Its the 19th century and we want to find the
speed of light.
For this setup, we will need a motorized rotating
wheel, which has large no of teeth and gaps
like a gear.
Its important that the width of the teeth
are exactly the same as the width of the gaps.
The next thing we need is, a light source.
Let's assume its a strong laser for simplicity.
The same can be achieved with say, a light
bulb or even a candle with an appropriate
set of lenses.
We will also need semi reflective mirror.
It is a partially glazed glass which allows
some light to pass through it and some would
get reflected.
We will keep it tilted for reasons which will
be obvious very soon.
And lastly we need a regular mirror on the
other side of the wheel.
With the setup as shown, when we switch on
our laser, the light passes through the semi
glazed mirror.
Some of the light would get reflected as well,
but we'll ignore that as its not relevant
to this experiment.
The light is pointed towards the outer rim
of the wheel where there are teeth.
If the wheel rotation is such that the light
encounters a gap, it will pass through it
and hit the mirror on the other side.
The light beam then gets relfected and traces
its path thorugh the gap between the teeth
again and hits the semi glazed mirror.
Some of the light passes through it but again
we'll ignore that part.
The remaining light will get reflected and
here's where we will observe the light.
Now lets start rotating the wheel.
Doing this will cause the light to flicker
at our observation point.
We'll keep increasing the speed of rotation
gradually.
As we do that, at one point we'll observe
that the light is completely blocked and no
light can reach our observer.
Let's see what causes this to happen.
This will only happen when the light passing
through the gap between the teeth, by the
time it reaches back to the wheel, the wheel
has moved exactly one tooth distance and so
it blocks the reflected light beam.
As it has moved exactly one tooth distance
all the light passing through the gap will
get blocked.
The light from rightmost edge of the gap will
hit the rightmost part of the adjacent tooth.
Light passing through the middle of the gap
will hit the middle and light passing through
the left edge of the gap will hit the left
edge of the tooth.
So all light is blocked from the observers
point of view.
From this we can see that the time taken by
the light to travel from the rim of the wheel
to the mirror and back is same as the time
it takes for the wheel to rotate by the width
of one tooth.
With this information we can figure out the
speed of light if we know the speed at which
the wheel is rotating.
Let's do some math and find out the speed
If the no of teeth on the wheel is say .. 720
and the speed of the wheel at which light
blocks is 13 revolutions per second which
means time it takes to rotate one full circle
is 1/13 seconds.
We can now find out the time it takes for
the wheel to move the distance of one tooth.
There are 720 teeth and 720 gaps of the same
length.
So if we divide the speed of full rotations
by (720 + 720) we get the time it takes to
rotate one gap length or one tooth width.
Now the distance between the wheel and the
mirror is 8 kms or 8000 metres.. yeah it has
to be that large.
So the total distance light travels from the
wheel to the mirror and back is twice of that
... that is .. 16 kms or 16000 metres
If we denote c as the speed of light, the
time taken by the light to travel 16000 meters
is 16000 divided by c
Now this time must exactly match the time
it takes to rotate the wheel by one tooth
distance to effectively block the light completely.
which gives us the speed of light to approximately
3 * 10 raise to 8 meters per second.
