Page:MichelsonEmission.djvu/2

 opposite direction, returning via DA to the starting-point, where it meets the first pencil, producing interference fringes which are observed by means of a telescope with micrometer eyepiece.

According to the undulatory theory the velocity of light is unaffected by the velocity of the mirror while the emission theory requires that

$\bar{V}=V+rv$

where $$\bar{V}$$ is the velocity of light after reflection, V the velocity before reflection and v the component of the velocity of the mirror in the direction of the reflected pencil, and r = 2 according to the elastic impact theory; while r = 1 if the mirror surface acts as a new source.

The time occupied by the pencil DEC is

$T_{1}=\frac{2(D+d)}{V_{1}}$|undefined

while that taken by the pencil CED is

$T_{2}=\frac{2(D-d)}{V_{2}}$|undefined

where D is the distance OE, d = distance the revolving mirror moves while light passes over DEC, and V1 the resultant velocity of the first pencil, V2 that of the second.

The difference in time is therefore

$T_{1}-T_{2}=2\left[\frac{D+d}{V+rv}-\frac{D-d}{V-rv}\right]$

But

$\frac{d}{2D}=\frac{v}{V}$

whence

$T_{1}-T_{2}=4\frac{D}{V}(2-r)\frac{v}{V}.$