Question
A point source of light S is placed at the bottom of a vessel containing a liquid of refractive index 5/3. A person is viewing the source from above the surface. There is an opaque disc D of radius 1 cm floating on the surface of the liquid. The centre of the disc lies vertically above the source S. The liquid from the vessel is gradually drained out through a tap. The maximum height of the liquid for which the source cannot be seen at all from above is
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7ffa4xPJQv9eKLwSCGZnaoxlWv6tIuyuFa4bm6RjOKz/qRWa5CmXjSlqRVpE5Un7nX1szKSQtimBQ4vJlRpZFfDJXxkqlnNZJgwNIYtXR85Mmx5df2/YExo+UA9SHOKHQioS2LYe6yYSqa4lSlNQvm5/EpjXpdPY+CUDgK84d/+IdtdmSQBig/f/npn/7pqy/+4i9uHp+xaW+UnhL6n5U3v/nN7T7pysT/pV/6pW1WGCmU+v3D2Zve9KbmJPDg1w/Xhz70oasHP/jBzbi3xLYN+d/ylre0P8apz5T5oAc9qMkSX9qTq7wMhCLi1//aZobxmMc8ZnXaaadtpweM0L9j3XDDDS2y0KfkIRd8jEp62uRqDMjfr52/7nWva7K65ZZbmuFanxtzf7l+9tlnNwfnM2KwfmBLm/zinTYZD45DffJkPI4X5LUY5i4ZpiIRQ1RuQlHKEDKYFEt98hlk4ZVf4xZaeU5pXv/61zcDUx5FpTif93mft/rar/3a9tukPSjoa17zmtU111zT6omS4Jf/e77ne1r5o36ph1FeddVVzSloH1AQM94Tn/jE1aMf/eg2I0MMF1GkX/iFX2gylA7S8eK58MIL24wTxc1s454x/sqv/Eoj4bk07aWkxgHv/e53v8Zbob3kc/XVV7d/zMIHeMnv277t21af9VmfNQxNtYsx4tVnsyWZpG71fuqnfmrLd9NNNzWHw3A5N45NCMw4fTazGjfEaKtx5ropFsM8ihNqmAzM7Ee5GKKw1D0DYTAxQIbx2Z/92U3Y0iAeF0Vps8tK0bea2a4U3Cw6UjgDi4+ipexAHQZa2cqUF8mH1IWXobj3TH0UhEzMeFXpYoDAiBG+IIanrYwZL5Kea+7TVvX5HDkkPFdGr+R41Cm60MYejCahew/16B9eZdS+qIdhx1CVjcglfwhkPK336YtxMK5mU1eRDKNlsNb7KWcTaNNimDs0TKwG1CYDMmAGywzJG/vMu55xxhltwMxYroRt4IRGmw7Y8UIbKXCMkOEYcMrICFEUc0sU223KZ9eUU/NV4GEAtT+5x4P6Z/kc44ysGVPWz4jie1ZpZGy7DX0gP04PmbGFxcJ4Y26jif7kx52tUzlhY+6z2VTbqxx6LIZ5FMdlmFgMEiF6RSHk/NVf/dXV7//+7zfv/mmf9mltHUiYPCbhRsko4Bxq2dUAtIkyrhvYAC+Kp0fampk0z0N7CfrXk35b71F68sxM6NmpBNkZK84NiY7yX6oMjKP23yTnnHPO6gu/8AubcXI0U21fDPMojskwZSUsXtIfjjJIf2RLYawP73Of+zRDJHyUNVUdhHWKxHB+7dd+bfXiF7+4hVkJ8Ri19nzlV35lq8PnKTBs5VASoXXCUpTy9hvIzVhkBhUaC1XRps5qt0AvQuSbzSXLGJt3dMRsama1EfaQhzxk9cmf/Mkt1NWfOvsvhnkUd/z+W+GGIvNuZhWDLATNjh5FJyTG+4Y3vKFtcjBMPLbRP+VTPqXRJ3zCJ7SwhdIog5BdCd91E+UxsNnAsUa1AWHjw6Db4DC4NhkoZNZmDM+MmLCUQQutKEe/XtzPMA76pz/66mp8GCpZ9PLVX/02TmTiWsN3sovjHAGvfELWyovoQ+oMKQdZD4ucsua0hLFZRA9sIPkHaWNJ18z88qcsfTR2dMC958Jh432YsHbGJGgDwUhe+9rXNk/GIz7wgQ9s2+kMkvIzVK8aCLMVfGsZiuYdGVedeedAWbTh+c9/flujfvd3f3cbmJtvvnn13Oc+t83SF1100eorvuIrmgOgnNdff3171aBOCqDtFEpbppRuvyN9M6NwjoyAclfIk9c4nC7ZkhEYD47UJhzDHkG04ZUKQ2LYgXLVe+655zYHXus15mRvF9fShl4xSCT9t3/7t1s+7dAeY2WX3QzKQPEvM+Zq/O0SQkMGnvcye/3sz/5sC0k+8RM/cfWMZzxjdcEFF6w+8zM/s4WrZibPvGKwtR