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Updated on : 2022-09-05

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Correct option is A)

Face AC is silvered means the light ray, falling on it will get reflected.

The ray re-traces its path means, it is moving backward along the same path through which it entered.

This is possible only if the ray is falling on AC perpendicularly.

$Given: $

$∙$ $∠A=30_{_{O}}$

$∙$ $μ=3 $

$To$ $find:$ $i=$ $?$

$Solution: $

Look at the triangle $△APQ.$

In any triangle, the sum of all angles is always $180_{_{O}}$

Since ray PQ is perpendicular to AC, $∠AQP=90_{_{O}}$

In $△APQ,$ $∠APQ$ $+$ $∠A$ $+$ $∠AQP$ $=180$

$∴∠APQ$ $=$ $180−∠A$ $−$ $∠AQP$

$∴∠APQ=180−30−90=60$

SInce line $PR$ is a normal, $∠APR=90$

By angle addition property, $∠APR=∠APQ+∠r$

$∴∠r=∠APR−∠APQ=90−60=30$

By Snell's law, $sinrsini =μ$

$∴sin30sini =3 $

$∴(21 )sini =13 $ $∵$ $sin30=21 $

$∴(sini)÷(21 )=(2×sini)=13 $

$∴sini=23 $

$∴i=sin_{−1}(23 )=60$

$Answer :$ The angle of incidence on the face AB is $60_{_{O}}$

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