Question

A point object is placed at a distance of 20 cm from a thin plano-convex lens of focal length 15 cm. If the plane surface is silvered. The image will be formed at

Answer 1

60 cm from the lens on the right side

Answer 2

The plano-convex lens with its plane surface silvered acts as a combination of a lens and a mirror. First, consider refraction by the convex lens. The object distance $u = -20$ cm and lens focal length $f_l = 15$ cm. Using the lens formula $\frac{1}{v_1} - \frac{1}{u} = \frac{1}{f_l}$: $\frac{1}{v_1} - \frac{1}{-20} = \frac{1}{15}$ $\frac{1}{v_1} = \frac{1}{15} - \frac{1}{20} = \frac{4-3}{60} = \frac{1}{60}$ So, $v_1 = 60$ cm. This is the position of the intermediate image formed by the lens. This intermediate image acts as the object for the silvered plane surface, which acts as a plane mirror. The distance of this object from the plane mirror is 60 cm. For a plane mirror, the image is formed at the same distance behind the mirror as the object is in front. Therefore, the final image is formed 60 cm behind the plane mirror, which is 60 cm from the lens on the right side.