REFLEXION AND REFRACTION. 25 



vertical angle of the prism ; or, denoting this angle by A, 

 that 



v + v ' = A ; 



wherefore 



A = u -f u' - A. 



(30) When a ray of light is incident nearly perpendi- 

 cularly upon a thin prism, the total deviation is constant, and 

 bears an invariable ratio to the angle of the prism. 



For in this case the angles of incidence and refraction, 

 being small, are proportional to their sines, so that 



u = nv, u' = jjiv' ; and u + u' = JJL (v + #') - /u A. 

 Hence 



(31) The deviation produced by a prism is easily deter- 

 mined when the angles of incidence and emergence are 

 equal. 



For we have seen that, generally, 



But since, in this case, u = ^^, there is also v = v' ; and con- 

 sequently 



Hence we have 



sin % (A + A) = ju sin ^ A ; 



from which A+ A, and therefore A is determined. 



It may be shown that the angle of deviation, in this case, 

 is the least possible ; and accordingly, if the prism be turned 

 slowly round its axis, the inclination of the emergent to the 

 incident ray will first decrease, and afterwards increase, ap- 

 pearing for a moment to be stationary between the opposite 

 changes. By this principle it is easy to place a prism, experi- 



