A thin biconvex lens of refractive index 3 2 is placed on a horizontal plane mirror as shown in the figure. The space between the lens and the mirror is then filled with water of refractive index 4 3 . It is found that when a point object is placed 15 cm above the lens on its principal axis, the object coincides with its own image. On repeating with another liquid, the object and the image again coincide at a distanc

Step-by-step solution

Let R be the radius of curvature of both the surfaces of the equiconvex lens. In the first case Let f 1 be the focal length of planoconcave lens of index μ 1 . The focal length of the combined lens system will be given by 1 F = 1 f 1 + 1 f 2 = μ 1 - 1 1 R - 1 - R + μ 2 - 1 1 - R - 1 ∞ = 3 2 - 1 2 R + 4 3 - 1 - 1 R = 1 R - 1 3 R = 2 3 R or   F = 3 R 2 Now, image coincides with the object when ray of light retraces its path or it falls normally on the plane mirror. This is possible only when