Fizeau Light Velocity Method
The first terrestrial method for determining the velocity of light was performed by Fizeau in 1849.
A bright source S emits light which after passing through a lens L and after reflection from the plate P is converged to a point H. The point H lies at the focus of the lens L1 and in a space between the two teeth of the wheel W. therefore, the light after passing through L1 is rendered parallel and after travelling a distance of few miles is allowed to fall on the lens L2. The light after refraction through the lens is brought to focus at A which is also the pole of the concave mirror M. The radius of curvature of the mirror M is equal to twice the focal length of the lens L2. Due to this, the rays are reflected along their original path. An image of S can thus be observed by the eye placed behind the eyepiece E.
The rim of the toothed wheel W is at H and the wheel is rotated about a horizontal axis. This is the important part of Fizeau’s experiment. The teeth and spaces of the wheel are of equal width. Fizeau used a wheel with 720 teeth.
Working: When the wheel W is rotated, an image of the source is observed through E as light passes through the space of the wheel towards E. The wheel is rotated at such a speed that the rays passing the space fall on a tooth on their return. When this is adjusted, then no image of the wheel is doubled, again the image of the source S is seen by the eye because the rays on their return journey again pass through the next space. When the speed of the wheel is three times the first, no image of the source is seen by the eye because the rays on the return fall on the next tooth. In this way, if the speed of the wheel is continuously increased, the image of the source S will be alternately blocked and seen.
If the distance between H and A is equal to d and the wheel makes a rotations per second when the first eclipse is observed, then the time taken by light to travel from H to A and back is
t = 2d/c
If the wheel has m teeth and m spaces, and in the time t, the wheel moves from the centre of the space to the centre of the tooth then,
t = 1/2mn
∴ 2d/c = 1/2mn
and c = 4mnd
If n2 is the number of rotations/second of the wheel when the second eclipse is observed then
In Fizeau’s actual experiment
n = 12.6 rotations/second
m = 720
d = 8633 metres
c = 4mnd
c = 4 × 720 × 12.6 × 8633
= 3.13 × 108 m/s
The main advantage of the method is that the principle involved is simple and Fizeau actually took the idea from the experiment attempted by Galileo (covering and uncovering the lamp).
It should be remembered that Fizeau’s experiment is not free from criticism due to the following reasons:
1. The complete eclipse or disappearance of light cannot be obtained due to scattering of light from the teeth.
2. The image of the source is very faint because the intensity of light is considerably decreased due to refraction and reflection at various surfaces of the lenses and the mirror.
3. Uniform speed of rotation of the wheel cannot be attained.
4. The appearance or disappearance is not abrupt but it takes place gradually from maximum to minimum and vice versa.
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