkvtlXJCMhWagWUZC/W8hIRECyRuS+UqYaHx2nTsJ+5CBscpM22fi4MROmNSvD24/Iq5UsnK1qRGrIlG22SM/kkI2QIk2TspJbklh356jFtnIXStfVcnWtOCWim4ttb0ZpkahNRUni86qO8ZtRHXksoKSiQ0xISi0luJmOyRNcykec8DICUUNGQ0ICMk26GQ2pJSAyGqquhLuiTF27zXnxnJBRgZKR3APJvCVbREPrVGFa1YyWLlIb/8tN2rqnT1Qpm9xzW0pJ9iAZVyaHp/m3bxapXZ4qgMurm8gpfrkdiexl8vfo1edQUhKpovgLinwL8qRBSUUHbZJavhzVNTWRIz4mMiiKNDTKqXWZinlra+AuFxFQ4QWVOskmRWteLszbNoWlszZNpVcmEd3IYZT3V8v7yyND3Jd9R2vEcetWozdjjZKPrCfJK5bIviTzlo2qHcC2LywjWcSWi3GVkBqvCyF1qqhMthMQcicoqehwX5LKEJKKF5JKXr4C1fX1kSM+ioqIbu0XkjUhszlcFzLo1T7ZcpW+nGJXHdYXz8N+4pi6gohc9CrrQXIWzJiaBMPiueHIZ8oEtThWN24UdHHidlIc9DOmwDBvFgzLFqmmR9PalUJCGeHZswN7VbOj8+IFuIV8VJ9RbTU8UkBtLWq/7Q/1Gt2SoqmoTkZ3TM3In4CSig59l1RFBTLXrcOkuDikLluGGvEzvEJELiEiR3itmazNqC1C6mvhuloBZ0kRnOdOq0jFtn9vWEAigunNWA2TWgS7BD0LhYRkDUiISNaB1Na084V4ZIFark2Ti2SlhJKXqUshyUjKvHUTrOK95MUkZWpnl4Vqkeq5LpeoKX01k9bWqhopgzI1kzNpss9ISFPNponvxNoQ+bhQUtGhj5Kyo7KsDNtWrkDi0CHYMnI4qlemwrZjq5KGXLYhp+XVdfxnTlF9QToR+chbuXeRal5MmPqBhPRSQkJOsiBtWpGsUjPZ+CjlI1Mwua+RvJik/fhhte2IQ0RDsjfJI9ek3RCRUHtbuOtaSEhGZwGrGfJKJmpJiIzgZJGakIcMJRUd+iYpux01ly5hX9IybOn3Oo7+9leofucNdAzpj7Z+r6D15V+h5dc/R8uvfoaW3/wCrb/7Ndrf+j06hg1Ql9DuTpgWnqZfk6bqSlYRVdmFfFRX9fVwV7VfycaiUkMlHBn5yD4i2cckox+RjjECIrEEJRUd+igpB2qlpJITsfUP/XD8jVdRJ+Sjl+mYnBVLWqr2MDJlpIcL0rtyVHont6mVkZBsAXCXXVYzcTIS8naEmxqljNS0feR3EfIoQUlFhz5LqurKFexIW4WU90Zg+6R41OXmqD4h2QYQrv8YEJDSkelWn6OdyHE3D1evuzkIiW0oqejQ98L51avIysjA1IkTsTIpCdUVFWpGTKVgvIwReQKhpKLDfUkqIysLE6ZMQdKKlahuaIgcQciTCSUVHe5LUh80c6Y8ObsgEHI3KKnooE1ST9BWLYTcDUoqOlBShGiEkooOlBQhGqGkogMlRYhGKKnoQEkRohFKKjpQUoRohJKKDpQUIRqhpKIDJUWIRiip6EBJEaIRSio6UFKEaISSig6UFCEaoaSiAyVFiEYoqehASRGiEUoqOlBShGiEkooOlBQhGqGkogMlRYhGKKnoQEkRohFKKjpQUoRohJKKDpQUIRqhpKIDJUWIRiip6EBJEaIRSio6UFKEaISSig6UFCEaoaSiAyVFiEYoqehASRGiEUoqOlBShGiEkooOlBQhGqGkogMlRYhGKKnoQEkRohFKKjpQUoRohJKKDpQUIRqhpKIDJUWIRiip6EBJEaIRSio6UFKEaISSig6UFCEaoaSiAyVFiEYoqehASRGiEUoqOlBShGiEkooOlBQhGqGkogMlRYhGKKnoQEkRohFKKjpQUoRohJKKDpQUIRrRLqlQ5Jb0BUqKEI0wkooOlBQhGrmbpCwfSCqEUMAHv9cFp90Kc68ZZrMddpcXXnFexUQ8FQog4HPDJT6fxWxGr8UGm9MLX0B89sghnzSUFCEaubukIqd3SAjKYYCx5RrKzx3Hwb1HsO9YKUobdOgWIvCHj4oy/6WekN8Nt7UTnXXiM53Yj325O7FLfMYjF67iaosReocf3qA4PvTJ6oqSIkQjfZGU19yKjvJD2J+5DLMnz8XkRZuRfaoGNUYnvOGjokz4s4UCTli76lB9Kge5K2djweTRGDVsEIYNHY7hcfMxZ81+7ClqRH2PE24RVX2SUFKEaOTe6V4QXmsXDFcP4UBaAuKGjUH/uJVYtvcKLnfZ4YkcFV2kcPwiwutA8+VDyFuRgDmjh2HMqJEYNWIghrzxAl549jd49rXxeG9ZHnJL29Dp/GRTU0qKEI3cW1JCU+5eOK+fxpn1CzBl+Bi8PSYV83MvoaTdCnfkmHvzcRRxe21JfLaAAy5DNWou5CFn/XqsXpuDXfkHcfJoLnavm4M5I9/AS795Db8ZvAjzt5WgossF3ydoKUqKEI30RVLw2xHsKMGlnFTMGTsRAyesxKJdpShq7oHV44Hf50MwdK8idQjBoE8c64FXvMbjDg+3233LkD9HhjjG7RGppj+AQPAOkvLZ4NbXo6WyCBcv1+LSDRt6nSL5DFphbSvE+e3zMWXIW/jdm3GYmHoY5+otcEe+Ukh81mAwKIZ4b78PPq/4TF5xK1LCD751yI9A5LN6feI48QE+juMoKUI00jdJOYSkSnFp53LMGTcRg+KSMXfzSRy/Uo2GG/W43nADje16dJldcHgD8CthffiUDoUC8DnNsOg70NXWitaW8GhpabllyJ8jo1U839mNLpMdNndASDDyRhJZBPcLOdpMsBn16LY4YPSJ8zzydMDRiOqTG5A8eQSGDJqAGSsP4GxtD+xOO9wWA3QdHWiT7603wNDVjo6mBjTUNaC+uQsdRhusDjvsvTro267jem0tauqb0aTrhckppKmxtkVJEaKRvknKqSRVujMVs8eMxR9GJCAuaT2ycnZg9/b12JCRhbVbj2DP+XpUd1ph8fhFRHLbyRzywmloRnPFBRSfPYmTBXKcQkFBwS1D/nwyPE6ewumLZSiu7UK72XubpMQQUVDIL6IdMeQM401ByXsBZxNqzmxD+pwpmBA3H0mbT6C4rgVdTeWoOrsPedu2YlNOPnYfKsCJowdwKHcjNqxdg7SsHGw/fA5nSkQqe+EECvZvx+aMdKxYmYl1u87gVJUO3VbPRwTcFygpQjTSV0kFlKSSMev9EXj9j+Pw7sxkJK1Zg/Wr5mPBlDgMHzMfE1LysaukCY29Lnhvn/IXknJISV29iJLzp3Dq1L3GaZwtvILSOp2S1EcCmFveX94L/yT+HbLBpS/HpUMbsHLhEsxZuhnbjpehvrUOzVf24cDqBEx7/z0MGzML05ZmImvTRmxeuxQLJ4/C8KHvY8SUxViYvhmbtm7B9k1rkDJvEsYOHYr+Y5ZgwbZCXGkxwXf7d+sDlBQhGrkvSe1IwqyRI/Ba/3iMXLgBWXuP4MyRzdieMg3vDxyNt8asROJ+IZYOK5y3WUXWo9zWHvS03UBTfS1qa2vUqKm586itrUNDYyuauy0wOXzic34kNvsoIT9Czk4YakWUtisTq1ZlY3VOIc5XtqK39zo6r+UhLzUOo97qh1f/EI+xC8VnP1yA06fzsGPFFMT1/z1efnMEhs5IR0buERScP4cjO1YhadzbeOW14RgwJweHy9tgF9/tfjVFSRGikfuTVDJmjxqDt4bPw9SMYzhS3gBdUyHK9qRg9rvv483B85Gw9TxON5pg83/4NA74XTC3VaH63EEcz8/Frp052LlzJ3Jybh85auzM3Y28w2dwoqwZDd0uuP23fJ67EPJZYW+/gsrTudizZQs27T6Dgms6tPU6EPB1wdp6Asczp2PiwIF4a/BczEw/hrPVrejQ1aP84Cokju6H378xHMNmZWPPuWo06k1oLT+CA8uGo/9r7+D349ZhZ9F1mAJ9EOZtUFKEaOR+CuelanYvHgPGLcfCXZdQ3NIDn7UWTQVZSBk7DgOGiBM/W4ihwQirfONbCPhs0NddROGetdiUlojkxGVIXJaIZbePpcvCIykFK7J2YsvxKpFi2eG89fPciaAHblMTrpccwfHd27Frr4iQKlrRZvdHerks8JqKcXHHIswZNRrDxq5A4vbLqOp2wuUzo61wG7IShmHg0HhMTNmL8zU6WPyAo7kYRZnxGNV/IN4cvxo5RQ0wCEndW5kfhpIiRCN9l1RJWFLjJqkWhMV55bjUYRbp1XW0nd2AFePHY+CQOUJSp1FQ3wPrh6QSQtDvht3Yjva6clReLkJpcRGKi4pQdJdRXFKKy1drUdXcA53ZC4/4oCLj+zAynFH1IZEO2rvQWVuIs/v2YM/uwzhVdgMtVt8tzaY2+MyXUJi7DPPHjseIuDSk7ixHndELX8iBrtKdyJ4zAkOGT8bUlQdQ1NADp3iVp/0SLm+YjHEDBuGtOCmpenSLKPG/CvV9g5IiRCN9klTAiVCXOFlzV2Bu3BQMil+lJHVZSsp1A23nNmJl3HgMGjoXCZvO4KSIpGy3SSokDBOQfUniXAwEfKo/SfZX+W4fsm9JPhfwIygjlqAQQkAM2St1pxwrJN7L0Q3D9UsoO3MUh0WKWHC5GU1m8R7hA8QfqRQLXL2XcTE3CQvGxmHkhHQsz70pKaeQVC42zXkPw0ZMxbRVB1F8U1Id4ntvnILxAwbj7QlrkVvSAL14O0qKkCjRJ0n57PC3FaJoWxISRsXhnbEpmL+zNJzu2US6dzIDyWNG4Z0BMzE1qwDHag2weG6V1MNASCvghsPUipbyApzZswnbs7di+6GLOF3dgYYOPXTt7ehoaUFbeyeMtg4YugpxatsSzB45CkNHL0fitkuRdM+Ctosi3ZsxDAMGxyM+ku5Z/UE4WsT3zpDF9v54ffQqbL1Qiy7xl3a/C6spKUI0cm9JiQjI0QNb7XGcWDsLcQOH4tUhczF1/UkUVDXC2FmCivwkzBs6EK++Ph6jU/ch70o7up3++442+kwoKP644ZI1qKJ87FmVgHkTRmP8pDlISM5E+qYdyN6yFRsy1iMzQ4gr7wQKK8tQU3sUBzJnIn7AAPQbPA+z1p1G4fVu6I0tqDq6Fqlj38ZrbwzH8LlbsL/kOjp7Lei+dhRHk4Zj4Iuv4IVBi5B2qAwNFjfckS74OwV3