
Bright Spectrum Lines. 487 
By means of a lens L these rays are brought to a focus 
in its focal plane, producing there an interference pattern, 
bright and dark bands according as 2D cos @, 4D cos @, &e. 
are equal to an even or an odd number of half wave-lengths. 
If we have a symmetrical cone of rays incident upon the 
plates, the system of fringes obtained on a screen placed in 
the focal plane of the lens will be concentric circles, having 
as their centre the point of intersection of the normal from 
the source upon the plates with the screen, C in the figure. 
The radii of these circies are equal to f tan 0, where fis the 
focal length of the lens L. 
The intensity of the light at~different points in this 
interference pattern was first worked out by Airy™. His 
formula is 
= i ha=e)" i 
FNS Apo oe 7a 
(1—0?)? + 46 sin? : ) 

where I, is the intensity of the incident light transmitted by 
the silvered surfaces, 5 the coefficient of reflexion of the 
silvered surfaces, and A the difference of path of the rays. 
We see from this formula that for a given value of 6, I will 
. IA e es . e e 
have a maximum when —— is an even integer and a minimum 
pA. : : , 
when 7 «is an odd integer. Hence the intensity of the 
bright fringes is Ip, while that of the dark fringes is 
he 2 
: (; it i) 
Fabry and Perot have calculated the values of I for 
different values of 6, and have plotted curves showing the 
relations between I and A for these values of b. The greater 
the value of ) the steeper becomes the intensity curve, so 
that the interference pattern consists of bright frmges which 
are very narrow compared with the dark ones (see Plate XXV. 
fig. 1). As we shall see later, the sharper and finer these 
bright bands are the easier are the radiations analysed and 
the components measured, thus, while on this account it is 
advantageous to have b very large by increasing the thickness 
of the silver film, it must not be so large that Ip, the intensity 
of the light transmitted, is too small. 
Let us now consider the light which is incident upon the 
plates not to be monochromatic, but to consist of two wave- 
lengths A and X+dA, then the screen in the focal plane will 
* Phil. Mag. [3] ii. p. 20 (1833). 
