Ch. IX] CRITICAL ANGLE AND TOTAL REFLECTION 275 



Abbreviated [ j ™ ( ). By means of this general formula one 



\sin rj Vindex i) 



can solve any problem in refraction whenever three factoi's of 

 the problem are known. The universality of the law may be illus- 

 trated by the following cases; 



(A) Light incident in a vacuum or in air, and entering some denser 

 medium, as water, glass, diamond, etc. 

 / Sine of angle made by the ray in air \ /Index of ref. of denser med. \ 



\Sine of angle made by ray in denser med./ \ Index of ref. of air (i) / 



If the dense substance were glass ( ) = ( -^ ). If the two media were 



Vsin r) V I / 



water and glass, the incident light being in water the formula would be: 



— \ = ( ^^ )• If the incident ray were glass and the refracted ray in 

 sin r) \^-l^) 



•srater: ( ^5_1 j = ( 1:^ ]. And similarily for any two media; and as stated 

 Vsin rj \1.52J 



above if any three of the factors are given the fourth may be readily found. 



§ 449. Critical angle and total reflection. — In order to under- 

 stand the WoUaston camera lucida (fig. 99) and other totally reflect- 

 ing apparatus, it is necessary briefly to consider the critical angle. 



The critical angle is the greatest angle that a ray of light in the 

 denser of two contiguous media can make with the normal and still 

 emerge into the less refractive medium. On emerging it will form an 

 angle of 90° with the normal, and if the substances are hquids, the 

 refracted ray will be paraUel with the surface of the denser medium. 

 ' Total Reflection. — In case the incident ray in the denser medium 

 is at an angle with the normal greater than the critical angle, it will 

 be totally reflected at the surface of the denser medium, that surface 

 acting as a perfect mirror. By consulting the figures it will be seen 

 that there is no such thing as a critical angle and total reflection in 

 the rarer of two contiguous media. 



To find the critical angle in the denser of two contiguous media: — 



Make the angle of refraction (i. e., the angle in the rarer of the two 



/sin i\ /index r"\ 

 media) 90° and solve the general equation: \-, — I = \^^^^^ , 



