Two identical thin plano-convex glass lenses (refractive index 1 . 5 ) each having radius of curvature of 20 cm are placed with their convex surfaces in contact at the centre. The intervening space is

Question

Two identical thin plano-convex glass lenses (refractive index 1 . 5 ) each having radius of curvature of 20 cm are placed with their convex surfaces in contact at the centre. The intervening space is filled with the oil of refractive index 1 . 7 . The focal length of the combination is:

TestHub · Accepted Answer

Consider the situation shown in figure. As 1 f = 1.5 - 1 1 R - 1 ∞ ⇒ 1 f = 0.5 R ⇒ 1 f c o n c a v e = 1.7 - 1 - 2 R ⇒ 1 f c o n c a v e = 0.7 × 2 R = - 1.4 R ∴ 1 f e q = 0.5 R - 1.4 R + 0.5 R Also, = - 0.4 R = - 0.4 20 ⇒ f e q = - 50 cm

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