The advance of photography : its history and modern applications (1911)

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136 THE ADVANCE OF PHOTOGRAPHY of the hole and /= the distance of the screen from the hole. Thus, suppose screen is distant from the hole 10", so that/=10, then, since ^j^, ^^Jrom which d2 = j^>, i.e. d = ^" very nearly. To give this in a general form so as to be used for light of other wavelengths, we have distance (d)=r2/\, where r= radius of pinhole and \= wave-length of the light being used. This can be shown as follows : — Let us assume that in order to obtain the greatest amount of concentration of light we must arrange the position of the screen with reference to the pinhole, so Fig. 54. that the distance a ray has to travel from the centre of the pinhole to the plate may differ from that which a ray entering at the edge of the hole has to travel to reach the same spot by A/2, then by the property of the right-angled triangle we have r2 = (d+\/2)2 -d2=d\+\2/4, which will be approximately =d\, since \2/4t is very small; so that d=r2/\. To illustrate this, let us suppose screen is 10 inches from pinhole, and light of wave-length 000001 7" to be the most active, then r= x/0000017 xl0= s/000017 =0.013", i.e. the diameter of the hole should be two", *•*« about ^y. Sir William de Abney has pointed out that, if it were not for diffraction, the smaller the hole the better would be the definition, yet for each working distance there is