Question

A plano-convex lens is made of glass with a refractive index of 1.5. The radius of curvature of the convex surface is 25 cm.

1. Calculate the focal length of the lens.
2. If an object is placed 50 cm in front of the lens, find the nature and position of the image formed.

Answer 1

(i) Refractive index = µ = 1.5

Radius of curvature of convex side = 25 cm = `25/100 "m"`

Radius of curvature of plane side = ∞

Applying the lens maker's formula,

`1/"f" = (µ - 1) (1/"R"_1 - 1/"R"_2)`

Or, `1/"f" = (1.5 - 1) (1/∞ + 100/25)`

Or, `1/"f" = 0.5 xx (100/25)`

∴ f = `25/50 "m"` = 50 cm

(ii) Focal length = f = 50 cm

Object distance = u = − 50 cm

When the object distance = focal length, then the image will be formed at infinity.

The image will be highly magnified, real and inverted.