ON THE COLOURS OF THICK PLATES. 1 73
of the axis of y is disposable, we may make the plane of y, z pass through the luminous point, in which case 6 = 0, and
For a given fringe II is constant. Hence the fringes form a system of concentric circles, the centre of the system lying in the* axis of #. If a be the abscissa of the centre
ah? ah ah \
(22)'
Now ah(h-c)~l and ah(h + c}"1 are the abscissa) of the points in which the plane of the mirror is cut by two linos drawn through the eye, one to the luminous point, and the other to its image. Hence we have the following construction : join the eye with the luminous point and with its image, and produce the former line to meet the mirror; the middle point of the line joining the two points in which the mirror is cut by the two lines drawn from the eye will be the centre of the system.
Hence if the luminous point be placed to the right of the perpendicular let fall from the eye on the plane of the mirror, and between the mirror and the eye, the concavity of the fringes will be turned to the right. If the luminous point, lying still on the right, be now drawn backwards, so as to come beside the eye, and ultimately fall behind it, the curvature will <lecrea.se till the fringes become straight, after wlnY.h it will increase in the contrary direction, the convexity being now turned towards the right. This agrees with observation.
12. The expression for R shows that the circle which forms the achromatic line of the system passes through the two points mentioned in the last paragraph but one. This is always observed to be true in experiment as far as regards the imago, and is found to be true of the luminous point also when it is in front of I/he eye, so as to be seen along with the fringes, provided the fringes reach so far.
Denoting by w0X, the value of R at the centre of the system of circles, taken positively, we get from (21) and (22)
?/ = —-——-.£
fJi\ (I I ~ C )