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  • If one face of a prism of prism angle and <img alt="\mu=\sqrt{2}" src="https://entrancecorner.oncod

If one face of a prism of prism angle 30^{\circ} and \mu=\sqrt{2} is silvered, the incident ray retraces its initial path. What is the angle of incident?

Option: 1

90^{\circ}


Option: 2

180^{\circ}


Option: 3

45^{\circ}


Option: 4

55^{\circ}


Answers (1)

best_answer

As in \mathrm{\triangle A E D}


30^{\circ}+90^{\circ}+\angle \mathrm{D}=180^{\circ}
\angle \mathrm{D}=60^{\circ}

Now as by construction
\angle \mathrm{D}+\angle \mathrm{r}=90^{\circ}
\angle \mathrm{r}=90^{\circ}-60^{\circ}=30^{\circ}

Applying Snell's law at surface AC
\sin \mathrm{i}=(\sqrt{2}) \sin 30^{\circ}=\sqrt{2} \times \frac{1}{2}=\frac{1}{\sqrt{2}}
i=\sin ^{-1}\left(\frac{1}{\sqrt{2}}\right)=45^{\circ}
 

Posted by

Ritika Kankaria

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