Question

Fig. shows a thin lens for which the radii of curvature of two surfaces are equal. Also μ₁ = 1.2; μ₂ = 1.5, μ₃ = 1.7. A parallel beam of light, incident in μ₁ , is bright to focus, in medium μ₃ , at a distance of 34 cm from the lens. The radius of curvature of the surfaces of lens is

(1) 10 cm

(2) 12 cm

(3) 11.33 cm

(4) 15 cm

Answer 1

(1) 10 cm

Let c be the magnitude of the radius of each surface of lens. Had there been only one surface; the incident parallel beam, after refraction would have met the principal axis at Q₁ , at a distance b₁ from this surface.

Form refraction at first surface of lens we have

For refraction at second surface, Q₁ acts as a virtual object, forming the real image at F. Therefore,

u₂ = +b₁ ; v₂ = +34 cm; R₂ = +c

From refraction formula; we now get