7yjs3ROMLesv+1MFgMkrGbGZWvHbwuR8ADUzaDHMhPgZB2UCg4qEYJMTAzGVlMyZdBCSfJhrFkbNyT29y4mDGNn9mt5zW2nOIIDNdmIEdNJxi2d6WuDO1rvuZrVt/+7d++evjDH97yeT31spe9rI2d9hi39O+wYjhjEoxZynrguuuuW1177bXNs3nBLp13zgIeu1BHWOIaxLjNYPJvaiQUTX2veMUr2mx73nnntcGkBN7ZHTlypL38/oZv+Ia21uRVhUcGGCipMEh9PLn2bXXxwCCyZQAcmVCfwxrNmKId8mGgPgfyijjslk5FM2QpOsKvnipHIaY1YvQgkEc9HGuWFxX46IRdZzojEvP+1iEJM6MoTX15j3xYZ8xJwzRTMZJf//VfbwbppI3BF5LsJgzmz//8z7dd3i//8i9vfzdvEA0ww/ypn/qpFoJ93dd9XTPMHmbT3/zN32xrEnw99rORMsa03xhRXO+LOTAbb71h7gcweE7VEuWnf/qnWz+croozWELZAkZgXcI4hBuPfexjWyi56TpxJxA+MS6DxRHwsEkXVnMgOSY2AsU1uyqDNxaK8eCUlmIH9X4/QHvTB7OY8NS7YlFKnQn3GzgYEZWZ0skq42Zz0fjvtzE6kbidYRKGtYd1oxCJwKz1eC+hB8Og7CGfGfJIORgJr24WrHzuzcb97KUM9VI6hscAEyZRRusbZTlZEoMdQbnaRGkNsMGmxAw7IZ1+qkP58vdtSZq8ue/zHC/UXSlI+dqkbUiaNpOZfpANGRoL6cYFkUvkGyJLMphqt3QOTx55K69XHcq0VBjxq9MYWs9XPu1UFuc4VS+ZKlcf5DVG2mG5dOaZZ7a6OVV1HFbcLpQ18HbEKMeTnvSk1VlnndUUxMLcjhrlDrDy4g5L2xTqw1wD4P2Vs5hZ2FNEPI94xCNWn/RJn7RteJ4ZHGGojQBGaZPJ6RGDLKT+yZ/8ydaWiy++uIWzo9BN+830lFaZleRXrt2/GGUMz1qJsUunNJSVU5EH4UV45cUzB8+VHQKhdfoLaZfn6qLo6k594LN0jsY9ZSXDlOOejOQh4wrPbJgJBUeyUjfDsr6zq66OQJuc2DK2wsnabkhUZVOnzm6u1q5f9EVf1HaLk16hH5ZMXr1lt1j5xtlGk/Z4L/4FX/AFbQ28hLJbIEwL+/vf//7bW9iEadbiRSvxep6NgI+xMRK88iJ8FLGHvAaMcXjFYoAZiM2gyy+/vD13wMBJkl5RpqAvVdG1g2fP9ztdeeh4e+RemsgBuU+emm+O+hkISesp+T1Xh42rtA1J0+bIWD/6vkfGkW0lyj4HY8TIej4U5zYFZY90QtrcbFf1IjphTcm5CGvp3Lq6DzpuN2NSBjOmjRXvC3ksisCQCIuCVIFRfB6VMHuFkc/gEbhr+PCYubyEjkdVPu/5Iz/yI21b3fs1mwAG8Jd+6ZeaV/aVLe8vbUwx3hH6GXMKtS391bM8d80z2NQhVIzqSrm1nlBFrXsKn/M5n9OWG72D1FazNFmPylEX+RoflJkdPMNL1iKhnj+hLFJGIB+y+SYCGdWrHm1NVJI+K8cM/mM/9mNt6eFbOd6TLruyW4YplCBwu6LWmLzYbkN9v/zLv9yO4tkqN6AUi8Fb6/rqk1l0pCQVmxrmQYIxsjYbhav7CWZah0XsvDNeZ66XUHYLlNk5Vx7N+yUz1clQcN7Vq5FnP/vZq5e//OWrK6+8cnXFFVe0EPaSSy5pJ0PWGeVhxUFxQCYHTlVYb4NvKio6DBgaplcj3idZe/ziL/5i2/ARuuymApgdvXi24eD3Z5Bjf9a5DjWYOTc1ysV49xfoFmP05QURj40fr8oO8zgOF0xmL7ueQokbb7yxncIR81sP1HUIMNasFyzge2Lcu2nQBlUd1iZICKuNB2UW2RSj/taxscFCPsbE1efIagqRbTZnKmWDZ6rebAylzpDNoWxIyUenGKV9BLu8li2+Mjg6HHKYMHnyxxa82ctrCgITWjho4JieDYHA4Nhq95rD2jDg7RRtu/1Rj3rUroWhlM4Laed5tdtGh7Z6pXEYPC4ZO5lFofvXVTZTvH4whsaGkWZcOF8nhpzoquNZYUfaqy56wTgDY27X3nnpPuRUNmP2KuS3fuu32oaecQFOwPh8yZd8SfvJE+2z0WdvwYF3m30OtKjLWVzPl5M/A9iZfeQjH9m+QSKcteZzmN3h5OyyZqB9RjxgKDt98uyWkVAKdaV+gykkthGiXQcV6ZtXSlNOiEFIZ5Bmxzo2mS3n1nH4ybMfW/f4YWpcY6CVL/UCfXrVq17V3lkzSksXewx2l6MzhxnDGZNQvCsUyro3K3mFIqR172s6+YUCG0UZfJ60B888tW1+IlAVQB2u3gP6NoUwSrsOIjgeM531t9kyr7V6MCwG0cuBrMywc2t3BhKDiiMI1OV112gnWF714VN/0pRHfxilJZLNReU4SGAGNTuCE14OSyjjsM6Ys4bp9QTByULAXnbbzhZ6MAYezs9FOOFhkKbC1amBP1HY6kKDewqhHwaXkfpMKdB+hD6RITIe5OwVFqO03DBrzr0qqfLpsW5sdsqL6A59oWOWHa9+9aubA/Wa5zM+4zOa/pi5o2sM0/dvF8O8FVMzJmFFIcyIZiGhLOFZBwhX7aJ5neHrWF4IU5TRgYOTBV0y8Lyz1z36hrRdeox0q+vbVxil7QZ6pc7nOI/IPMQYrc/I1/qOwuaQxqmS8xzoBfnb8OEgvRv3PU5tteNvlvfu1bJD38hbn10PqmHqj/WzDTD3+msMyUBUWTG7+WNtydshChNlwSI/A2Wc7u3AMUivOJybJXyhlvUPweOL8vVQvoYaTGVvNamBJ1WOa88vH0ND+CvMIDqrfgqCtJGiWOfw4NKyQxmoA+Hv21zbVe+nMNVfvHEMKcdn9XFolcjU4Nml9DlLA3kD9/pJTlN1krHIQb9rvYBX+SMZa1dkrIxAPvVyDPiVp3zjQL50gyH6YS67rtrmNBCD5MDpl/o4++qMlHMQDVO/TBK+0phfhNBfZ9FthvVfYZw1TB7N9+SErwqNMhCmWdK5Ve887bzZ/cvXrAwQ5TEAKkb1Jyj6wbf757uW/YEG9Sj/6U9/evv9IQYeyENZ7AY7S8tBVGVV/1d/9Ve3zSuQH2lbiNK88pWvbGXIHwOgaPrOwWirdsRBIZ/ROuhvFJgS+kwJOQRy1lft0A8OQvvI1PqdEuuv9sRoDKgX8H56IzJyVb4vBfjSwZQDMy54vSvkscOvH94V+wHtGEsgDwWiA/iyw6r8zODf+I3f2OSkTLvz9iJyIJ5M9YOu2Nzx7RGGpozUz/jiLJTrehANk97QNwdoyCObXPRMOG/WrJg0TKEsw8rvr5htIlCD6QXw4x73uDaYKiVEZcRAHe1Tcbw+w7S1rlxrCp8ZgMEwY/mWgu31flteg31PD18MG7RDnV7l2JpPu/PMvbO12cAKPEPapo2MksJri3a6UjptJLT0d0S9AfTQBnlcMwMrT2TgsLrZWzmMk2KTo1dLDEUbwuuKj2zJiOL6nPr1xc+8GI9qWIG85IrXN4TirUH9lP7xj39889rqq9A2YSgZc6Cea6u1u36ol/Hoj8+MTHsoHgUUOamL49R+9UHkSsYMj/MhI+kH0TA5xje+8Y1N/s57m3DIkvOic/24zc6YNn8IGW1la3AfResHUl4CNQMYCF7ClWLYwTVgyna1k0jwvGo8KRjIkDSD5hplCrQjTiEDHsir03WWrcCbtioj9UHq1cek9f0/FqSMIHW7VgJtrvUGnutj2lshr37inUL6ilIXuKcUHGjta0idCfnN8MbRYROGw1lLo3SUiyN3MEW4yvGmL8Ja71L9TI36A/cc51Oe8pQ2/gfZME1uP/MzP9Nk6f2xfnNco7GG2c0fhjli2hR4EUXiYTXODIfMFmZDA5nBFBIJjygZojC5rsNWN7ZxLO3Gu5N+nmz0fYVN2z/FK50RxtElxGZ8HKsDCgzGupEhii4cNrEPYeNPhEHJYFTHyLGCvJwGpB0HzTD1yW70M5/5zCY/+vzkJz959a3f+q3NgdHxXjYbG6brlHAN6FYxt0F4kAHPBkw8bb7rqG7fTRQKGYj8YLTdRyGzmTVTfqWkTXmdBf8fxscYMDZGF8pnIahxyJgwPlczpdnUGFAi4a6x8dmGDgN1zWytnqoLxsX4RA8qGCTdQSAv3oM4Y5Klc8DkeeTIkbYO59gYqBnUJlrFWsMkzHhSg9gbobxCTVbfC14+fAbeVd6Qz5RBmcIjDdYGxosYadYsGSDv7syyroiiuGajhAL0FIVA6p3C3LO9gCrzHhS8pyh8HTvOsFLCUySCIS8KEsqOcGTuiowFQ6z1jdonTf3qNoZ9nuiNesEYyHMQDTPQP/s2fnjMZpxzAN/8zd/cnF3FWsMkNAaiMAeNCSwwIJ7nN2YJuUI5Tnh4oSyMNUjS8BlYJ4jsnBogMBBmU0qCGKwrxYmxMtQYdAif8syuZtnMtPHslAvx/HEevSHmc58+wiZ51qFX0hFqnj6/z4hMbcaQVa7kZeYL2ZiRLroggxC5u8YQOTiG55p78pMv45Z63RsP1xHk5xCEwcI44x/nHH7nqJ3VVY/PeXaQDRPorI24Sy+9tE0u3/Ed39HW5xUbzZgEagHPyAy054DVvRNAtsKj9IFnysNnqz35XeW1++goVjwmeIaqEhighMF2FDOr+px7s3LlQRU1jRFTNsroWu+jpPLEm1sTuOa+fq6UWbnKB2lXZi7kvn5OWr3qD8XX31xzn88GWNlB6k0btCdt0hfOqYafuYb0K/n1h4HbseaUyTrQRgbr1Q7nh2cEfc/egvGvxufeoXVhHOcgLc8OumHqF5t40Yte1PTMWtPrwIqN1phbWW53DTKYI8g74kt+1yleyLPK25dnkCmqdWoNz8wSMeaqzNpLUSuZTeoVxeC0AU+Mr1Ke5b72RftCMU7XSlNpjNMAhhhq7vNMXgMbZ8KxxODMQgn5EzVoI6SNta2519