The refractive index of the material of a prism is $$2$$ and the angle of the prism is $$30o$$ . One of the two refracting surfaces of the prism is made a mirror inwards, by silver coating. A beam of monochromatic light entering the prism from the other face will retrace its path (after$$ reflection from the silvered $$surface) if its angle of incidence on the prism is

Question

The refractive index of the material of a prism is $$2$$ and the angle of the prism is $$30o$$ . One of the two refracting surfaces of the prism is made a mirror inwards, by silver coating. A beam of monochromatic light entering the prism from the other face will retrace its path (after$$ reflection from the silvered $$surface) if its angle of incidence on the prism is

Infinity Learn · Accepted Answer

For retracing the path shown in figure, light ray should be incident normally on the silvered face. Applying Snell’s law at point M,$$sinisin30$$°$$=21$$⇒$$sini=2$$×$$12sini=12$$ i.e., $$i=45$$°

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