Formation by Crystalline Media. 253 



the same as if the light were being refracted into a substance 

 of index «jV w i« 



2. linage formed by direct refraction through a plane 

 parallel plate of uniaxial crystal of thickness t, the faces being 

 normal to the axis. — The light is refracted into the crystal in 

 accordance with the law developed in the preceding section,, 

 and is refracted out according to that of the first example 

 considered. Thus, it' the source of light is at P in fig. 2 at 

 the distance p from the first surface M, the virtual source of 

 the refracted pencil is B, at the distance n 2 2 p/n x from that 

 surface (as in Section 1) and consequently at the distance 

 t + n^p/n^ from N at the second surface of the plate. The 

 image formed by the second refraction is therefore by (5) 

 situated at S at the distance p + tnjn 2 from N. 



The distance from the final image to the original source is 

 t{l — n l /n 2 2 ), (7), so that the image is " drawn up " toward' 

 the observer by this amount, which is the same as for an 

 isotropic plate of index n 2 2 /n 1 and is independent of the 

 distance of the source. 



3. Image formed by direct refraction from one uniaxial 

 crystal to another through a plane surface of separation which is 

 normal to the axis of each crystal. — The set of waves forming 

 the image is extraordinary in both crystals, since the plane 

 of incidence and refraction is a principal section in each. 



One m;iy deduce the law for the image position in this 

 case from the laws developed for refraction from air to 

 crystal and from crystal to air. Suppose for the moment 

 that the two crystals are separated by a plane parallel air- 

 space of thickness t, and that the light is refracted from 

 crystal 1 into this air-space and then into crystal 2. Accord- 

 ing to (5) the image formed by the first refraction is situated 

 at the distance n-ip/nj* from the first refracting surface, and 

 therefore (t + ni'p/nj 2 ) from the second. Since this image 

 forms the source with reference to the second surface, it 

 follows by (6) that the distance of the final image from this 

 surface is (t + n{p\n^)n4 ]2 jn{ 1 . 



Now the direction of the final nart of any of the rays 

 forming this image is independent of the thickness of the 

 air-space, and is therefore the same as if the thickness were 

 indefinitely diminished, i. e., as if the crystals were in optical 

 contact. Hence the required image position, which is deter- 

 mined by the direction of the rays for optical contact, is the 

 limiting position of the above image when the value of t is 

 reduced to zero. Its distance from the surface of contact 

 will therefore be 



n 2 m !n 2 f2 



p ni " J n,' 



