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What is the required condition, if the light incident on one face, does not emerge from the other face ? |
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Answer» Solution :For no EMERGENCE, `r_(2)gttheta_(c)` `A-r_(1)gttheta_(c)` `sin(A-r_(1))gtsintheta_(c)` `sinAcosr_(1)-cosAsinr_(1)gt(1)/(mu)` `SINA[cosr_(1)]-cosA[(sini)/(mu)]gt(1)/(mu)` `impliesmusinAsqrt(1-sin^(2)r_(1))-cosAsinigt1` `impliesmusinAsqrt((1-(sin^(2)i)/(mu^(2))))gt1+COS Asini` `impliessinA*SQRT(mu^(2)-sin^(2))igt(1+cosAsini)` Squaring both sides, `sin^(2)A(mu^(2)-sin^(2)i)gt(1+cosAsini)^(2)` `mu^(2)sin^(2)A-sin^(2)Asin^(2)igt1+cos^(2)Asin^(2)i+2cosAsini` `mu^(2)sin^(2)Agt1+(cos^(2)A+sin^(2)A)sin^(2)i+2cosAsini` `mu^(2)sin^(2)Agt1+sin^(2)i+2cosAsini` The greatest value of sin `i=1` `impliesmu^(2)sin^(2)Agt1+1+2cosA` `mu^(2)(2^(2)sin^(2).(A)/(2)cos^(2).(A)/(2))gt2(1+cosA)` `4mu^(2)sin^(2).(A)/(2)cos^(2).(A)/(2)gt4cos^(2).(A)/(2)impliesmu^(2)gt(1)/(sin^(2).(A)/(2))` `mugtcosec((A)/(2))` . 
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