074 Formation of Images by means of an Opaque Disk. 



first minimum following the central maximum is given 

 by V,=0. 



Taking, in illustration, the data for the case of the 

 photograph which is reproduced, we have a = 63 cm., 

 6 = 170 cm., c = *44 cm. \ = *00005 cm.; whence the value 

 of y (which is independent of the point Q) is 83 m. 

 Lommel has calculated the values of V as far as y = &7r 

 only ; but in our case it is unnecessary to calculate them 



a 



-Q 



further because the vanishing of V practically coincides 

 with the vanishing of J , as zjy is then exceedingly small 

 and J is changing fast. This occurs when ^=2*40 ; the 

 corresponding value of r is '0074 cm. Hence the whole of 

 the bright spot must be within this radius and the visible 

 part of it may be considerably within. 



For points of an extended source which lie off the axis, 

 the above formula no longer, in strictness, applies ; but it 

 may still be used approximately for points sufficiently near 

 to the axis. The corresponding bright spot is then on the 

 secondary axis through the centre of the disk, and the 

 distance of the spot from the principal axis is given by the 

 ordinary law of transverse magnification in geometrical 

 optics, i. e, width of image/width of object = b/a. In the 

 above numerical case, the length of each side of the 

 triangular source was '21 cm., and of the image was "58 cm. 

 This latter is nearly 40 times as long as the diameter of the 

 bright spot. It may be pointed out that this ratio is indepen- 

 dent of 6, and is inversely proportional to a; there is therefore 

 .an advantage in placing the disk fairly near to the source. 



Contrast should be drawn between the optical definition in 

 this case and in the complementary case of pinhole photo- 

 graphy. It would be impossible to have obtained a 

 photograph of the triangle with an aperture of the same size 

 instead of a disk. 



