The angle of a prism is A . One of its refracting surfaces is silvered. Lihgt 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. `mu`, of the prism is

Options

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

Answer

B

Explanation

`therefore 90^(@)-A+r=90^(@) rArr r=A`
From snell.s law
`(sini)/(sinr)=mu`
`(sin2A)/(sinA)=mu`
`(2sinAcosA)/(sinA)=mu`
`2cos A=mu`