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604.


Problem 43.42 (RHK)


A ray of light is incident normally on the face ab of a glass prism , as shown in the figure. (a) Assuming that the prism is immersed in air, we have to find the largest value for the angle so that the ray is totally reflected at the face; (f) we have to find if the prism is immersed in water.

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Let n be the index of refraction of the glass prism and be that of the outside medium in which the prism is kept.

For total internal reflection to take place, it is necessary that

.

The critical angle for total reflection is determined by the condition

And this angle fixes the largest value of the prism angle for the incident light to get refracted along the edge of the prism, as shown in the figure. We have

(a)

When the prism is kept in air, we have

(b)

When the prism is immersed in water .