Question

A tank is filled with water to a height of 12.5 cm. The apparent depth of a needle lying at the bottom of the tank is measured by a microscope to be 9.4 cm. What is the refractive index of water?​

Answer 1

Given :

Real depth tank = 12.5 cm

Apparent depth of needle = 9.4 cm

To Find :

Refractive index of water.

Solution :

At near normal incidence (small angle of incidence i) apparent depth (d') is given by

• d' = d / μ

» d = distance of object from the interface or real depth

» d' = distance of image from the interface = apparent depth

» μ denotes refractive index of medium with respect to air$.$

This formula can be easily derived using snell's law and applying the condition of nearly normal incidence.

By substituting the given values;

➙ d' = d / μ

➙ 9.4 = 12.5 / μ

➙ μ = 12.5/9.4

➙ μ = 1.33