A light ray is incident normally on a prism (see figure below). Find the angle (

Question

A light ray is incident normally on a prism (see figure below). Find the angle (relative to the normal) of the light ray transmitted back into air at the point where light first emerges from the prism. (The index of refraction of the prism is 1.5. Take = 65.1°.)

A light ray is incident normally on a prism (see figure below). Find the angle (relative to the normal) of the light ray transmitted back into air at the point where light first emerges from the prism. (The index of refraction of the prism is 1.5. Take theta = 65.1 degree.)

Explanation / Answer

as the angle theta is given to be 65.1 degrees the angle that the ray emerges from the first face with the normal of the second face is 65.1 degrees as 1.5sin65.1

is greater than 1 we have total internal reflection there

at the other face the angle that the ray and normal to it make is 90-65.1=24.9 degrees

here refraction occurs as 1.5*sin24.9 is less than 1
the angle of emergence of the ray is 43.46 degrees with the normal at this point
this normal makes 180-65.1degrees with the original ray
and

the answer is 180-65.1-43.46=71.44 degrees ..................................ans

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