Question

A convex lens of focal length 20 cm is placed coaxially with a convex mirror of radius of curvature 20 cm. The two are kept at 15 cm apart. A point object lies 60 cm in front of the convex lens. Draw a ray diagram to show the formation of the image by the combination. Determine the nature and position of the image formed

Answer 1

Let us first locate the image of the point object S formed by the convex lens.

Here:
u = -60 cm

and f = 20 cm

From the lens formula, we have:

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

`=>1/v=1/f+1/u`

`=>1/v=1/20+1/((-60))`

 `=>1/v=(3-1)/60=2/60`

 ⇒ v = 30 cm

The positive sign shows that the image is formed to the right of the lens, as shown in the following figure.

The image I₁ is formed behind the mirror and hence, acts as a virtual source for the mirror. The convex mirror forms the image I₂, whose distance from the mirror can be calculated as:

`1/v+1/u=1/f`

Here:

u = 15 cm

And 

`f=R/2=10 cm`

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

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

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

⇒ v = 30 cm

Hence, the final virtual image is formed at a distance of 30 cm from the convex mirror, as shown in the figure below.