# Lens in the Water

## Objective

To study the effect of water surrounding the lens.

## Introduction

The focal length of a lens depends on the curvature of the two lens surfaces and on the refractive indices of the lens and surrounding medium. The equation for focal length of a lens is given by lens maker's formula,

\begin{align} \frac{1}{f}=\left(\frac{\mu_2}{\mu_1}-1\right)\left[\frac{1}{R_1}-\frac{1}{R_2}\right]\nonumber \end{align}where \(\mu_2\) and \(\mu_1\) are refractive indices of the lens and surrounding medium, respectively. Thus, if the lens is kept inside water instead of air, its focal length will increase.

## Apparatus

two laser torch, a long trough, convex lens of focal length about 10 cm or less.

## Procedure

Take a convex lens and measure its focal length (approximately) by imaging distant object on the wall or a paper. Choose a lens of short focal length, preferable 10 cm or less. Put water in a long trough made of transparent plastic box and put a few drops of soap solution in it. Take two laser torches and fix them on same base, parallel to each other. Position the laser base so that light may go in water along the length of the trough. Switch on both the lasers. The laser beams will go in the water. The beams will be clearly visible from the top. The beams are quite narrow and you can treat each of these as ray of light.

Put the convex lens inside the water so that the axis is parallel to the beams of light. You can ask audiences to hold the lens from the top, so that it stays there. The two beams will bend towards each other and will intersect. Ask a volunteer from the audience to measure the distance of the lens from the place where the two beams intersect.

## Discussion

Measured distance is focal length of the lens in water. Check that the focal length in water is much more than the focal length in air.