# 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 from each other. 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.

#### Lens formula for convex lens,1v−1u=1f

1v−1−60=120

v=30 cm

Image (I1) formed by the convex lens acts as an object for the convex mirror.

Since the mirror and lens are separated by 15 cm, distance between I1 and mirror is 15 cm.

i.e. u=15

For convex mirror,

f=R2=10 cm

From mirror equation,

1v2+1u2=1f2

1v2+115=110

v2=30 cm

Hence, image is formed 30 cm right of the convex mirror.

From the ray diagram, it can be observed that the image is virtual.