Total internal reflection, refraction of light, prism

Topic :Light

Total internal reflection, refraction of light, prism.

Question.

Refer to the figure as under. Monochromatic light is incident normally on the face OY of a prism made of glass whose index of refraction is such that the critical angle is 42 degrees.

Redraw this figure showing the path of light through the prism, any reflections as well as refractions, until some of the light emerges from the prism.

Answer.

As the incident ray is normal to the hypotenuse, it passes undeviated and hits the vertical surface of the prism at 30 degrees with the vertical or 60 degrees with the norm.al at 8 cm below O.

As the critical angle is 42 degrees, the ray wiull undergo total internal reflection as its incident angle is 60 degrees which is more than the critical angle and hit the bottom surface at some point with the incident angle of 30 degrees and come out with refraction.

If r = angle of refraction                       

sin i / sin r = 1/sinC

=> sin r = sin i / sinC = sin30 / sin42

=> sinr = 0.7472

=> r = 48.35 degrees.