At what angle should a ray of light be incident on the face of a prism of refracting angle 60° so that it just suffers total internal reflection at the other face? The refractive index of the material of the prism is 1.524.

Given:


Angle of prism, A = 60°
Refractive index of the prism, μ = 1.524


Emergent angle, e = 90°



i1 = Incident angle
r1 = Refracted angle
r2 = Angle of incidence at the face AC
According to Snell’s law, for face AC, we can have:


…(1)


From equation(1) we have,


⇒ sin r2 =


Putting the values in the above equation we find that,


r2 = sin


r2 = 41°


We know that, refracted angle r1 is given by,


r1 = A- r2


r1 = 60-41 = 19°


Therefore r1 = A−r2 = 60−41 = 19°
According to Snell’s law, we have the relation:


μ =


Sin i1 = 1.524 × sin19° = 0.496


⇒ i1 = 29.75°


Therefore, the angle of incidence is 29.75°


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