Lord Rayleigh on Pln-liole Photography. 89 



Thus, if X= 1/40,000, r= 1/10, 



/i=800. 



The image of the sun thrown on a screen at a distance 

 exceeding 66 feet, through a hole ^ inch in diameter, is 

 therefore at least as well defined as that seen direct. In 

 practice it would be better defined, as the direct image is far 

 from perfect. If the image on the screen be regarded from a 

 distance f lt it will appear of its natural angular magnitude. 

 Seen from a distance less than f ly it will appear magnified. 

 Inasmuch as the arrangement affords a view of the sun with 

 full definition [corresponding to aperture] and with an in- 

 creased apparent magnitude, the name of a telescope can 

 hardly be denied to it. 



" As the minimum focal length increases with the square 

 of the aperture, a quite impracticable distance would be 

 required to rival the resolving power of a modern telescope. 

 Even for an aperture of four inches/, would be five miles"*. 



A more practical application of these principles is to be 

 found in landscape photography, where a high degree of 

 definition is often unnecessary, and where a feeble illumina- 

 tion can be compensated by length of exposure. In a recent 

 communication to the British Association f it was pointed out 

 that a suitable aperture is given by the relation 



2r*=f\; (i) 



and a photograph was exhibited in illustration of the advan- 

 tage to be derived from an increase off. The subject was a 

 weather-cock, seen against the sky, and it was taken with an 

 aperture of ^ inch, and at a distance of 9 feet. The amount 

 of detail in the photograph is not markedly short of that 

 observable by direct vision from the actual point of view. 

 The question of brightness was also considered. As the focal 

 length increases, the brightness (B) in the image of a pro- 

 perly proportioned pin-hole camera diminishes. For 



B oc r 2 // 2 a r 2 X 2 /r 4 oc \ 2 /r 2 a X/f. ... (2) 



There will now be no difficulty in understanding why a 

 certain aperture is more favourable than either a larger or a 

 smaller one, when /and X are given. If the aperture be very 

 small, the definition is poor even if the aid of a lens be 



* u On Images formed without Reflection or Refraction," Phil. Mag. 

 March 1881. 

 t Brit. Assoc. Report, 1889, p. 493. 



