u 2 u It will be observed that, while the total intensity is proportional to ab, the intensity at the focal point is proportional to a 2 b 2.
At the focal point (E =o, n = o) all the secondary waves agree in phase, and the intensity is easily expressed, whatever be the form of the aperture.
So long as there is no sensible discrepancy of phase there can be no sensible diminution of brightness as compared with that to be found at the focal point itself.
In the case of the circular aperture the distribution of light is of course symmetrical with respect to the focal point p=o, q=o; and C is a function of p and q only through 11 (p 2 -}-q 2).
Thus, if x = R cos 4), C =,r2R2J1(pR) pR and the illumination at distance r from the focal point is 4T2 r 21rRr1 fX (2 fKr) a J The ascending series for J 1 (z), used by Sir G.