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Question: A prism ABC of angle 30<sup>0</sup> has its face AC silvered. A ray of light incident at an angle of...

A prism ABC of angle 300 has its face AC silvered. A ray of light incident at an angle of 450 at the face AB retraces its path after refraction at face AB and reflection at face AC. The refractive index of the material of the prism is –

A

1.5

B

32\frac { 3 } { \sqrt { 2 } }

C

2\sqrt { 2 }

D

43\frac { 4 } { 3 }

Answer

2\sqrt { 2 }

Explanation

Solution

For 2nd surface

C = 0 ̃ r2 = 0

r1 + r2 = A

r1 = 300

m = sin⁡isin⁡r1=sin⁡45∘sin⁡30∘\frac { \sin \mathrm { i } } { \sin \mathrm { r } _ { 1 } } = \frac { \sin 45 ^ { \circ } } { \sin 30 ^ { \circ } }

μ=2\mu = \sqrt { 2 }