d4KSIkQj95SU3AWhtxW6sv04tHoWprw3Ev1HzkPCugM4VFyO69WncH6nSKHGjED/gRMRl7wLucWNaLV64enrGXy/hEQq6DGjt7EYF3elIHHCQAx88w30GzAcg98fhzFjx4oxBsNHTsCo+MVYvGYXjl48h4qyfdiXNVt8ByGd9+Zh9prDKLhSj4br5SjKX43kie9iwMDRGD1/I3JOV6C2uQn1hXnYs2wsRvZ7G2+9twipey6ivNMCh/iLo6QIiQJ3l1Tk9At44Oltg67qHC7kb8LG9HQkp21B9t7TOF9WgbqqIpQU5GJbRhqSUjOxNqcAJyta0G71iGij7yfxfRH0qUXPpqZLKDm4EZnJQprTZ2D6jATMnDULs2YlIGH2HEyfm4SFK7dh26ELuFJ1FU3VZ1F4eAuy0laJ77AJ2fni52u1qK+vQNmZfORkpiElJR2rtxzEseIq1N5oQN3lkzi2Yy3Sly0Tr9mKnSfLUd1phsMTXqrT175OSooQjfQlkvK7LLAbO9HVLE5acc5craoXJ3ArOrq6YTSIx9sb0VAnHq+sRXVDK9oNFtg8ftzWKvWAEG8ql8T4XHCZdehsrMa1slIUFRai8OIFXLxwHufluFiI80VlKKmoR31rJ4wmA2ymTujarqNWfgfxWesa29Cp74HRKOtXzWioFe91tQrVdU1o6dSjx2SEQdeG5oYaVAt3VFXX43qbeNzmhtcfDC/VoaQIebjcuyYlzsKQDInCZ6O8kTseyB0EQrKpMdIJLis04cfFz+I2cvhDQH6eyG+Un0V8NDkDGN7VQAxxrsvzPXDzZzXEZ5V1LPWPfHnkc8rH5a38Wb6XuA3JWpN6TrxO/Cwb58Mzi+JOZISPl7fhj9MXKClCNHI3SfFCDA8WSooQjVBS0YGSIkQjlFR0oKQI0QglFR0oKUI0QklFB0qKEI1QUtGBkiJEI5RUdKCkCNEIJRUdKClCNEJJRQdKihCNUFLRgZIiRCOUVHSgpAjRCCUVHSgpQjRCSUUHSooQjVBS0YGSIkQjlFR0oKQI0QglFR0oKUI0QklFB0qKEI1QUtGBkiJEI5RUdKCkCNEIJRUdKClCNEJJRQdKihCNUFLRgZIiRCOUVHSgpAjRCCUVHSgpQjRCSUUHSooQjVBS0YGSIkQjlFR0oKQI0QglFR0oKUI0QklFB0qKEI1QUtGBkiJEI5RUdKCkCNEIJRUdKClCNEJJRQdKihCNUFLRgZIiRCOUVHSgpAjRCCUVHSgpQjRCSUUHSooQjcSypEKR8RFCIfnnztzt8U8YSooQjcSupISIggEEfB74PC543B643V54PD54fV74/T4ExPB5vXB75PDD5w8iSEkR8ngRs5IKCeH4hJxsBhg7m9B8vR61tQ2ob+pAh94Ei60XVlMXutpb0NTaiTa9FRanH8JTMQklRYhGYldSIQQ9Vti7alB3cR/yN6VjefIKrNiwH/suVKO2sQb1ZQUoyN+NPYfO4nRVJ1p6vYjVUholRYhGYrkmFfTZ4dDVoPb0FmxcNBbD+72G1wdNxbS0fBwoOIKT+VlYvyoda3ccw7FqHVosIuWjpAh5vIhlSSEUQMDdC3NzCc7lJGLesFfx2kv98M6YxUham4FtOzZhY85hHCm9gRsWD2z+UKzWzSkpQrQS05JSCPF4TdBVFeDo2qmYPvg1vPXGUAyLX4TErYdw8FIjms0+eCNHxyqUFCEaiX1JCYI+uE1NaCndgW0