A plano convex lens of refractive index 1.5 and radius of curvature 30cm. Is silvered at the curved surface. Now this lens has been used to form the image of an object. At what distance from this lens an object be placed in order to have a real image of size of the object.

Options

A. 20 cm
B. 30 cm
C. 60 cm
D. 80 cm

Answer

A

Explanation

A silvered lens behaves as a mirror . For the image to be of same size as of object must the object be held at the centre of curvature of mirror when
`(1)/(f_("silvered lens")) = (1)/(f_(1)) + (1)/(f_(m)) + (1)/(f_(1)) = (2)/(f_(1)) + (1)/(f_(m))`
`(1)/(f_(1)) = (mu-1)/(R) , (1)/(f_(m)) = (2)/(R) implies f = (R)/(2mu)`
Therefore `(1)/(f) = (2(mu-1))/(R) + (2)/(R) = (2mu)/(R)`
The radius of curvature of this mirror
= `2f = (R)/(mu) = (30)/(1.5) = 20 cm`