Question

Find the focal length of equivalent mirror if concave surface of a plano concave lens is silvered. Radius of curvature of concave surface is R and refractive index of material of prism is `mu`.

Answer 1

`(1)/(f_(r)) = (mu - 1) ((1)/(oo) - (1)/(R)) = (mu - 1) ((1)/(R))`
`(1)/(f_(m)) = - (2)/(R)`
So, focal length of equivalent mirror (F) is
`(1)/(F) = (-2)/(f_(t)) + (1)/(f_(m))`
`= (2(1-mu))/(R).(-2)/(R)`
`= (-2mu)/(R)`
`rArr F = (-R)/(2 mu)`
System behaves as a converging (concave) mirror.