Question

A symmetric biconvex lens of radius of curvature R and made of glass of refractive index 1.5, is placed on a layer of liquid placed on top of a plane mirror as shown in the figure. An optical needle with its tip on the principal axis of the lens is moved along the axis until its real, inverted image coincides with the needle itself. The distance of the needle from the lens is measured to be x. On removing the liquid layer and repeating the experiment, the distance is found to be y. Obtain the expression for the refractive index of the liquid in terms of x and y.

Answer 1

Given, Radius of curvature of the convex lens is R and μ=1.5

When lens is placed on a layer of water then focal length of the combination is f. Thus the first measurement gives the focal length of combinafioni.e. f =x.

In the second measurement, we get the focal length f₁ of convex lens i.e. f₁=y, therefore the focal length of Plano connex lens of water f₂ is given as

Now again for the plano-convex lens of air, if image coincide at 2f₁ then for case II we have

This is the required expression for the refractive index of the liquid.