## Measuring the velocity of light

If light is reflected off a rotating mirror into another stationary mirror such that the beam returns along the same path then on the return the mirror will have turned through a small angle.

If the angular velocity of the rotating mirror is W degrees per second and the path between the mirrors is d meters then the angle turned in the time for the beam to return is:

2dW/c degrees

If the light is reflected from the rotating mirror again then the angle X through which the returned beam is turned away from the incident beam is:

X=4dW/c degrees

Experimental details: A is the clockwise rotating half silvered mirror, B is the straight through reference mirror, D is the half silvered mirror, E is a collimator.

Light travels from the lamp L through the semi-silvered mirror to B and back to the telescope, another beam, split at mirror A travels to C and back to A where it is reflected through D to the telescope.  The small angle of turn of the light is measured.  The velocity of light may be determined by substituting in:

c=4dW/X

This experiment was carried out with primitive apparatus by myself in 1962 as part of a thesis.  I do not have the results.  (I was treated by a psychiatrist...)

Another method I used was by making light pass through two slits in two rotating disks on the same shaft. Vis: If the angle between the slits in W (degrees) and the distance between the slits is D (meters) and the rotation rate is T degrees per second, then when light passes through both slits and the collimator slits then the velocity of light c, is given by:

t=W/T where t is the time taken for the second slit to line up with the old position of the first slit.

c=D/t

so      c=DT/W

if the speed of revolution is F  rotations per minute then T=F*360/60 or T=F*6

c=6DF/W

to calculate the approximate values c is approximately 3E6 meters per second and for D=1 then if F=1000 rpm then W needs to be W==6DF/c=0.002 degrees so for a separation of 10 meters and an angle of 1 degree the angular velocity has to be 50,000 rpm.

Folding the optical path using mirrors would also reduce this angular velocity so a 1000 fold increase in optical path with mirrors would make the angular velocity 50 rpm.  This could be done using two parallel mirrors and introducing the beam from another mirror just beyond the slit and collecting the emerging beam from the other end with a mirror near the second slit.  With a mirror separation of 1 meter, 998 reflections would be needed, the angle of the entrant beam would decide the number of reflections with the length of the parallel mirrors.

Again, I do not have the results as I was treated by a psychiatrists.  He said I had a brain tumour.

Chris.

17/12/2010