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At what angle...

Question

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.

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Solution

The incident, refracted, and emergent rays associated with a glass prism ABC are shown in the given figure.

Angle of prism, ∠A = 60°

Refractive index of the prism, µ = 1.524

= Incident angle

= Refracted angle

= Angle of incidence at the face AC

e = Emergent angle = 90°

According to Snell’s law, for face AC, we can have:

It is clear from the figure that angle

According to Snell’s law, we have the relation:

Hence, the angle of incidence is 29.75°.

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