A convex lens and convex mirror are placed co axially and separated by distance d. The focal length of both is 20cm each. A point object is placed at a distance 30cm from the lens. Then the value of d so that image on the object itself is

 Given parameters are

The focal length of the convex lens is f1=20cm.

The focal length of the convex mirror is, f2=20cm

The distance of the image placed from the image is, u1=30cm

At convex lens; 1/f1 = 1/v1 + 1/u1

Substituting the value of focal length and the object distance from the lens 1/20=1/di + 1/30

1/20 − 1/30 = 1/di

Where, di denotes the distance of the image at convex lens.

1/di = 1/60

At convex mirror:

1/f2 = 1/di + 1/uo

Substitutes the values of the focal length and the image distance;

1/20 = 1/60 + 1/do

1/20 − 1/60 = 1/do

Where do denote the distance of the object to the convex mirror.

1/do = 1/30

The distance of the value d; 1/d = 1/f

That is 1/d = 1/f =1/di + 1/do

1/d = 1/60 + 1/30

1/d = 90/1800

d=20cm

Therefore, the value of the d is 20 cm.