A parallel beam of light is incident from air at an angle α on the side PQ of a right angled triangular prism of refractive index $$n=2$$. Light undergoes total internal reflection in the prism at the face PR when α has a minimum value of $$45$$°. The angle θ of the prism is

Question

A parallel beam of light is incident from air at an angle α  on the side PQ of a right angled triangular prism of refractive index  $$n=2$$. Light undergoes total internal reflection in the prism at the face PR when  α has a minimum value of  $$45$$°. The angle  θ of the prism is

Infinity Learn · Accepted Answer

At A,  $$1sin$$$$π$$$$4=$$μsinr⇒$$12=2sinr$$ ⇒$$r=300$$ As   α$$min=$$π$$4$$,$$rmin=$$π$$6For$$ TIR at B,  θ$$+r$$≥θc     ⇒θ$$+r$$≥$$sin$$−$$11$$μ⇒θ$$+r$$≥$$sin$$−$$112$$⇒θ$$+r$$≥π$$4$$ ⇒r≥π$$4$$−θ⇒$$rmin=$$π$$4$$−θ⇒π$$6=$$π$$4$$−θ⇒θ$$=150$$

A parallel beam of light is incident from air at an angle $α$ on the side PQ of a right angled triangular prism of refractive index $n = \sqrt{2}$ . Light undergoes total internal reflection in the prism at the face PR when $α$ has a minimum value of $45 °$ . The angle $θ$ of the prism is

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A parallel beam of light is incident from air at an angle α on the side PQ of a right angled triangular prism of refractive index n=2. Light undergoes total internal reflection in the prism at the face PR when α has a minimum value of 45°. The angle θ of the prism is

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Ready to Test Your Skills?

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A parallel beam of light is incident from air at an angle $α$ on the side PQ of a right angled triangular prism of refractive index $n = \sqrt{2}$ . Light undergoes total internal reflection in the prism at the face PR when $α$ has a minimum value of $45 °$ . The angle $θ$ of the prism is