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 cm . The lens is made of a different material having refractive index μ 1 = 3 2 and μ 2 = 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 sys

Step-by-step solution

(i) P eq = 2 P ℓ1 + 2 P​ ℓ2 + P m ...(1) For plano-convex lens : 1 f ℓ 1 = 3 2 - 1 1 ∞ - 1 3 0 f ℓ 1 = - 6 0 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 = ∞ ⇒ P eq = 2 P ℓ 1 + 2 P ℓ 2 + P m P eq = - 1 0