A thin equiconvex glass lens of refractive index 1.5 and radius of curvature 20 cm for both surfaces is placed horizontally on a plane glass slab. A few drops of an unknown liquid are squeezed between the lens and the slab, forming a plano-concave liquid lens. If the equivalent focal length of this combination is 30 cm , what is the refractive index of the liquid?

Step-by-step solution

The focal length f_g of the equiconvex glass lens is calculated using the lens maker's formula: 1 f_g = ( _g - 1) ( 1 R₁ - 1 R₂ ) 1 f_g = (1.5 - 1) ( 1 20 - 1 -20 ) = 0.5 2 20 = 1 20 cm ⁻¹ The liquid forms a plano-concave lens. For light travelling downwards, its upper surface matches the lower surface of the glass lens ( R₁ = -20 cm ) and its lower surface is plane ( R₂ = ). The focal length f_l of the liquid lens is: 1 f_l = ( _l - 1) ( 1 -20 - 1 ) = - _l - 1 20 The equivalent focal length of the combination is F