At what angle will a ray of light be incident | vedclass

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(B) For an equilateral prism,the prism angle $A = 60^{\circ}$.When the emergent ray grazes the second surface,the angle of emergence $i_e = 90^{\circ}

Vedclass · Accepted Answer

$90$

Vedclass · Answer

(B) For an equilateral prism,the prism angle $A = 60^{\circ}$.When the emergent ray grazes the second surface,the angle of emergence $i_e = 90^{\circ}$.At the second surface,the angle of refraction is equal to the critical angle $C$. Thus,$r_2 = C$.Using Snell's law at the second surface: $\mu \sin r_2 = 1 \cdot \sin i_e$.Given $\mu = 2$ and $i_e = 90^{\circ}$,we have $2 \sin C = \sin 90^{\circ} = 1$,so $\sin C = 0.5$,which gives $C = 30^{\circ}$.Therefore,$r_2 = 30^{\circ}$.From the geometry of the prism,$A = r_1 + r_2$. Substituting the values,$60^{\circ} = r_1 + 30^{\circ}$,which gives $r_1 = 30^{\circ}$.Now,applying Snell's law at the first surface: $\sin i = \mu \sin r_1$.$\sin i = 2 \cdot \sin 30^{\circ} = 2 \cdot 0.5 = 1$.Thus,$i = 90^{\circ}$.

At what angle will a ray of light be incident on one face of an equilateral prism,so that the emergent ray may graze the second surface of the prism $(\mu=2)$ (in $^{\circ}$)?

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