OP THE REFLECTION AND REFRACTION OF LIGHT. 
7 07 
(^+ 62 ) sin i— ^ a sin r 
di 
. • . // 
Cn . sm i cos i— -c, . sin r . cos i 
iirsv 
di 
a( 1 + cos 3 r) sin i 
(cij—bj) cos i—a cos r 
and from these we must solve for a, b, and c in terms of a v However, c x , the com¬ 
ponent introduced at right angles to the original plane of vibration by reflection, is the 
only one of much interest, though the alteration produced in the values of the reflected 
component by assuming — to differ from unity are noteworthy. Calling T the period 
/L 
• S 1 LL 
of vibration of the wave we are considering, we may put - = —, and if we call — = y, 
A, -L fJb j 
we get for c the equation 
47 TV 
ci =“Y a 
(1 + cos 2 r) sin i sin 2 i 
which if x = l reduces to 
1 (sin 2 i + x sin 2r)(sin i cos r +y cos i sin r) 
47 rv (1 + cos 2 r) sin 2 i cos i 
T ’ ‘ i’ sin 2 (i + r). cos (i —r) 
In the second case, when the direction of the vibration of the incident ray is perpen¬ 
dicular to the plane of incidence, we must evidently assume 
(q= — cos i sin <f>\ £=c cos r sin <£ 
p 1 = a 1 cos (f>i J rb 1 cos (f>\ rj=a cos 
£ x = — c x sin i . sin <f)' 1 £= —c sin r . sin (f>__ 
(B) 
and, as before, it is evident that c is generally very small so that and vt, may be 
omitted, and our equations become 
civ 
dz dx K \dz dx) V dz 
dr/i K x d/i] 
dz K * dz 
£i=£ vi=v 
and when the values above are introduced into them we obtain 
— c 1 cos i—c cos r 
(cq — b\) sin i cos i=ax ■ sin r cos r 
a 1 -\-b 1 —a 
sin r Arrrv sin i cos r 
— C\ — — X ' • —.c+ r ,rct - 
1 ^ sm i T 
cos r 
