# Verification of the Lens Formula Using Convex Lens

## Introduction

The object distance \(u\), image distance \(v\), and the focal length \(f\) of the lens are related by,

\begin{align} \frac{1}{v}-\frac{1}{u}=\frac{1}{f}. \nonumber \end{align}The pole of the lens is taken as the origin and principal axis as the \(X\)-axis. Usually, the positive of the axis is taken along the incident rays. The distance between the pole and the object (candle) is \(u\) and the distance between the pole and the image (screen) is \(v\). Note that \(u\) is negative and \(v\) is positive in present case.

## Apparatus

A convex lens, V-stand, screen, screen-stand, candle, matchbox, scale.

## Procedure

- Firstly, find the approximate focal length \((f)\) of the convex lens. Then fix it vertically on a V-stand. Draw a long straight line on a table and place the lens in the middle. The pole of the lens should be exactly above the line.
- Light a candle and place it on one end of the line. The flame of the candle should be at the same height as the pole of the lens.
- Fix the screen on its stand. The screen should be vertical. Place the screen on other side of the lens.
- Analyse the nature of the image by moving the screen and/or lens.
- For three different values of \(u\), find the value of \(v\). Calculate \(f\) by substituting in formula given above.

## Discussion

Write the results in the form of a table.