An object is placed 40 cm from a convex lens of focal length 30 cm. If a concave lens of focal length 50 cm is introduced between the convex lens and the image formed such that it is 20 cm from the convex lens, find the change in the position of the image.

Explanation

Given data: For the convex lens,` f_10 = +30 cm` and
Object distance `u_1` = -40 cm, therefore,
Formula : `(1)/(f_1) = (1)/(v_1) - (1)/(u_1)`
` (1)/(+30) = (1)/(v_1) - (1)/(-40)`
` (1)/(v_1) = 1/30 -1/40 = 1/120`
` rArr v_1 = + 120 cm`
a real image is formed.
On introducing a concave lens,
` f_2 = -50cm`
and ` u_2 = 120 - 20 = + 100 cm` from the concave lens
` (1)/(f_2) = (1)//(v_2) - (1)/(u_2)`
`(1)/(-50) = (1)/(v_2) - (1)/(+ 100)`
` therefore (1)/(v_2) = 1/50 + 1/100 = - 1/100`
` v_2 = -100 cm`