b0w7rIaxKvlMzGyaN91pp+dNvuesrtkbK0M5+D1JH7XOU5iJs/GVv3dNB7e7u0DuR4HWjmrNh482c/oBpHTwHhmGETKveUdIY8Moape9eaDpldY+j1fvS5pplFKCXK66R6RQxQn7eGsF3n6FhBbpyR9vRQXqKUEwX1KfcgGab+0AsTBRvj1MjNstAvSPrhcgdwONiKA2WYkPbWdtd73Y33ymzlGqrpW6Jp1ymCUV5QbwjqjNVTny4vyqxd7/MZhTd1BvVz/+xYkLaMUPt9IqAu5R0kwyQjUZzvC1trizzAlw+c1rKUi4OtGBqmTDlgMDUosMmgRHFGmOM/Xj7YhDd5al73oRF63h5TvPhGbV5XXviSr5ZR79e1dwpTfLCbvDDil4aXYe72174YjE1ES51sholWRFPq1Rbhv7SdQD3K86okp6WUKXTVJ0sPjrbHpGHWzZ+pQVjnMfGFeszxHi9fgG/KoZgNpzDHt5O+4sM/hal68YWmMFfvbsl4jhffXF9hit9n43MyDFPZ1s5XXnlle5/oB6rt5P/cz/1cOzanPieSGM6pwOyMaafVMSpn/MTIUR6CZ7h+3tJZyH4gCFhcbefJIteWeQbBlYfwMyUEXgcnA+OsrSNcvuwsHgfNtDHDWeTXwXvl0T790F7ttlas5fNST33qU9uGRU0H9fgZDXzO0Oa5vtlIcQ7VDiLUeuVD+qivTjVFHtLJwa+hf9mXfVlbR9R6lRO54+vb68gWPqdqRn3l8e14OmSeJUjAK59//vlt53Nk9I5KqpeMtRevOrRReEXG5D2ql+cnY1v+NtQCY6etXpqTdZ0JlKMOBqHN/mtVmwPPrZudFSZvOrBbhqku4aWfyTxy5EgzQHJmhN/7vd/bTjkZb+s/m2ry98ubHvpGNqGdYm0JBthgZbpHPhu00RRc4bl8ePJaIvyjECGDp2P4Um94pdmImOs4/trmvl688vQIX9pbqfa1H5h8Vm42bWqdSPpUnSh84c19rXcKno/6iubkNDU2aKq9gXIj4/CGImPglBixXyyIg1VubXPqd5U20ovdgI0XszJj9Fcd2sAhe63jgDknHNkzSo7ksssua3+oPKIf//Efbw5SKHwiMLv546CtQdLAfqB4Dx4ts8MI+EI98Bq4ETLwrrVeTU29vYEEGXj8x9JmeWu9FerCZ4CmEN5RX/FNtRlfZHS8Mj6eNte+9jLGY2ymZIwn/KM2W0d51ULRHe1z4ENkZZNjTs6gzX4DaDdDWW18yUte0n6/WPk/9EM/1JyUrw8yPgdfvuVbvqXNltooKvjRH/3RFsWZafs+k5P1qJ9IEaX4FlXSYW78eqhP+WsNcyS8AGsqH6FV0HUimOOd44N1HZ3jn+Od49utvsKp4J3jy7O5se/51WMjxSkjO6qWMZY/dMiv+AlPU17PG0gzPvlGEufAcPBbWp0IaKf3iN/3fd/X3tFaUn391399ewfuhb96fS3LMi3O0mzvq2++VcPpjGDGd0jAFzKE5ICPPVkubALOytfgLGFmDXM/vi5ZsDMwDAbByCjWXJQQ0BH5hIfCOet0619K7+coHXCgdOugHMQ4rDG1wyxrjS68nHIyI5gBGbUQVdQXxFi+8zu/s7268CV8X0xX57Oe9aw2MzNM4W12TM3cz3ve81o4W9fUFcJwv2Hkb+z1FzgAs7J/qVvXdv3WZl88d0xxx4Y59XwTIR4v707qhKXeMa98jIGS+gV+s54ZIvyuU3VKt3llTSmMpaiU3EabZ5u2FazT1IuHQTu9ZEbaFJwEg7bRxzEw0EAoKiRlhNL91aPy7cY6icOZeOFvhhbS6geZ2BASDWSt3EM78Zg1hcDAoDkru8xkNxqHQF85ATOuMnZkmHnmWgXv8yZxtXzHwzviA2kGxXUOo+fSjqfe8EkblRuMeINRWjDFJ203+qoep5+EbcK7OmOmHXj7coWp3tXlp16Ec5RcGJq8eOf6GtBBBs4gzFqOrTmTu258AnUwFN/vZSx1xrTutVFjFmNkvktqF5rRcUYMWhhr1nQIQDnKY2QZ5xH0kWGhhOzykh/eTZAy2ubbrcytpmMxTBXzahbptr6FPVX4tsp5KovgET84FO8VgV0wkA+vhgkjCGu0xuGN/QxJfqk7fIi3oQgW4lvd2oZ8wiuHsrWb0tXyeTknMQxG5cVHsNZNDnOrP4opH4+qrfk5kL5edRh0cvIlWWXVes0q/m5OyNXXS65mLd/dqzOXwRba+T0j797w9fX6TEZ4GVkvS20eja++aa+xwdcrVb54wGBSpzKQNaVXKF5BkBeD8romMEN5DcHI+vZC2mJ2qmtMf8lIl0Y8U1AWXUrbQF/onb96VDYZMkR9Mo7qpdd+g8e3paSFd6cgV+OWGdd4MPpqyBV3/P5b4cbAM5K8SyOQKcOSJta2SLeAth6wJc7L8Uga4WssYm0V9yBgPBbUFKfyMhiGTViVV53K9dz7RopOcfCFtFm9hN0PIn6GySgZGCOhgKnbgODNO04ClF/cb0C1V18t5LUTD17rFO/uODLtxReFSL2+kUPR1cvxpV47lgaHI6IEPbSJfLwzjIzTXuVyRGRFybTRwBtkRFZ2NtWpDDwhTthMor9pJ7jHJ4868QnF1Gk25JQ4Pc5LaCkvObsizo3R2ehRlpk3hwXw0jEv882m4e1JuryMXH/I32ZIdOlYSBtq/+i2MJbR+7qhHVThKjnYNbaW5diFksal8u4UxpIc6C4HkAmJLNTV47hDWQKkEBRxq4htqGjqNQvIjzdUQanwjbwVPqROfH29BjFeyDOLb/cURnvjsVJvLV+9+LXbPYVk+H5U2Xa/chiqMirCp14Gx4D83IYZMHldGU7fZvXjo+RJr23S5vC5D+RRp7oNuEHmIHzjg1J5przwoorwox741EVO2t23l3wi4x6eRy+Q+hm1q5ndOBhX/CPgV99unJVVLuf4wz/8w80Yvumbvqk5/6m2nEioW5Tn70VEMda5xsu7Ul/54tj7dqydMQ3+CNINEqXqKco9BeVrCMXIy+WQgcM/Ar4YQuUJKbPWqz88vb5RFOUqH43qxasOSser+QaA0MdAmgXMFpUnfPKLIOxG+jlM4ZtZO23xfKrN6suXmeVLGuDvZZx2mo04D6eN1ClEj2HioQxTMkaeVaML0v9NZdzDM3m0U34bKxyb0Fc75njTb5GEGZORK4dzNAY7ASdDH8jMKxzOk6NInbsFMqYbIjV1P+EJT2ihuaiLo+BwvCLpdX5omIRXQ9lQkHuVTlFF33mfRzyVkq/iWPjcm/GuuuqqdqrfbEc5CCDKMcVLMYWsfvpBFMHrW4/w+jDisRb0Y77WWAxYxMGYa95KYEYQoVxzzTUtrOc5KTGk75WHcpkhOQu/CsEDcx6ciDr95bsQlWH0vCNSR+oJfB7lrRRswkvWkXdm/Z4PatpuGCZwlta9fuPW2EROuwkyYFuu6kb00BjGSTj6qp8V0+5rCwqsVxilzaHPd7x8wRy/Z4gymEHcO5Ts2NR3fdd3tb+SFyoJ1eZAUcyy1jveX73gBS9o5SQ8DZQvzVrOjqSZz3+7MOYo5AieGRh/1ORfs609eNYoaPqYKyhbHQyZEwWOVF/0te4iVr4pTOVbx59nfR6fe6OTxsBq3p4vmEo/ESBvxiiiIKuTYZRAHhwC40N0xasZa3iztk0mM3eP4RpTJ3hemws8uY0WMXEUTeFmD9vhvHw8YaAx8vDkFJYS1QEzI9m19WK3h+Zog19/51XMKnil48t/KAqLemif+F171UuRhXjZDcXjx4/8VKYBsuC3WcFbMcJstJAFozEL8t5mWRs01tzabG2AR7uUa3b9iZ/4iTaLMRThm51Ls6ZyvRdzXEt4CORFNrbn/fq89ZTNDZsPopTA/bnnnrs9U+ubEIizcFWfNa02mtHr7y5RPN+Y0Ncqe/DZBghHQ8ZkGxnj0z+bIjHyCjJWHxlbN4lEAv3SVq8bGEH0JbDmF77hU0aeq8PY0CftPRnfLjnZ0EfO2o9wieLomJ9m8UNcoqReVtMu/VYQtGmYUQotQtY3vDtBT0FDeHJb/pWXcuHH2w96lMOACNkoeeVVlnope69sAYdAWfAmfKXgFIayuOfB5FNO2qCv8qtDG+3+epZTJwyTs4px6JvneMx2lJjTYGDCE4plXaEdCWWSn6NgVAxfmvZIT736SkZkkJldPu23YWFnU/8pMyfFEzNI9Sijyrh3mqAs5SpfvipjYy2dfEZQL7mpq+dVL151qqOHNHzRCX1F+KSRwdS47ndUmWcy4Jw5dfreY3bGzK6sLFvZtiGPAegtvSI8PW8V/mggRvVB8no2VW/45KUEwlDrvjgJC23vDUUDIH/6GFBys5k1pllHuMlA3VMoCpmdNPIy65mBpb/0pS9d/eAP/mCbkbzK8AKbc1AHZfcqwoxhRtYeA6UMBuzMppnKzFrlknt9Vn/6ZJvfu1ehkTr8/0g1ivDVsqD2td6DvJFJzxeEp+eFyjPin+JNXtfd2JXdC+DQTCx0w7lcSxJH+OzMMtaKoXZHaIREGYSQlLVS0ucwxUuhPRsNHHgmD6p8ygpNIXWmXjOYQRXmCQt5KDOcMFdeBLWvlNsMmz/nZcw2ksyCwlRrObMVOTEu+ey0mfmUY6PinHPOacI2CygzfXW1AeBkCWM2qzkoINxVHuONjPDV9pnNhNuWF9rl1wk5UDO1ELCXGd7UWyEtfU3ekDRljPiC8PfjE37Pp/jn6kUHGeTF0eSdKf3gzEcz5vR0dysoCiVFFKZS9cxTCH/Pi+Z4p+pN2qa8wDDNbkgEYOdSCGENy3vJFyUKL2NjXHkZjtesxpPLkxmNItkxNPsKM332nKLhY3iuaQultJ6w9vQqwaAwTO2yJhXemOV51vQ3fZWm3TZ/DCSjzKzNKDmP8IXCO0L6WvMjaWnvHOb45zDHN9fe/Yy+z/SEvtAFGz/0osesYa5DPCNSeCiKvg5TvOv4N+EjDOnWh9Zl1pZmOzOZXTnhp1MgQtyen