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Question: Angle of a prism is 30<sup>0</sup> and its refractive index is \(\sqrt { 2 }\) and one of the surfac...

Angle of a prism is 300 and its refractive index is 2\sqrt { 2 } and one of the surface is silvered. At what angle of incidence, a ray should be incident on one surface so that after reflection from the silvered surface, it retraces its path

A

300

B

600

C

450

D

sin⁡−11.5\sin ^ { - 1 } \sqrt { 1.5 }

Answer

450

Explanation

Solution

This is the case when light ray is falling normally an second surface.

Hence by using μ=sin⁡isin⁡A\mu = \frac { \sin i } { \sin A }

⇒\Rightarrow 2=sin⁡isin⁡30∘⇒sin⁡i=2×12⇒i=45∘\sqrt { 2 } = \frac { \sin i } { \sin 30 ^ { \circ } } \Rightarrow \sin i = \sqrt { 2 } \times \frac { 1 } { 2 } \Rightarrow i = 45 ^ { \circ }