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Question

# A ray of light is incident on the face AB of a glass prism ABC having the vertex angle A equal to 30∘. The face AC is silvered and a ray of light incident on the face AB retraces its path. If the refractive index of the material of prism is √3, the angle of incidence on the face AB is :

A
60
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B
30
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C
45
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D
90
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Solution

## The correct option is A 60∘Now look at the diagram carefully. 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=30O∙ μ=√3To find: i= ?Solution:–––––––––––Look at the triangle △APQ. In any triangle, the sum of all angles is always 180OSince ray PQ is perpendicular to AC, ∠AQP=90OIn △APQ, ∠APQ + ∠A + ∠AQP =180∴∠APQ = 180−∠A − ∠AQP ∴∠APQ=180−30−90=60SInce line PR is a normal, ∠APR=90By angle addition property, ∠APR=∠APQ+∠r∴∠r=∠APR−∠APQ=90−60=30By Snell's law, sinisinr=μ∴sinisin30=√3∴sini(12)=√31 ∵ sin30=12∴(sini)÷(12)=(2×sini)=√31∴sini=√32∴i=sin−1(√32)=60Answer–––––––––: The angle of incidence on the face AB is 60O

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