LhuHdl36LX78eh7HpR3GszghzIHJcDENJEaKRR0JSIpoKeoSMWs7gROYkxL/6S/zs/72B16dkI7uoEx2uyGECpnuEPGY8GpIKwmvpQEfFERzZtBjzxr+LP778CvoNmITpWadx8oYddnFUrApKQkkRopGYl5RI9XwOA7pqSnBh7zbs3LoF6zdvRPqs9zF5wJsYPG4pEveWo8zghYWFc0IeP2JXUkI3AS98Nh26a0/j3L4tyMzIxdYDpSi6UoJLB5Zj7cR+GPTmHzFwWgZWF9TjapcNTiGqWIoBb0JJEaKRmJWUbOZ0m2FrK8e1Y1nYunY5lmSdwO6iLrTrmqGvPoDDqydh6uA/4K0h0zA5/TAOlLWgw+6NyZk+SooQjcSqpELBIPx2A3obi3H5yFbs3LINmw5ewbkGM/S9Bljay1BxbDM2L1+MefOTkZi1H/sK63Gj1wV35D1iCUqKEI3EbCQVDCHgFulbTys6GipRXVWL6mYD2s0e2JwOuK0GGNsaUH+1DCVFpSi+UoOaFj16HCJFFC+XtalYqk9RUoRoJJbTPbkLQlCcu0FxG5ILjsVjgUBQnc/ycRltBcXPfn8APr8ffvm4fJ18eWTECpQUIRqJJUmFpGBuGY8TlBQhGolFST2OUFKEaCTWJOXzeWG1WmEwGGA0muByuR4LcWmWVE1NTeQIQp5M/OL8b7MHPiIpi++TEYPdblPBw969edixYwcKCwvR1taG3t5eJSy/349gMPjIieu+JJWVlYUpU6YgLS0NTY2NkSMIeXIx+IE9LT5MLraqcajDD0/kuWgj5dPQ0ICUlBS8805/vD9qFBITk7B7926UlpaitbUVFotFnNPRj/Q+DvclqYyMDMTHx2PZsmW4cuUKXG43B8cTOdxi2Jxu1Pc4kF3Vi7Fn9Grk1JqhszrhFpGLPOZOr30Yw+l0qvP0+vXrWLhoEX78T/+Mr3/jm/jHH/4Ib/brh9lz5mDr1q04d/acOOaGiK7M8Hq9KrKKde4pKTmFeVNS6emrMWTIULz77rtYuWoV8vft4+B4Isc+Mfbk70fWnsOYsP0sXt5YIkYxpm0/ie15+7E/f6865k6vfRhj797w79u0aTNGjHgP3//bH+Azn30Kn33q8/jmt57BT/7lX/HKK69i3LhxWL58BfLz9+Hy5ctob28XaaJdBSOxSh8kFVT5bEVFBZKTU/Dcc8/jBz/4P/jXf/s3PP+rX3NwPJHjV2I89+sX8NMXX8P/fX0Unu4/W4xZ+IfXhuMXv34Rv37+eXXMnV77MMZzz/8Kz4vxs5/9XEVPf/P01/CFL35JSOpzanzu81/AV77y1+Lc/d/49//4Kd54401MmTIV2dmbUCJSQVlslzWrWOSekpJ5rsfjQW1NLdasWYsXX3pZmfnpr30N33rm2xwcT+R4Rt5++7v45g/+Dl/7yS/w1Z+9ia/+/E1x/+f45vd+gGfEOaKOidKQ5+S3vvVtfOOb38JX/+ZpfPkv/0qJSQpKRlSf+sxn8Wkxnvrc59Vz3/3e9/Hss88hfuJE7Nq1S6WJ8jyPRfokKWlYg96A4uJirN+wAXPnzsX06dMxY8ZMDo4nd8xMwMzZc5GwOAmzUlZjVuoazFycjBmz5ojnZ3z0+Ic4pk2fgenidkL8RLwuoqS//4d/xJf+4sv41Kc/o+Qkb//sU59WkpK1qp/9/Ocq9duYnY2SkhJ0d3fD55OLYmKPPknqpqhkca7XZIJe3w