Q15 of 26 Page 1

Three rays (1, 2, 3) of different colours fall normally on one of the sides of an isosceles right-angled prism as shown. The refractive index of prism for these rays is 1.39, 1.47 and 1.52 respectively. Find which of these rays get internally reflected and which get only refracted from AC. Trace the paths of rays. Justify your answer with the help of necessary calculations.


Given:


Refractive index for ray 1, R1=1.39


Refractive index for ray 2, R1=1.47


Refractive index for ray 3, R1=1.52


Refractive index for air, μ1=1


Calculation:


The condition for total internal reflection is given by,


sin C = μ/R


Where C = critical angle


μ=Refractive index for air


R=refractive index of ray


For ray 1:


sin C1 = μ1/R1


C1=sin 1(1/1.39)


C1=460


For ray 2:


sin C2 = μ1/R2


C2=sin 1(1/1.47)


C2=42.860


For ray 3:


sin C3 = μ1/R3


C3=sin 1(1/1.52)


C3=41.130


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