THE REFRACTING TELESCOPE. 



183 



the telescope is a, but it will appear to an eye looking into the eye- 

 piece to lie at an angular distance y8 from the axis. The magnifying 

 power of the telescope is therefore equal to the angle /3 divided by the 

 angle a. 



The distance A of the focus of the converging waves from the 

 axis is very small, and will equal zero when the luminous point is on 

 the axis, when F will equal the focal length of the object-glass and f 

 of the eye-piece. Extremely small angles being proportional to their 

 tangents, the diagram shows the following expression to be true : 



A 



Magnitying power 01 telescope = ^ = '- = !^ = — -, proving 



F 



that the magnifying power of a telescope equals the focal length of 

 its object-glass divided by the focal length of its eye-piece. 



We have just seen, by similar triangles in Diagram 6, that the 

 focal lengths of the object-glass and eye-piece are proportional to the 

 diameters of the cylinders of plane wave-fronts entering the object- 

 glass and emerging from the eye-piece ; it follows, therefore, that the 

 magnifying power of a telescope equals the diameter of the entering 

 cylinder of light divided by the diameter of the emerging cylinder of 

 light. 



The easiest way to measure the magnifying power of a telescope is 

 to divide the diameter of the clear aperture of the object-glass by the 

 diameter of the little circle of light seen in the center of the eye-piece 

 when the telescope is pointed at the bright sky, it being assumed that 

 it is in focus for an infinitely distant object. This small circle of light 

 seen in the center of the eye-piece is i-eally an image of the object- 

 glass formed by the eye-piece ; but, when the light-waves emerge with 

 plane fronts, the size of this image is exactly equal to the size of the 

 emerging cylinder of plane wave-fronts, so that this method of find- 

 ing the magnifying power is strictly accurate. 



We have seen that, with an eye-piece not exceeding two and a half 

 inches in focal length, luminous points appear through the telescope as 

 many times brighter than they do to the naked eye as the area of the 

 object-glass exceeds the area of the pupil of the eye ; and it also fol- 

 lows directly from what has been already stated that, with this eye- 

 piece, the apparent angular distance between two luminous points is 

 proportional to the focal length of the object-glass used. A curious 

 thing following from this is, that surfaces having sensible areas appear 

 no brighter through large telescopes than they do to the naked eye ; 

 and it can be stated generally that, using a two-and-a-half-inch eye- 

 piece, which gives the brightest image of an object with any sized ob- 

 ject-glass, the surface will appear equally bright, whether seen by the 

 naked eye or through a telescope of any size. The apparent dimen- 

 sions of the surface, however, will increase directly with the dimen- 



