BRIGHTNESS OF LUMINOUS RADIATION 113 



rected by means of a convex cylindrical lens (+ cylinder), so chosen as to 

 increase the refraction along the meridian in which the cornea has the 

 least curvature; conversely, the refraction along the meridian of great- 

 est curvature can be diminished by means of a concave cylindrical lens 

 (— cylinder). 



A simple experiment illustrating astigmatism can be performed by 

 closing the eyelids over a normal eye until only a narrow slit remains, 

 so that the watery fluid bathing the eye forms a concave cylindrical 

 lens which alters the curvature along the vertical meridian. The 

 question is, why is the fluid lens concave? Which meridian is out of 

 focus? 



Brightness of Luminous Radiation 



The amount of radiant energy necessary to produce a fixed luminous 

 sensation of brightness varies enormously with the wavelength of the 

 radiation. By brightness is meant the luminous flux per unit of emissive 

 area viewed on a plane set perpendicular to the line of sight. It is 

 measured in lumens per square centimeter — a unit called the lambert. 

 Thus, when a diffusing surface reflects all the light incident upon it, its 

 brightness in lamberts is equal to its illumination in lumens per square 

 centimeter. 



The total visible energy emitted by a source per second is called the 

 total luminous flux. The unit of flux, the lumen, is that flux emitted in 

 unit solid angle by a point source having a luminous intensity of 1 

 international candle. A uniform point source of 1 candle intensity thus 

 emits 4x lumens. 



One millilambert equals 0.929 lumen per square foot, or the brightness 

 that would be produced by 0.929 foot-candle on a diffusing surface of 

 100 per cent reflection factor. Since most of the diffusing surfaces 

 are ordinary " white " surfaces of 80 per cent reflection factor, 1 foot- 

 candle produces a brightness on a white surface of 0.86 millilambert. 



Daylight brightness at sunrise and sunset is usually less than 100 

 millilamberts. The average brightness of an ordinary blue sky is 

 about 500 millilamberts, but a moderate haze increases the brightness of 

 the sky to 1500 millilamberts. 



The eye operates normally under intensities comparable to the bright- 

 ness of white paper in full sunlight (10 lamberts) as an upper limit, and 

 to a threshold of vision of 7 X 10~ 7 millilambert as a lower limit, or in a 

 range of 20 billion to 1 — a greater range of sensitivity than most physi- 

 cal instruments. 



It was found, however, that, when the brightness of a field of constant 

 area varied by a factor of 10 billion, the retinal sensibility varied by a 



