PROBLEMS. 493 



the candle power of B in the direction towards the screen ? Ans. 

 35.3 candle power. 



170. The lamp, B y of problem 169 is placed at a distance of 0.70 

 meter from the center of a large mirror which reflects the light 

 from B along the photometer bar towards the photometer screen ; 

 and when the screen is again adjusted to equality of illumination 

 on both sides, it is 1.85 meters from the standard lamp and 1.82 

 meters from the center of the mirror. The lamp, B, presents 

 towards the mirror in this case the same face that was presented 

 towards the screen in problem 169. Find the factor by which 

 the apparent candle power of any lamp, when measured by the 

 light reflected from the above mirror, must be multiplied in order 

 to correct for the loss of light at the mirror. Ans. 1.13. 



171. A beam of light consisting of parallel rays has a sectional 

 intensity of 300 luxes. Find the conical intensity of the beam 

 after it passes through a lens of which the focal length is 50 

 centimeters. Ans. 75 hefners. 



Note. The sectional intensity of the conical beam of light at the lens is the same 

 as the sectional intensity of the given beam, namely, 300 luxes, that is 300 times as 

 great as the sectional intensity of the light at a distance of loo centimeters from a 

 Hefner lamp, or 75 times as great as the sectional intensity at a distance of 50 centi- 

 meters from a Hefner lamp. Therefore the conical intensity of the convergent beam 

 is 75 hefners. 



It is perhaps more intelligible to state the solution as follows : Let us take as the 

 unit of light flux the amoun. of light in one square centimeter of a beam of which the 

 sectional intensity is one lux. This unit of light is one lux-cm. 2 Consider one 

 square centimeter of the surface of the lens. The cone defined by lines drawn from 

 the periphery of this portion of the lens to the focus has a solid angle of i cm. 2 divided 

 by (50 cm.) 2 which is equal to 5-^^. This cone contains 300 lux-cm. 2 of light so 

 that the conical intensity of the conical beam is 300 lux-cm. 2 divided by ^sW 

 which is equal to 750,000 lux-cm. 2 , and it only remains to reduce this to hefners 

 To this end consider one square centimeter of area at a distance of 100 centimeters 

 from a Hefner lamp. The amount of light passing through this area is one lux-cm. 2 

 and the solid angle subtended by the area is T ^^, so that one hefner is equal to 

 10,000 lux-cm 2 . 



Solid angle is measured by a pure ratio, area divided by radius squared ; and 

 therefore light flux and conical intensity of light have the same physical dimensions, 

 and both may be expressed in lux-cm. 2 



