Prof. Pctzval on the Camera Ohscura. 8 



tliffraction of light, it will be useful to enter into further details; 

 We may suppose the defect in sharpness to be measured by the 

 diameter of the above circular spot, conceived to extend up to 

 the commencement of the first dark ring. To obtain this dia. 

 meter, let a right line be drawn from the centre of the hole to^ 

 the screen so as to be perpendicular to the plane of the shutter. 

 Upon this line, from the centre of the hole, set oif a portion 

 equal to the diameter of the latter. From the extremity of the 

 line thus set off conceive another line to be drawn at right angles 

 whose length X is equal to that of a wave of light, i. e. -—-^ in. or 

 y^^^ in., according as the light is red or violet. If, lastly, a 

 line be drawn through the centre of the hole and the extremity of 

 the last perpendicular, it will, on being produced to the screen, 

 determine a point in the circumference of the circle, whose centre 

 is in the line first drawn, and whose diameter, D, is required. If 

 p be the radius of the hole, and A its distance from the screen, 

 wc have already 



2p:A=X:|, orD=^ (1) 



This formula is only an approximate one, applicable when p is 

 very small; in the case of a larger aperture, its diameter must be 

 added to the value above given, that is to say, 



D=2p+— . 

 P 



From the last formula we can at once deduce the best value 

 for p ; in other words, the size of the aperture which corresponds 

 to the least ])Ossible value of D, and therefore to the sharpest 

 possible image. In fact, differentiating the last expression, and 



setting, in the ordinary manner, -j-=0, we find at once 



P='/|AX, (2) 



D = 2\/2AX. 



For instance, if A = ll in., then for red and violet light wc have 

 respectively 



p =0010 in., p =0-007 in., 



D = 0042 in., D = 0030 in. j 



whence wc learn that, on the whole, it would be useless to dimi- 

 nish the diameter of the aperture beyond ^'^th of an inch, and 

 that, under the most advantageous circumstances, the image of 

 a luminous point is a circular spot ^\\\ of an inch in diameter. 

 The picture we should obtain under these circumstances would 



B3 



which corresponds to 



