Question

The size of the image of an object; (which is at infinity) as formed by a convex lens, of focal length 30 cm, is 2 cm. If a concave lens, of focal length 20 cm, is placed between the convex lens and the image, at a distance of 26 cm from the convex lens, the new size of the image would be

(1) 1.05 cm

(2) 1.25 cm

(3) 2.0 cm

(4) 2.5 cm

Answer 1

(4) 2.5 cm

Fig (a) shows the image P₁Q₁ , being formed due to the convex lens alone. The image is formed in the focal plane of L₁ . Fig (b) shows the concave lens, L₂ , placed between L₁ and image P₁Q₁ . For the concave, P₁Q₁ , acts as a virtual object. For concave lens

u = + 4 cm; f = - 20 cm, v = ?

From refraction formula

m = magnification due to concave lens = v/u = 5/4 = 1.25

∴ The size of final image = |m| x P₁Q₁

= 1.25 x 2 cm = 2.5 cm