Question

A convex lens of focal length 20cm is placed coaxially with a concave mirror of focal length 10cm at a distance of 50cm apart from each other. A beam of light coming parallel to the principal axis is incident on the convex lens. Find the position of final image formed by this combination. Draw the ray diagram showing the formation of image.

Answer 1

Since rays are coming from infinity,

For first image,

1/v = 1/u + 1/f

f = 20 cm

u> 2f therefore, infinity

1/v = 1/20

v = 20 cm

For second image mirror is placed.

it can be 1/u + 1/v = 1/f

u = -30 cm = infinity since greater than 2f.

f = -10 cm

Therefore, 1/v = 1/-10 + 1/30

v =-15 cm from the mirror

Again, applying the lens formula for the lens,

1/v-1/u = 1/f

u = -35 cm

f = 20 cm

1/v-1/-35 = 1/20

v= 46.6 cm to the left of the len