377 
sensitiveness of Michelsons Interferometer. 
diminished in different ratios by a refraction, the azimuth of 
polarisation of the incident light requisite to cause one of the 
emergent beams to be circularly polarised is different from that 
required for the other. Both these difficulties can be overcome 
by placing the compensating plate parallel and very close to the 
inclined plate, the distance apart being that which corresponds to 
the first bright ring in Newton’s rings. This arrangement has the 
further advantage that the amount of light reflected at the thin 
film of air is four times as great as that reflected at a single air- 
glass surface. 
If the amplitude of the light-waves incident on the air-film is 
A, the displacement in reflected wave is 
g 
2 (1 + b 2 ) sin 2 - sin </> — (1 — b 2 ) sin 8 cos cf> 
Ah £ _ 
y 1 - 26 2 cos 8 + b+ 
and that in the transmitted wave is 
^( 1 - 
(1 — 6 2 cos 8) sin </> — 6 2 sin 8 cos </> 
1 - 26 2 cos 8 4- 6 4 
where 6 is the ratio of the amplitude of the wave reflected at a 
single air-glass surface to that of the incident wave, 8 is the 
relative retardation of beams reflected at the two surfaces of the 
film, and cf> is an expression of the form r (t — x/V). Since the 
value of 6 depends on the plane of polarisation of the incident 
light, the two parts of each beam in general undergo a different 
alteration of place at reflection or refraction. In our case how- 
ever 8 = 7 r and no alteration of place occurs. We see however 
that the condition 8 = it must be satisfied with considerable 
accuracy. The above expressions are then 
A 
7 n and A 
1 + 6 2 
1 - 6 2 
1 + 6 2 ’ 
respectively, where 6 is given by Fresnel’s theory of reflection. 
Each beam is reflected once at and transmitted once through 
the thin film, and undergoes four other refractions, two at an air- 
glass surface, and two at a glass-air surface. If therefore the 
incident light is polarised in a plane making an angle <£ with the 
plane of incidence, the parts of either emergent beam that are 
polarised in and perpendicular to the plane of incidence are 
respectively 
A cos <£ . 
26 x 1 - W 
1 + W 1 + b? 
ctf, 
A sin <£ . 
26 2 1 - W 
1 + 6o 2 I + b 2 
cif?, 
and 
