. Figure A shows two identical plano-convex lenses in contact as shown. The combination has focal length 24 cm. Figure B shows the same with a liquid introduced between them. If refractive index of glass of the lenses is 1.50 and that of the liquid is 1.60 , the focal length of the system figure B will be

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Two identical plano-convex lenses in contact give 24 cm, so each has f = 48 cm: 48 1 ​ = ( 1.5 − 1 ) R 1 ​ ⇒ R = 24 cm . The liquid (μ = 1.6) trapped between the curved faces is a biconcave lens: f l ​ 1 ​ = ( 1.6 − 1 ) ( − 24 2 ​ ) = − 20 1 ​ . Combination: F 1 ​ = 24 1 ​ − 20 1 ​ = − 120 1 ​ ⇒ F = − 120 cm . Hence (A).

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