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.

A synunetdc bionvex fens of radius of curvature Rand made of glass of refractive index 1.5, is placed on a placed on top of a plane mirror as shown in the figure.An optical needle with with its tip on the principal axis of the lens is moved along the axis until its real, inverted images conicides with the needle itself. The distance from the lens in 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.

An equiconvex lens with radii of curvature of magnitude R each is put over a liquid layer poured on top of a plane mirror. A small needle, with its tip on the principal axis of the lens, is moved along the axis until its inverted real image coincides with the needle itself. The distance of the needle from the lens is measured to be 'a'. On removing the liquid layer and repeating the experiment the distance is found to be 'b'. Given that the two values of distances measured represent the focal length values in the two cases, obtain a formula for the refractive index of the liquid.

Fig. shows an equiconvex lens (of refractive index 1.5 ) in contact with a liquid layer on top of a plane mirror. A small needle with its tip on the principal axis is moved along the axis until its inverted image is found at the position of the needle. The distance of the needle from the lens is measured to be 45.0 cm . The liquid is removed and the experiment is repeated. The new distance is measured to be 30.0 cm . What is the refractive index of the liquid ?