Question

B) a right angled prism of refractive index n has a plate of refractive index n1 so that n1 < n, cemented to its diagonal face. the assembly is in air. a ray is incident on ab. i. calculate the angle of incidence at ab for which the ray strikes the diagonal face at the critical angle. ii. assuming n = 1.352, calculate the angle of incidence at ab for which the refracted ray passes through the diagonal face undeviated..

Answer 1

i) sin c = n1 / n         (90 – r1) + 45 + (90 – c) = 180          
             r1 = 45 – c                     
  sin i / sin r1 = n      
 sin i = n sin r1 = n sin (45 – c)    
                                  = n (sin 45 cos c – cos 45 sin c)                                                  
 = n/2 (cos c – sin c) 
 = n/2 ([ 1 – sin2 C] – sin c)                                            
       = 1/2 (n2 – n12) – n1              
                                   i = sin-1 (1/2 (n2 – n12) – n1) 
 ii) r2 = 0  r1 + r2 = 45  r1 = 45 
sin i / sin r1 = n 
sin i = n sin r1 = 1.352 sin 45 = 0.956 
sin i = n sin r1 = 1.352 sin 45 = 0.956

Answer 2

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