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^[1] 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

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

while that taken by the pencil CED is

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

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^[2]

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

1. According to the theory of Ritz (Annales de chimie et de physique, Ser. VIII, 13, 1908) the velocity of light is not affected by reflection from a moving mirror, but is affected by the motion of the source.
2. Omitting quantities of the second order; v should be replaced by v cos α, but since a is only 3°, the factor cos α may be taken equal to unity.