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A biconvex lens of refractive index 1.5 has radii of curvature 20 cm for both of its surfaces. It is completely immersed in a liquid of refractive index 1.25 . A plane mirror is placed behind the lens. A point object is placed on the principal axis in front of the lens such that its final image coincides with the object itself, irrespective of the distance between the lens and the mirror. The distance of the object f

Correct answer

50

Step-by-step solution

Using the Lens Maker's formula for the lens immersed in the liquid: 1 f_l = ( _g _l - 1 ) ( 1 R₁ - 1 R₂ ) Given _g = 1.5 , _l = 1.25 , R₁ = 20 cm , and R₂ = -20 cm (for a biconvex lens): 1 f_l = ( 1.5 1.25 - 1 ) ( 1 20 - 1 -20 ) 1 f_l = (1.2 - 1) ( 2 20 ) = 0.2 1 10 = 1 50 f_l = 50 cm For the final image to coincide with the object irrespective of the plane mirror's position, the light rays emerging from the lens must be parallel to the principal axis. This ensures they strike the plane mirror normally and retrace

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