# Study the magnification by a convex lens as a function of object-distance \(u\)

## Introduction

The magnification by a convex lens is given by \(m=v/u\) where \(u\) is the object distance and \(v\) is the image distance. The relation between \(v\) and \(u\) itself is given by \(\frac{1}{v}-\frac{1}{u}=\frac{1}{f}\) or \(\frac{1}{|v|}+\frac{1}{|u|}=\frac{1}{f}\). You can work out the expected relation between \(m\) and \(u\) (in terms of \(f\)). It will be \(m=\frac{f}{f-|u|}\). You can also write \(\frac{1}{m}=1-\frac{|u|}{f}\) or \(|u|=f(1-\frac{1}{m})\).

In this experiment you will experimentally measure the magnification for several values of u and see if it is consistent with the equation.

## Apparatus

A LED bulb with bulbâ€“holder, a convex lens in its stand, a white movable screen, scale, measuring tape

## Procedure

- Measure the diameter of the bulb given.
- Paste the measuring tape on the table.
- Arrange the bulb, lens and screen on the table so that the edges of their stands are along the edge of the tape and you can measure the positions of these on the tape.
- Keep the lens at a distance of about 25 cm from the bulb. Put the bulb on. Adjust the position of the screen to get the most clear image of the bulb. LED bulb given to you has a hemi-spherical outer cover which glows. The image on the screen will be like a semi circular disk. The diameter of this disk will correspond to the semicircular periphery of the bulb. The ratio of the diameter of this image and that of the bulb gives the magnification m.
- Measure the diameter \(D\) of the image and the object distance \(|u|\) and enter in the table.
- Change \(u\) by 3-4 cm and repeat 6-7 times.
- Draw graphs of \(m\) versus \(|u|\) and of \(|u|\) versus \(\frac{1}{m}\).
- Question: Can you obtain from these graphs? Suggest the process.

\(u\) | \(D\) | \(m=D/d\) | \(1/m\) |
---|---|---|---|

## Note

Table to be made