Question

figure shows a right angled isosceles prism of glass of refractive index 1.414 the angle of incidence i at AB for which of the refracted ray through diagonal face AC goes undeviated is​

Answer 1

Answer:

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Explanation:

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

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Answer 2

Answer:

) 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

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