9HIH8NioGZIYajQE+RlFF5TeAZVsTxnaIw0UI80fGY+M6DZk4EJeQ1S7z2VY1C96/RXeDYQfPvAaRhlq1PIzAH1ip0+RUahpE8hz3vedXzBTngPGmKQIicTAf3hkJ2aowcmCjrU47iO5IEKKZEKef1ckYZkIKb4effwVV5lxqv0vBQPJW/lQ57hoQhBQiVkpiMMV2EpJWesBKM9kHrlc68sfXVQwaaPcBUPg1Zn+iqvUx3CZLuLdaaUR37tDZ93q3YmbZkzMkZpnah8bVWm/pCHzZGrr766jY+D2TaXOI/0dSQrwKsuYxsZIenapo891BlFkrcfG3ypd4ToRXjDr9/S8U3xpg/kYi2tLI7sRL3HPBWgV3bOX/ayl7WvgGXvQrqfUbEE0rdeJsd9iJ318/p5lZJ8hMl7m5kYtrxbVdwGtumzCQL45ZOfsmowhet5vSqwxuoPsatXSGmXknJXPooG8tspZTy+N6jPdjQZBqMgqP4Qu/boH4G+6lWvakYsP6WWjxE5X2nG87Lf+1Lf3bMGjCJaz3pNIBTVFnzqB+te5za1GTxD+qVe8hV2G0x1CVnJVSSgvcKh2t5AmvW0nV/rY+0IyEqb8xtGgTo947DImEJVGSMzPC8/evemDsuAHLzX/tSLl7M321tbjdqceg7S5g+HxKZEZ+mTicGeguWIkHbkIMeuawMYMFOymYQnZ2AhIR8vOQXCN6ULz/BWfkrEW/YDl0HTUQals+EJv3Qdl7eCges8pTP7yGdzxyKcsfiZCYZuZumhToKMYjCUHCpXp/5Txr69gbZos9cCWacyYJ8pN76Q9rmm/drjXaMTPgxXaO25uiPjvq+QNM6TU4icIisyNnbK6iHNLMcBVhmHV7tjrCNUveh5pc3pxUEEZ2rG92vrF198cfvlBAdd7PBbgoyMEo77EDvPn3AlChVQZOuuhGQ95E1I51p5GRH+vGKokE+9FJYBZiYMKDpe9Y6gndqLlwJxDozE2s1Lca8qfLukL1e9+BiwmYBcRASEioSVDEd46oRQnTHBVV9dhcPKwWc3tn5TvkJe7zuVybjMNCKCOBghXmgKNYysMIsZn9Gsp69kExmrK8Cnr1knjxC9QMoJjCV+cjJGI8ij/oP6uuRYcNyGKT3C7qHI3lh7hHdUPt6qEBXr+NQ5Vy/e2maGRvnNEP4aXkjaK466KJwFu7xw0UUXbTsP9TIsZ2VHhpk2a5cZ2jssYaQwVijTOwKfzYg2qMzk1qzWlYwpbd/rMsbb869rs/yeLYa5g1A2QuYVe6JYcwMHnss34p9SGFjHt67e2mbleEnvmJ4Zwgtfa9BeKZUpTV4zBWO2DjMrKGOuvYEyhHjKB2tEhtbzqtcGnO9++uaI9bZD12aqvu3r+rpOVlNYx7euXnlG/Ju0ecFRrDXMeD6K2VNV3jkcL/9O6p3iReGnJAzN6wqzJUOzprMGo0g9n9DPZpFwl3EKhUdt6fnkQdaiZgKbR9YddXMr5VgXMkobKA5FeBFt1phDyu/rTd1zOF4+mOJFc/xzdYYOO9YaZryfdUrWhSHpcx5UuueUvOcVpkgf8UpDIz6UNk0Br+fq6HlTbyCv2UhoKWSyrvMHMLbsKz8eZXqZb63nu5cMjUIFtd21Tn1gxDY/7FTaWa2/Bo8ncmKQDuALp615bVLl+RS0q68Taf+UnGpbexn7jG+KFzIGvYzxIuWOoM7w9fXiQXN9PSyYXWNSVh7cusirDSEWoXnualfJlq/438yzVdRtYAfRqwJXA4JXPhs0QjTK577n1R4Kar1hAAP1Mg7b/V7LjAZR/vy2j51fUC8SPqrToYNap9lLePrCF76w8alD+RRFPhsefguGUdqV9VrkB37gB9rrA23QB69TLrnkkvZNEq9V0jb1Mn7GZlfTWd38Fo6yhdHqZJRO9jBgr0FsDAl5c/RuBPzOXuIlY4iMjYlQ2OsNaRXalldPZnGGET7ORtjulZV3ttIq5NNmUQOyi57yXa29/cWCSKTCMwZp3WxsjY12pF4yEyGQpb7Iu6wxJ0BolNNAMNJ6NQsQbJ01KiJwgy4vvspL8PL0CB8DCx+ekM/9LmaQ8jiBWp+rssxyMZgK9VECvw1qNmMgZs58OwSf9ghnGQulo9CUW1vUm3bLm7qRMuKgvIM0CwZ4tMcrBYfRzaiM3fvUtDdljxB+O7C1r2kzGY8QPn2qbUXqVd7cuCJ60fMidSdfD2Uam9rO8Kl3Tp8OE7ZnTJ48f05DMDy0nUCCMgCMaytrg3ueDfHMo0GQB29IWcmnDgptJuoHAl+UxiC6Tzpkux6NIB/e1Au1Xm0evWZIvcJU3yihnL4vx1DNeOmv1xcOHFiL2jgSWSiXYdmRfc5zntN4UjeFc0jA6Y+nPe1pbbaPY1Gnd6uiFbu6ZjczpNla382y8k69YgDGh1JfoE1kpO090lfjGhmTkfTIaE7G8qdOVMfffeTVQ/nyZ2x9DuTXVw4PybfMmLeiChcySJSCgBwdCtnmF7IQZs8XSPfcLIMfT/iFLXX7vwKfAcInX60T4ZtSGMDP8LwzC0+td6SogE+5FMF7ShC2UkDtjxMR3jk/K+TMRhGk3alXfQmHzZpCdwZbnQIFdUJHaGezx7tNywjtVAYZzBklkLGxSB9rX8lqhLQVXx0bV5/XyZgcyLH2NYR/ZJSgXv3Bl/pC0pQpD0r+w4htqyDozESQcCMezXVEm2DEh9ZhxBPaBCO+0BQ8IwtG4qW+HVLGKWQNKJ1w1M5qTshkxoGUn7qEqdbK3gs7QJ+85Gtt6adIGJE1rDBZ/eFNWetQ8/c0h1H+0DqMeEJzmMqfGZwjlMZxMNQ5B3FQsW2YhEA5eDNKI+andAx0HeQf0SYY8YXmMMof2gQjvhAFMdPZOLFJ5GSQzRWzm2dkZda0QSLkspkhPYiigXeXzgXb5XUA3cyQ52bbfP3MdzrzCkUbevRtDG2CEV9oDqP8oXUY8YRGIBO6ZtMvxwXJYm72PcjYNkwGyZsLnYCymAmsp4RivPgI0gkOf09TPIHnvOGId0pBQbrnIz7lTfEFeKfqrW1mfE7n2CF1CNnuNF6RhR3p7Mjmp0Z6aIfZ0hrSOVezoXCNvOxI+hUCm0LqyNE8ClkNO30dyVjaTmU8hbl6N5Gxeqf0oq9XWfpsnyOvlBipvCKTqXD8IGN784eCWQfZ/ubh7egZAB6eQlHEKFVgc8RWvfURTxeFcpXPa4P8clsPeRg9XsophAkMlNcS+UpMygUDri6vQ7SVQeS5PtgttT7EN1JaA+5dpR1S9QfKYBhC2PymjjROSV0vf/nLW5+s/7LryLM7nUM2F154YZsV/SdGjuSRjx9fMqtaX4pIHOameOp2IF5ZfpTJXwdoe+2rNtg4sgbVXgae567GQ1/xaVvlDczKZMxB1OhHfjO4jSiOpucl43wjRmgZkLFIId/iGSEyQ/qZcVAHI7OG59RAm8iAUTqGqF66IIS1ASlq4SBHOnSQsf19TEoQz0owZkwD4j6vCuRBQNgGwPca89cBZgEDQcCUlPDz1a8R5PEeTZjIU+LHiww6/t5bKouCMkprv8zqSBmQ2SdtraAcnAle6z586vUOU7le/juZE17yYFDkgMfJIMYlLyXynCPLbKgvzra6p2x+dIvyMXgOyI6v3+xxLzph1OryNSDhc22zvjJusiVjBp6+aq/3h2RkRh/Nfsoym5MxJ0CukbGr+jihnle9ymaYviKnjIyte2PiTPHUJhq9IFu82m5JhFe9ZOYdMQenb5ybdOOoTrwchU0yDoBctW80lgcZ2zNmwCMadAKlcBRSFoNF2SiS79OZkTJ7Eia+HnUzaQQ8DL568gCf8kdGjU+d1ZODduJT79xAhjf1Jq+rOtOvQBvMXFdeeWWbBSgz46OYnItDCQ4MUNgjR460GdOygGJ6BSJq8J1L9TFcr02snUQUDFK9oxAP9Cnt7YbqNnxT/VVn7WtFHPGIl4zxqbsiMsY3GhtIm1H0Qh3SfXZv3Bkpo2WQaR/ZmylFTKKOw2iUcDvDBELjyXhonr3OmFF8iiXEQDy/dAM1NVj7GfpNocwafgXPt0wuuOCCZowUx6kojko6w2SoPvsepZnCbGlzx713nWYdX3IWppHdYAgODGKMDC/RF2fGGEVlMV4GKcphlL4nawJY52APMrZD2QrKRiiUi+H5nJktAhaGEDIBWzNJizcM3FeqSBpDrnnQOhwvH0zxojngyXtB/RYeUiDyEUEIJxmc9avZlMGREa8vNHbvAIfnjNSrEeWpd84wPd9JX9HJkHGexRARnWF8WT9a73JudKae8iEr62QhLlkJsadm8sOCoWECgQnVzIw2gCgRY41h5krwhExZzbIo61ODpByGDVXQ6wZ6DsrsURVjDlP1SqMoU/BcvYyQd7dWtFnGwyPP1E1OXrFQtmycSbde875SGOxkT9aWMNfmufbupK/HwzvH55nZz0YOuZgVLYkYpHBV2GpdzkHJR16WRtaa1vWcnHUl+R3W8LViGMpWeExhCdPMyNvxgAlHpHmegSRwBo0YMjLLhJJm08gazDtAdWTQhcRmFKGeAUrzPFePgbYTarfQIMcgPLPpY5eSx+2NDD+HYaYTegor8eaZMMrPPdipTJ3gGQdkplNvNjCsFaU7QudHexmhNOXrg882L/TFcuCyyy5rGzhmBYasb+q3/vTrCZS01gsU3IYTOXF8kRGn6J1ndnL7voJ81sN4LUnwBu79ULQd2T5d2TZi9NUmWZYwynN1SMKOLHmRf4hsXckE5Z6DhuiIfooyOCbj5J7zz5q1tucwY3LGDAiKwCgbYxPeEigBIzOD9MyKBpYRG5g6i5pVK1FWiuOaQUUGkrL53mM/SD5zBIxaWMQ7y48ogQ0XhsUB9EqOVz47qja1OBWfKZ6r515p5GtWgfQ4BE6EQ4K8QhK+ko2r87PCVYbvRA8ebVG+tiZEU556EXlaq0qvUK8+kQ/DIkvlIOnkbkcW/6iv0sxY2clNP8NvhvJuVd4