206 Mr. C. V. Raman : The Experimental 



determined by integrating the effects of these secondary 

 waves. I£ the amplitude of the disturbance in a secondary 

 wave in the direction in which the diffraction-pattern is 

 formed varies rapidly with the obliquity, such variation would 

 have to be taken into account and we should have an 

 explanation of the difference between the observed result and 

 that predicted by the ordinary theory. In no diffraction- 

 experiment so far known, with apertures of ordinary size, 

 has the variation of the amplitude with the obliquity, in a 

 secondary wave, manifested itself. In the well-known 

 Fresnel-Arago Circular-disk experiment, the fact that as the 

 disk is approached the illumination along the axis of the 

 disk decreases, cannot be taken to be an obliquity effect, it 

 being more or less entirely due to the ]arge increase in the 

 effect of minute irregularities in the rim of the disk or of 

 minute inaccuracies in its setting, as the latter is approached. 

 Some authorities have gone so far as to deny that an obliquity- 

 effect is possible at all. The present paper will show that 

 this last view is erroneous. In the case considered in this 

 paper, if we assume that the effect of an element at (fig. 1) 

 of the reflecting surface is zero at points on the lines OA, 

 OB and a maximum in the direction ON, the rate of variation 

 with respect to 6 of the amplitude in the secondary wave 

 ANB would be a maximum in either of the directions OA, 

 OB, and zero in the direction ON. If plane waves of light 

 are incident on the reflecting surface at a very oblique angle, 

 the diffraction-pattern (as observed in a telescope focussed 

 for infinity) is formed in the neighbourhood of the direction 

 OA, and the variation of the effect of an element with 0, the 

 angle of diffraction, would have large effects. The intensity 

 in the diffraction-pattern would be zero in the direction OA, 

 and at a point at which 0>i, would be less than at the corre- 

 sponding point at which 6 < i. 



The point will now be investigated mathematically. Take 

 the case of an aperture of any shape and of dimensions large 

 compared with \, cut in a thin perfectly reflecting sheet of 

 infinite extent, and let parallel waves of light be incident on 

 the aperture at an angle i. The light passing through 

 the aperture falls upon the object-glass f focal length/) of a 

 telescope focussed for infinity. Let x, y be coordinates in 

 the plane of the aperture and £, rj in the focal plane of the 

 telescope, y and rj being parallel, and assume that the effect of 

 an element dx, dy of the aperture is, in the focal plane, 

 equal to 



-~dxdy¥(i,6)sm~(Vt--c-'P), 

 V x 



