Reflection and Refraction of Light. 161 



The equations of motion give 



© 2 =7 8 (a 2 +&*) =/K 2 +#*) =7 /2 (a /2 + Z> 2 )=^' 2 (a //2 + 6 2 ); 

 whence 



v; 



gV- 



• V— 1= iui/s/ — 1, say; 



«"=-»\/l-^sV-l=-6«'V-l, say, 



the negative sign being taken, as the second medium corre- 

 sponds to negative .£. 



From equations (8) and (9a) we get 



u ^y -1+ (A+A 7 ) = -t/'B"*/ -1 + 1, 

 6B // -a(A-A / )=6B // -a , 3 



The last two of these equations give 



(10) 



-t 



A+A / =t s =/.«, 



where /x. is the refractive index, and 



B "= J» B "= ^ttf B "=>*°* B "> sa y- 



Substituting in the first two of equations (10), we get 

 (m„B„ + «"B") V~=l = 1 -/*«, 



b"= ^ 2 " 1 vcn 



whence 



and 



/*a\ + « 



A - A -^ + >'- B ") 



where 



M: 



= ^ + > 2 -l)M^-l ; 



/VS/ + W " 



