102
OX THE COLOURS OF THICK PLATES.
focus, tlie difference of retardations of two waves starting from L and Ly and reaching the same given point. Then
R = ( L to 4) + PM - PLB - {(M to M,) + PL - PMJ =
when*
r == />J/ / Y,3 - ( />/, - Ply = V - V", suppose.
According to the* explanation given in the preceding article, when the position of /> changes JiT remains constant, to the degree of approximation which it is proposed to employ, but the value of V depends upon tin* position of P. We have
and ;: b>,(-/> '"'^'//"^ nearly. Expanding, we get
r' r. : I'/ j Irf/', when4 [r./ is the sum of the terms ' ^ and j\ an«l 1' the sum of the terms containin 6 and
!4M M.ic;i jt.n t«> wriir down [r|/f', since it, maybe deduced
f»;< v, i:?iir/ A, // for r/, ,/•. Taking lrr to denote for I7" what
:«" !-I I", we '^'t't h\ inteH'hanging r/ and a/, r/,} and a<t',
jd.T fl.-i" ?^r rin.ijs mav he formrd on a screen with perfect
fi« ;T ; in-eiv-.-arv thaf flu- diilercnee of phase of the
p,t;i .»! rn-ams which coine from the several points of the
i 'n'.jV' . ii-Hild he ihc same; in other words, that the
*!"!. // ii'ttjld he indepriident of ,/• and //. Deierring for
* u' ?li«- in?»«->.fixation «>f the conditions of distinctness, we
.-! .- 'I.-,-f v, hen these conditions are satisfied the expression