The angle of a prism is A- One of its refracting surfaces is silvered- Light rays falling an angle of incidence 2A on the first surface returns back through the same path after suffering reflection the silvered surface-The refractive index mu- of the prism is -2 sin Adfrac -1-2- cos A2 cos Atan A

Question

Toppr Admin · Accepted Answer

To retrace its path light rays should fall normally on the reflecting surface. So
$r_{2} = 0$

$\Rightarrow r_{1} = A - r_{2} \Rightarrow r_{1} = A$

Now applying snell rule between incident ray and refracted ray.

$(1) s i n (2 A) = n s i n (A) \Rightarrow 2 s i n A c o s A = n s i n A$

$\Rightarrow n = 2 c o s A$

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 :2sinA12cosA2cosAtanA

To retrace its path light rays should fall normally on the reflecting surface. Sor2=0⇒r1=A−r2⇒r1=ANow applying snell rule between incident ray and refracted ray.(1)sin(2A)=nsin(A)⇒2sinAcosA=nsinA⇒n=2cosA