Two identical thin plano-convex glass lenses (refractive index 1.5 ) are placed coaxially such that their convex surfaces are in contact at the centre. The radius of curvature of the convex surfaces is 20 cm . The intervening space between the lenses is filled with an oil of refractive index 1.6 . If the magnitude of the equivalent focal length of the combination is X cm , the value of X is

Step-by-step solution

The system can be considered as a combination of three thin lenses in contact: two plano-convex glass lenses and one biconcave liquid lens formed by the oil. For the first plano-convex lens (light entering the plane surface): R₁ = , R₂ = -20 cm Power P₁ = 1 f₁ = ( _g - 1) ( 1 R₁ - 1 R₂ ) = (1.5 - 1) ( 1 - 1 -20 ) = 0.5 1 20 = 1 40 cm ⁻¹ For the second plano-convex lens (light exiting the plane surface): R₁ = 20 cm , R₂ = Power P₃ = 1 f₃ = ( _g - 1) ( 1 R₁ - 1 R₂ ) = (1.5 - 1) ( 1 20 - 1 ) = 0.5 1 20 = 1 40 cm ⁻¹ Fo