2dTqe+GAfHkz300Onl6IHOIIa4lY/d+diHN7q6usStHrW1tUhLS8fPf/EL/MWX/xL//X/8TzwloimZ/v3wRz8WmdBLGDd+PDIyM3H+/Hl0dnaq81qe3/I8j0XuKSlCyKODXghz9eo1+Ol//j88/bWv4yt//VX83d/9PX73u1dEBjQP+fn5uHatUgUZNpstpgvmN6GkCHlMkIuGm5ubsXjxEvzyl8/iNy+8gPdGvo/k5GQlp8rKKlgs5sjRjw6UFCGPATJVk2lbbW2d6meUdap14rawqEilg7In6iaxmtbdDUqKkMcAKR7ZzyiXwch2oYqKq+q+XTz2qEnpdigpQh4DpIhktCQbMz2eWNxfUzuUFCEkpqGkCCExDSVFCIlpKClCSExDSRFCYhpKihAS01BShJCYhpIihMQ0lBQhJKahpAghMQ0lRQiJaSgpQkhMQ0kRQmIaSooQEtNQUoSQmIaSIoTENJQUISSmoaQIITENJUUIiWkoKUJITENJEUJiGkqKEBLTUFKEkBgG+P+9TufY1WS90wAAAABJRU5ErkJggg==)
physics-General
physics-
Find the variation of refractive index assuming it to be a function of y such that a ray entering origin at grazing incidence follows a parabolic path y = x2 as shown in fig
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)
Find the variation of refractive index assuming it to be a function of y such that a ray entering origin at grazing incidence follows a parabolic path y = x2 as shown in fig
![](data:image/png;base64,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)
physics-General
physics-
A light ray travelling in a glass medium is incident on glass - air interface at an angle of incidence q . The reflected (R) and transmitted (T) intensities, both as function ofq , are plotted. The correct sketch is
A light ray travelling in a glass medium is incident on glass - air interface at an angle of incidence q . The reflected (R) and transmitted (T) intensities, both as function ofq , are plotted. The correct sketch is
physics-General
physics-
A cubic container is filled with a liquid whose refractive index increases linearly from top to bottom. Which of the following represents the path of a ray of light inside the liquid?
