# Attenuation of radiation

##### Class practical

This activity provides a good introduction to exponential decay.

#### Apparatus and materials

Jelly 'fibre' approx 22 cm long

DC voltmeter, 2 V full scale deflection

DC power supply, 4.5 V or 5 V

Knife (plastic type will be safer)

Graph paper, laminated if possible

#### Health & Safety and Technical notes

Read our standard health & safety guidance

For construction details see apparatus entries.

#### Procedure

**a** Place the jelly fibre on the graph paper.

**b** Place the transmitter and receiver at opposite ends, making sure that the diode and receiver are in good contact with the jelly and that they are aligned.

**c** Adjust the pre-set potentiometer so that, with a length of about 22 cm of 'fibre', the output voltage is about 0.1 V.

**d** Cut about 1 cm from the fibre.

**e** Without readjusting the potentiometer, move the transmitter and receiver so that they are again in good contact with the jelly. Record the output voltage.

**f** Repeat and collect a set of readings showing how output voltage, *V*, varies with length, *x*, of fibre.

Display the results on (a) a linear graph of *V* against *x* and (b) a graph of ln(*V*) against *x*.

Discuss whether the graphs show exponential attenuation (they should!).

Use the graphs to obtain a value for the attenuation coefficient.

#### Teaching notes

**1** Unlike the more traditional examples of capacitor discharge and radioactive decay, here students can easily obtain their own data and 'see' the decay occurring without needing either to keep track of a rapidly-occurring process or to deal with background noise and random fluctuations.

The activity models the attenuation of signals along an optical fibre (or, indeed, through any absorptive medium). In a real fibre, many kilometres of fibre are needed to produce appreciable attenuation.

In this example, absorption is mainly by water molecules, which are good absorbers of infra-red. The purpose of the gelatine is merely to enable the water to 'stand up'.

**2** To a very good approximation, the attenuation is indeed exponential and is described by

*V* = *V*_{0} exp ( *-m**x*) where *m* is the attenuation coefficient.

A graph of *V* against *x* shows the characteristic shape associated with exponential decay, including a well-defined 'half length' over which the output voltage halves.

ln(*V*) = ln(*V*_{0}) *-m**x*

A graph of ln(*V*) against *x* is a straight line with gradient *-m*.

*This experiment comes from Salters Horners Advanced Physics©, University of York Science Education Group.
Diagrams are reproduced by permission of the copyright holders, Heinemann.*

*This experiment was safety-checked in December 2004*