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

`(1)/(F)=(1)/(f_l)+(1)/(f_m)+(1)/(f_l)`
`=(2)/(f_l)+(1)/(f_m)=2((3)/(2)-1)((1)/(infty)-(1)/(-30))+(1)/((30)/(2))`
`=(1)/(10)`
`F=10cm`
The silvered lens behaves as concave mirror of focal length 10 cm.
If object and image coincide, object should be placed at centre of curvature of mirror.
`u=2F=2xx10=20cm`.