Angle of prism is `A` and its one surface is silvered. Light rays falling at an angle of incidence `2 A` on first surface return back through the same path after suffering reflection at second silvered surface. Refraction index of the material of prism is

Options

A. `2 sin A`
B. `2cos A`
C. `(1)/(2) cos A`
D. tan A

Answer

B

Explanation

For the condition giving in equesiton, ray diagram will be,

From the ray diagram,
`ltMON=90^(@)-A`
So, `lt Rr=90^(@)-(90^(@)-A) Rightarrow gt r=A`
By Snell's law, `(sin i)/(sin r)=mu Rightarrow (sin(2A))/(sin(A))=mu`
`(2sinA cos A)/sinA=mu Rightarrow mu=2 cos A`