KfBwvo7TLzTkYL2MonUGKGqSRBTIjClE5LOOTcdFP0UWMkczMkJyKkFX4b4ZcjPL2WDtjjoAFMUIDnhnUwBjAeErPsrgn9BAwZAPCqDOb5nNm28wqGbRclZc2VHgenqluaTPqnys3G1g95FVn+NIPCnnttdc2IzSDe0XAgJJHPxjdV33VV7XZWFqQ+tWn3vos6OutqH0dQXn48KMKz/ChyDL1uBqzOI7MfIwNJV0efJXSF8ZoLBHD45A4TVTHddTnBUdxXIYZZEDqoBpEBspYEY9rQJMnFBicSgbMgGYmRj4b7Ay4q8Ed8eYeRoM/6q60Pt8IPa/PZl7fJrHbag2ln4H69cOflfpltLS5x6Z1b8IrX9rgPp9zHzIG1QCRsUOM0Zi57/lQoH/6FGJ0DLGGqvqf5/34LJjGjgxzBEqQcCmDLVQV4phNXIVB8boxWNcokIGrg9mTdMbJO8dQ3cdbu0Ke4YGqFHPX3FeM0tTD8Vx66aXtZBCHpA8BHmFcb5gjkU+lJX107dPUHWOT5t5Y5FopskdV/rn3XBnaG5nnGvkLa/WPMSJGyDjJPVd5Fxw7TrhhjmCwq6G68sgMNWtOlLWm/LVZ/T1licIwDtdQFAiiRMmXzzW9TwuljjnCrx8OEVxxxRUtnNW3gPLaADr//PNX5513XuPR/k2JHDahGFI1Lvz1c39NHaBd9Qrpn4jFMoMRhhijq/5VQ4zcFuwcJ8UwIYpQiefuDTbESCl91jg1X5QQemWqyOcoGcp9fx09D2+976+U3FrTt0SQjSVplNX2v11bO7M2PfQZ6jX3UD+76mN/rTTKE0zdg8/6yJCqYaEYIsqzSkmLjEKQ64Kd46QZ5giqHhElyxqHYTLIhGD1noGG8jlXxhFS5m5B2RRSGOuguFcN2kCB7TrmEAJF3m1oRwwOJaxHo3tX1BteDFSeGF5PC3YXp9Qw56BZaVp/ZbgMLjOoa51ZQzFaeevMUmmUhgLPQ/mca+4hn2saVEWu13VpIYYWqp9zn/Ax6dXgGFcMrRod6o0u9eaa+wWnBnvWMEfom5rPrlP3ucZA62xbr/2zGCje/hoaPc89UO5qRLnmvlL/HGXWQwwpRlfv81lePKk313qfa+6D/vOCU499Y5iMxbtSL/LNBLbjUWaMddDNSiOjqs/CM7rC1LOaB2rbqlH06UGfpxpsno3S0H4DWXnFJPx3L/T3rnPTMT3IuMOtSvh/+0EI1pz+wuDyyy9vg+eFvR+usjuYmWLB/gJjdGTQ6yY79L4a56twdn0PvWHeKpzbuvgFCxacYqxW/w+E96sHTEx4cQAAAABJRU5ErkJggg==)
- 1.50 cm
- 1.64 cm
- 1.33 cm
- 1.86 cm
The correct answer is: 1.33 cm
Related Questions to study
A ray of light strikes a plane mirror M at an angle of 45° as shown in the figure. After reflection, the ray passes through a prism of refractive index 1.5 whose apex angle is 4°. The total angle through which the ray is deviated is
![](data:image/png;base64,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)
A ray of light strikes a plane mirror M at an angle of 45° as shown in the figure. After reflection, the ray passes through a prism of refractive index 1.5 whose apex angle is 4°. The total angle through which the ray is deviated is
![](data:image/png;base64,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)
A rod is fived between two points at 20° The Coefficient of linear expansion of material of rad is and Young's modulus is
. Find the stress developed in the rod if temperature of rod becomes 10°
A rod is fived between two points at 20° The Coefficient of linear expansion of material of rad is and Young's modulus is
. Find the stress developed in the rod if temperature of rod becomes 10°
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