Light spreading out

What happens to light as it spreads out from a source?

Wrong Track: Light gets weaker as it travels away from a lamp just because it is gradually absorbed by air or any other material in its path.

Right Lines: Even if there are no absorbers in the way of the light, it gets dimmer, or its intensity lessens, because it is spreading out.

Bernard's butter gun

Thinking about the learning

As light spreads out from a source, its intensity decreases due to the processes of absorption and spreading.

Thinking about the teaching

The butter gun story offers an interesting approach to introducing the way in which light intensity decreases as it spreads from a source.

Bernard the inventor has a fantastic new idea. His friend, Julia, runs a sandwich shop and is always complaining that she and her staff spend all of their time buttering bread. Bernard decides that he will try to help out and comes up with his idea of a butter gun.

The butter gun works so that melted butter squirts out, in pulses, from the barrel of the gun at high speed, a bit like water from a hose-pipe.

Bernard finds that if he places one slice of bread 1 metre from the gun, the bread gets a covering 1 cm deep (too thick). Alternatively, Bernard finds that he can place 4 slices of bread at a distance of 2 m, such that they are all covered by the cone of butter and each one gets a covering of 14 centimetre of butter.

Julia encourages Bernard, for the sake of economy, to move the gun just 1 metre further back.

Here they find that that they can fit 9 slices of bread into the cone and that each slice gets a covering of 19centimetre of butter.

Julia is really happy about this! Now she can cover 9 slices of bread with just one squirt of the butter gun.

Julia has spotted a pattern in these figures:

distance	number	thickness
1	1	1
2	4	14
3	9	19
4	16	116

As Julia explains:

Julia: The greater the distance of the bread from the gun, the less the thickness of the butter on each slice. This is because the butter spreads out as it travels away from the gun. So, for example, after travelling 3 metre, the butter has spread out to make a cone which will cover 9 slices. Since there is only one squirt of butter from the gun, this butter must be 19^th the thickness of the butter achieved with one slice at 1 m distance.

Julia makes a mental note that if business becomes bad she will move the butter gun to a 4 m distance.

What has Bernard's butter gun got to do with light? More than you might imagine! Light spreads out in just the same way as the butter from the gun. In other words, as light travels away from a point source its intensity is reduced simply because it is more spread out (just like the reduced thickness of butter).

If the distance from the point source to a light detector is increased:

from 1 metre to 2 metre, the intensity of light falls by 14;

from 1 metre to 3 metre, the intensity falls by 19;

and so on.