GENERATION, CONTROL, AND MEASUREMENT 143 



One of the principal advantages of mirrors over lenses is the lack of 

 chromatic aberration. Spectroscopes with mirror optics do not require 

 the extreme tilting of the photographic plate necessary in lens instru- 

 ments, and the focal adjustments are the same for all wave lengths. 



Aperture. The brightness or intensity of the image produced by paral- 

 lel rays from a distant object incident to a lens or mirror, as well as the 

 flux-gathering power of a condensing system, is primarily a function of 

 the diameter and focal length. This determines the solid angle w sub- 

 tended by the bundle of rays converging upon an image at the focus or 

 diverging from a source at the focus. It is evident from the lens formula 

 that, as the focal length is decreased and the solid angle is increased, the 

 image becomes smaller and more intense. The image intensity is pro- 

 portional to the subtended solid angle, which is the angular aperture or 

 aperture of the lens or mirror. Since, in radian measure, co = A //^, where 

 A is the area on a sphere of radius /, the aperture is given approximately as 



CO = Md/f)', (3-10) 



where d is the diameter of the optical element. 



The // number for camera lenses is the ratio f/d, which is also known 

 as the "aperture ratio." The exposure required for a photographic lens 

 is proportional to the square of the // number, or aperture ratio. Con- 

 versely, the speed of the lens is inversely proportional to the square of 

 the aperture ratio. The linear aperture is equal to the effective diameter 

 of circular optical elements, but for a rectangular element such as a prism, 

 there may be two linear apertures referring to the effective height and 

 width. The aperture area is the effective area of the optical element. 



ABSORPTION OF RADIANT ENERGY 



When radiant energy traverses matter, it is attenuated to a degree 

 depending vipon the probability that a photon will be captured by an 

 atom or molecule in its path and converted into some other form of 

 energy. In the far infrared the quantum energy is small, and the conse- 

 quences of absorption can result only in an increase in the rotational 

 energy of the molecules and the immediate degradation of the photon 

 energy to translational or heat energy. In the near infrared both the 

 vibrational and rotational energy levels of the capturing molecules may 

 be increased. As the photon energy increases in passing to shorter wave 

 lengths, the site of interaction moves deeper into the atomic structure. 

 In the visible and near ultraviolet the interaction concerns mainly the 

 outer valence electrons, and valence bonds may be altered, thus bringing 

 about a photochemical reaction. In the far ultraviolet the energy may 

 be sufficient to eject the outer electron completely from its atom and pro- 

 duce ionization. The X-ray photon can interact with the inner electrons 



