Apparatus :
The apparatus used by Fizeau for determining speed of light in air is shown in Figure.
(i) The light from the source S was first allowed to fall on a partially silvered glass plate G kept at an angle of `45^@` to the incident light from the source.(ii) The light then was allowed to pass through a rotating toothed-wheel with N teeth and N cuts of equal widths whose speed of rotation could be varied through an external mechanism. (iii) The light passing through one cut in the wheel will get reflected by a mirror M kept at a long distance d, about 8 km from the toothed wheel. (iv) The toothed wheel was not rotating, the reflected light from the mirror would again pass through the same cut and reach the eyes of the observer through the partially silvered glass plate.
Working : (i) The angular speed of rotation of the toothed wheel was increased from zero to a value `omega` until light passing through one cut would completely be blocked by the adjacent tooth. (ii) This is ensured by the disappearance of light while looking through the partially silvered glass plate.
Expression for speed of light:
The speed of light in air v is equal to the ratio of the distance the light travelled from the toothed wheel to the mirror and back 2d to the time taken t.
` v = (2d)/(t) " " ....(1)`
(v) The distance d is a known value from the arrangement. The time taken t for the light to travel the distance to and fro is calculated from the angular speed `omega` of the toothed wheel. (vi) The angular speed w of the toothed wheel when the light disappeared for the first time is,
` omega = theta / t " " ...(2)`
(vii) Here, `theta` is the angle between the tooth and the slot which is rotated by the toothed wheel within that time t.
` theta = ("total angle of the circle in radian")/("number of teeth + number of cuts")`
` theta = (2pi)/(2N) = (pi)/(N)`
Substituting of `theta` in the equation (2) . for `omega`
` omega = (pi//N)/(t) = (pi)/(Nt)`
Rewriting the above equation for it ,
` t = (pi)/(Nomega) " " ...(3)`
Substituting t from equation (3) in equation (1)
` v = (2d)/(pi //N omega)`
After rearranging ,
` (2d N omega)/(pi)`
