Question

An equiconvex lens, of focal length 20 cm, is made of glass (μ = 1.5). The lens is placed so that its one surface is in contact with air and its other, with a transparent medium, of refractive index 1.3. A parallel beam is incident on the lens from the air side. The emergent beam, would then meets the principle axis, at a distance x from lens, where x is

(1) 14.3 cm

(2) 18.6 cm

(3) 20.0 cm

(4) 30.0 cm

Answer 1

(2) 18.6 cm

Let c be the radius of curvature of each surface of the lens. From lens maker’s formula, we have

Fig. shows lens placed with its second surface in contact with the medium of refractive index, μ₃ = 1.3.

Consider the refraction at the first surface of the lens.

Had there been only this refracting surface, the refracted raywould have meet the principal axis at P. For the second surface of the lens, P acts as a virtual object; which forms the final image at F. Now