A cubic container is filled with a liquid whose refractive index increases linearly from top to bottom. Which of the following represents the path of a ray of light inside the liquid?
physics-General
physics-
A plane mirror is placed at the bottom of a tank containing a liquid of refractive index m . P is a small object at a height h above the mirror. An observer O, vertically above P, outside the liquid, observes 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 a tank containing a liquid of refractive index m . P is a small object at a height h above the mirror. An observer O, vertically above P, outside the liquid, observes P and its image in the mirror. The apparent distance between these two will be
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)
physics-General
physics-
A ray of light travels in the way as shown in the figure. After passing through water, the ray grazes along the water air interface. The value of mg interms of ‘i’ is ![open parentheses mu subscript w end subscript equals 4 divided by 3 close parentheses](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAFEAAAAUCAYAAAD1GtHpAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAPUJuPDwAAAnhJREFUeNrtWUFEZVEYvp5kZERGxpjFkKRVhoxkjBGzyJMkMpJkRGYx0iIyxhizG2kxnvFIkiSRtEhGmyRp0SbJSCKtZ5PR4nnavL6f7z53zj3nvnN64/benT4+df/3+3vnO+f857snzwsjCw5599BhGPxRKinLxKTjObhfhpBZ04c94Op/sqLmytxta9QrhCOwtUpFkQEVLHMbwQswpcS7wJ9gDsyDZ+B38JGmRiv1+gsvwN0qFfAheOIg4ifwsya+A/aDtcq23zLU2aVuRUjRj1Uq4iw4ailiiquw0aH+lSEuen0JBtbBtCFZEqcc4nHiJbjN321EHATnHeo3gaeGz9LUrQiZnceGZDls+hziLihY0ATZdsfgMwcR98B2izzR4h37omlxPaFuReQ0jdaHFHrqEI8L38APyoSUa2vUCZwo0RpynsUXCCUSNYZ4XGjTCFJKRBdb08BddgC+jsi7tvkCHTy1VHQa4nFtZxlcs4OIJltjc/If2Ipo2s7SiBc1cekXC3e4El2FN9kaG+Rtd6npYMmA40qsl8f+aIVZncI/tDXBtnEWcfhc2FicdZrNB2ALV59YhA1NfrCGnJy/KbigDjxnnbhFtLU1Yp4H2O9TfIMRkUZsLY7JbF+y9+X5sysQr4to3BMclH+ZMQl+vaOVaGtrXoGbHKs/3p6I/JDZbucfU33YH8fbjWnOoqy6JbaDmjK2UyVDOzmHygVEaLmWgFiCZfA9X9zfgiuB5yRBewEheMNe52OEK8mlsNyC/KIJ7+bzaeCtIinYCLS2EGbAsVsWTrEv+auuns8rCRNwjDpFIuPd/nb7UnkVzNMmJAXafw/cACTXqlBmBszjAAAAvXRFWHRNYXRoTUwAPG1hdGggeG1sbnM9Imh0dHA6Ly93d3cudzMub3JnLzE5OTgvTWF0aC9NYXRoTUwiPjxtZmVuY2VkIHNlcGFyYXRvcnM9InwiPjxtcm93Pjxtc3ViPjxtaT4mI3gzQkM7PC9taT48bWk+dzwvbWk+PC9tc3ViPjxtbz49PC9tbz48bW4+NDwvbW4+PG1vPi88L21vPjxtbj4zPC9tbj48L21yb3c+PC9tZmVuY2VkPjwvbWF0aD6bzsVDAAAAAElFTkSuQmCC)
![](data:image/png;base64,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)
A ray of light travels in the way as shown in the figure. After passing through water, the ray grazes along the water air interface. The value of mg interms of ‘i’ is ![open parentheses mu subscript w end subscript equals 4 divided by 3 close parentheses](data:image/png;base64,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)
![](data:image/png;base64,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)
physics-General
physics-
A reflecting surface is represented by the equation
. A ray travelling in negative x-direction is directed towards positive y-direction after reflection from the surface at point P. Then co-ordinates of point P are
![](data:image/png;base64,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)
A reflecting surface is represented by the equation
. A ray travelling in negative x-direction is directed towards positive y-direction after reflection from the surface at point P. Then co-ordinates of point P are
![](data:image/png;base64,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)
physics-General