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. 

For convex lens,

Focal length, f = + 20 cm

Object distance, u = - 60 cm

Now, using the lens formula, we have

 

Putting in the values, we get

Image distance, v = + 30 cm 

Now, for convex mirror

Object distance, u = + (30- 15) cm = 15 cm

Focal length, f = + 20/2 cm = +10 cm

Object distance, u = + (30- 15) cm = 15 cm

Focal length, f = + 20/2 cm = +10 cm

Now, using the mirror formula we have

Putting all the values, we get

Image distance, v = + 30 cm

Therefore, the final image is formed at a distance of 30 cm from the convex mirror or at a distance of 45 cm from the convex lens to the right of the convex mirror.

Therefore, the final image formed is a virtual image.

Ray diagram for the image formation is given below: