A thin plano-convex lens fits exactly into a plano-concave lens with their plane surface parallel to each other as shown in the figure. The radius of curvature of the curved surface $ R=30 \mathrm{~cm} $. The lens is made of a different material having refractive index $ \mu_{1}=\frac{3}{2} $ and $ \mu_{2}=\frac{5}{4} $ as shown in the figure. If the plane surface of the plano-convex lens is silvered, then calculate the equivalent focal length of this system (in $ \mathrm{cm} $ ).

Question

A thin plano-convex lens fits exactly into a plano-concave lens with their plane surface parallel to each other as shown in the figure. The radius of curvature of the curved surface $ R=30 \mathrm{~cm} $. The lens is made of a different material having refractive index $ \mu_{1}=\frac{3}{2} $ and $ \mu_{2}=\frac{5}{4} $ as shown in the figure. If the plane surface of the plano-convex lens is silvered, then calculate the equivalent focal length of this system (in $ \mathrm{cm} $ ).,

MARKS App · Accepted Answer

(i) P eq = 2 P l 1 + 2 P l 2 + P m . . . 1 For plano-concave lens : 1 f l 1 = 3 2 - 1 1 ∞ - 1 3 0 f l 1 = - 60 cm ⇒ P l 1 = 1 0 0 f l 1 ⇒ P l 1 = - 5 3 D For plano-convex lens : ​ 1 f l 2 = 5 4 - 1 1 30 - 1 ∞ ⇒ 1 f l 2 = 1 120 f l 2 = + 1 2 0 cm ⇒ P l 2 = 100 f l 2 ⇒ P l 2 = + 5 6 D For plane mirror : P m = 0 since f m = ∞ Effective power of the combination is P eq = 2 P l 1 + 2 P l 2 + P m P eq = - 2 × 5 3 + 2 × 5 6 + 0 ⇒ P eq = - 10 6 D ∵ P eq = - 1 f eq ⇒ f e q = 60 cm

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