Question

An object is placed 15 cm in front of a convex lens of focal length 10 cm. Find the nature and position of the image formed. Where should a concave mirror of radius of curvature 20 cm be placed so that the final image is formed at the position of the object itself?

Answer 1

Given that the object (OA) is placed at a distance 15 cm from lens.

i.e. u = -15 cm

Focal length of the lens. f =+ 10 cm

By lens formula we know that :

`1/"f" = 1/"v" - 1/"u"`

⇒ `1/"v" = 1/"f" + 1/"u"`

`1/"v" = 1/"10" - 1/"15"`

`1/"v" = (3 - 2)/30 = 1/30`

v = 30 cm

The image(I) gets formed at 30 cm to the right of the lens and it will be inverted.

The rays from the image(I) formed further falls on the mirror and forms another image(I').This image should be formed in such a way that the rays from I' on refraction from the lens should form an image(I'') at the same point O.

For the image(I'') to be formed at O, the rays incident on the mirror should form the image(I') at centre of curvature of the mirror. This happens only if the image formed by the lens(I) lies at the centre of curvature of the mirror.

Hence d, the distance between the lens and the mirror will be:

d = image distance(v) + radius of curvature of the lens(R)

v = 30 cm, R =20 cm

The image formed at the point O (O I'') will be inverted.