690 Prof. C. V. Raman and Mr. K. Seshagiri Rao on 



The expressions for the path-difference and the direction 

 of the emergent ray are respectively : 



£(jUCOST/r — cosyfr') . . . Fig. 3(a). 



I Fig. 3 (b). 



— ^(cosr + cosi/r')— fjbt sin — -X | 



+ ^ui(cos a + cos yjr) — 8 

 and sin 6 = sin r f —fi sin (^r' + r — i). J 



juut (cos i— sin r— i)— 'f'eos ■?• — 8 



and sin = fi sin (2r — / + t/t). 



Fig. 3 00- 



In rig. 4 we have a representation of the three-dimensional 

 case of the laminar edge running parallel to the plane of 

 incidence. 



FiR\ 4. 



Taking the direction of the edge to be the £-axis and 

 the meniscus to be a section of a semicircular cylinder, 

 /, o, n to be the direction- cosines of the ray incident 

 on the meniscus, /', m\ n' to be the direction-cosines of 

 the ray after one refraction, V\ m" ', n" its direction-cosines 

 after two refractions on emergence into the liquid, the 

 path-difference between this and another ray emerging 

 paiallel to it which has passed wholly through the liquid 

 and is totally reflected at the surface of the meniscus may 



