A plano-convex lens of refractive index 1.5 and radius of curvature 30 cm is silvered at the curved surface. Now, the lens has been used to form the image of an object. What should be the distance of the object from the lense in order to have a real image of the 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`