Attenuation of radiation
Practical Activity for 14-16
This activity provides a good introduction to exponential decay.
Apparatus and Materials
- 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
For construction details see apparatus entries.
- Place the jelly fibre on the graph paper.
- 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.
- Adjust the pre-set potentiometer so that, with a length of about 22 cm of 'fibre', the output voltage is about 0.1 V.
- Cut about 1 cm from the fibre.
- Without readjusting the potentiometer, move the transmitter and receiver so that they are again in good contact with the jelly. Record the output voltage.
- 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.
- Unlike the more traditional examples of capacitor discharge and radioactive decay, here students can easily obtain their own data and
seethe 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
- To a very good approximation, the attenuation is indeed exponential and is described by
- V = V0 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 lengthover which the output voltage halves.
- ln( V ) = ln( V0 ) -m x
- A graph of ln( V ) against x is a straight line with gradient -m .
- This experiment comes from...
Diagrams are reproduced by permission of the copyright holders, Heinemann.
This experiment was safety-tested in December 2004