The inverse square law
Activity: the balloon
The drop off in light intensity might follow some rules. You should perform the
experiments below to determine these rules.
Aim
To model how the light intensity varies with distance from a point source of
light such as a light globe, using a balloon.
Procedure
1
Imagine the light globe is always in the centre of your balloon.
The inflating balloon surface is a representation of a wave front travelling in three
dimensions from the light globe.
2
Inflate a round balloon until it has a diameter of around 10 cm.
Do not tie off the balloon.
Record this as radius 1 unit in the table below.
3
Use a marker pen to draw a 1 cm by 1 cm square on the balloon where the
balloon is thickest opposite the inflation tube where you blow up the balloon.
Record the area of the square in the table below as 1 cm2. This square represents
the energy of the light at that radius from the light source.
a) What will happen to the area of the square as you inflate the
balloon?
__________________________________________________
__________________________________________________
b) What would be happening to the fixed quantity of energy from a
light source as it is spreading out from a point source in terms of the
amount of energy per unit area?
__________________________________________________
__________________________________________________
4
Inflate the balloon until it has a diameter of around 20 cm. The distance to the
centre of the balloon has now doubled.
Record this as 2 units in the table below.
5
Measure the size of the square on the balloon now.
Record the area in the table below beside 2 units.
c) Has the area of the square doubled or increased by around 4 times?
_________________________________________________
5
Inflate the balloon until it has a diameter of around 30 cm. Be careful not to
explode it. The distance to the centre of the balloon has now tripled.
6
Measure the size of the square on the balloon now.
Record the area in the table below.
d) How has the area of the square increased now? Is it three times bigger or
around 9 times bigger?
_________________________________________________
Distance units from the balloon centre
Area of the square
1
1 cm2
2
3
e)
Describe the relationship shown by this data. That is, how does this increase
in area relate to the distance from the source?
_________________________________________________
_________________________________________________
f)
Would it be accurate to say to 'the area increase is proportional to the
distance unit squared?'
_________________________________________________
_________________________________________________