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.

Explanation

`F_(q) = x`
`F_("convex") = y`
`(1)/(F_(eq)) = (1)/(F_("convex")) + (1)/(F_("plance concave"))`
`(1)/(x) = (1)/(y) = (1)/(F_("Plance concave"))`
By using lens makers fromula,
`(1)/(F_(C.I)) = (mu -1) [(1)/(R_(1))-(1)/(R_(2))]`
`(1)/(y) = (1.5 - 1) [(1)/(R) + (1)/(R)] R_(1) = R_(2) = R`
`(1)/(y) = (0.5 xx 2)/(10 xx R)= R = y`
Again using lens makers formula for plane concave.
`(1)/(F) = (mu - 1) (1)/(cancly) = (( y-x)/(x)) + 1 = mu`
`mu = (x2x-y)/(x)`