with the Aid of a Grating. 417 



The observed value of z for the two positions was about 

 1*3 cm. The computed value for 1 = 45° was the same. 



On the other hand, when reflexion takes place from the 

 same face of the grating while the latter is displaced z cm. 

 parallel to itself, the relations of y and z for normal incidence 

 at an angle I are obviously 



y cosI = r. 



For an oblique incidence i, where i — T = a, a small angle, 

 the equation is more complicated. In this case 



y 



= £{1 + 2 — - -. sin I ) /cos I. 



\ COS I J J 



This equation is also true for a grating of thickness e, whose 

 faces are plane parallel. For the direction of the air-rays in 

 this case remains unchanged. 



Finally, a distinction is necessary between the path 

 difference 2y and the motion of the opaque mirror 2N which 

 is equivalent to it, since the light is not monochromatic. 

 This motion 2N is oblique to the grating, and if the rays 

 differ in colour further consideration is needed. For the 

 simplest type of interferences, in which the glass path 

 difference, as in fig. 5, is efi/cos R, and for normal incidence 

 at an angle I, let the upper ray y M and the grating be fixed. 

 The mirror moving over the distance AN changes the zero 

 of path difference from any colour of index of refraction /n D 

 to another of index /^ E , while y ND passes to ?/ NE . Then a 

 simple computation shows 



AN=e(fi D cos R D —/i E cos H E ). 



This difference belongs to all rays of the same colour 

 difference, or for two interpenetrating pencils. 



If reflexion takes place from the lower face the rays are 

 somewhat different, but the result is the same. If the plate 

 of the grating is a wedge of small angle <£, the normal rays 

 will leave it on one side at an angle 1 + 8, where 8 is the 

 deviation 



8=G*-1)+. 



The mirror N will also be inclined at an angle 1+5. to 

 return these rays normally. We may disregard d8 = (pd/.i, 

 if (f> is small. 



