IGO NUMERICAL APERTURE. 



invariable ratio bet>veen the sines of the angles of incidence and 

 refraction. 



D C 



The value of the fraction — — - when light passes from air into 



O L 



anotlier medium, is wliat is known as the refractive index of the 



substance ; this makes the refractive index of air unity. 



It is evident from the figures that rays perpendicular to the 

 surface M N suffer no deviation, but are only retarded. 



If;;/ be taken as representing the refractive index of the i)as- 

 sage of light from air into another medium, the refractive 

 index of the passage of light from the other medium into air is 



the reciprocal of ;;;, or — ; for the two parts of the refracted beam 



are mutually dependent ; this is easily deduced from the figures. 



Therefore, the passage of light from a medium into air is given by 



^, ... sin r 

 the equation, sin i = 



If r = 90*^, the radius is equal to the sine, and sin r = i ; 

 in this case the refracted ray lies along the surfice of the medium. 

 Take, for instance, the case of crown glass. 



Then sin i = ^ = 



m I "5 2 



or /= 41* 8h' (nearly). 



This angle is called the critical angle of glass, and a ray 

 having a larger angle of incidence cannot pass out, and is totally 

 reflected. The critical angle of water is 48*^ 35'. 



From this it follows that an angle of 



90^ (air) = 48° 35' (water) = 41^ 8h (glass) 

 in the amount of light-rays it contains ; so that the denser the 

 medium the more the rays of light are squeezed together. 



Now let A B (Fig. 3) represent the section of a lens. This 

 may be either a single lens or the front lens of a system. Let 

 D C be drawn perpendicular to the lens, and passing through its 

 centre. Then D C represents the principal axis of the lens ; and 

 let F represent its focus, and A F and B F represent the extreme 

 boundaries of the cone of light-rays from F, passing into the lens. 

 Then the angle A F B is called the ''Angular Aperture'' of the 

 lens. 



