The angle of a prism is A . One of its refracting surfaces is silvered. Light rays falling at an angle of incidence 2A on the first surface returns back through the same path after suffering reflection at the silvered surface. The refractive index μ , of the prism is :-

Question

The angle of a prism is A . One of its refracting surfaces is silvered. Light rays falling at an angle of incidence 2A on the first surface returns back through the same path after suffering reflection at the silvered surface. The refractive index μ , of the prism is :- (A) 2sinA (B) 2cosA (C) (1/2)cosA (D) tanA

Tardigrade Admin · Accepted Answer

<img class="img-fluid question-image" alt="Solution" src="https://cdn.tardigrade.in/q/nta/p-wjgewpxeatcpd5vp.jpg" /> μ =(sin 2 A/sin A)=(2 sin A cos A/sin A),μ =2cosA.

Q. The angle of a prism is $A$ . One of its refracting surfaces is silvered. Light rays falling at an angle of incidence $2 A$ on the first surface returns back through the same path after suffering reflection at the silvered surface. The refractive index $μ$ , of the prism is :-

$2 s in A$

$2 cos A$

$\frac{1}{2} cos A$

$t an A$

$μ = \frac{s in 2 A}{s in A} = \frac{2 s in A cos A}{s in A}, μ = 2 cos A .$

Q. The angle of a prism is A . One of its refracting surfaces is silvered. Light rays falling at an angle of incidence 2A on the first surface returns back through the same path after suffering reflection at the silvered surface. The refractive index μ , of the prism is :-

2sinA

2cosA

21​cosA

tanA