sensitiveness of Michelsons Interferometer. 377 



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 



2 (1 + b 2 ) sin 2 ^ sin <£ — (1 — b") sin 8 cos <j> 



Ai. i 



1 - 2b* cos 8 + ¥ 

 and that in the transmitted wave is 



(1 — 6 2 cos 8) sin <£ — b' 2 sin 8 cos <£ 

 (1 ~ ^ ~ l-26 2 cos8 + 6 4 



where b 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 <f> is an expression of the form r {t — xjV). Since the 

 value of b 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 = 7r 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 » an d A r „ , 



1 + b 2 1 + 6 2 



respectively, where b 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 * • TTK- TTb? Clfl> 



2b 1 — 6. 2 

 and A sin <j> . j-^ ^—^_ c 2 2 / 2 3 , 



