The angle of incidence for an equilateral pri | vedclass

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(A) For an equilateral prism,the angle of the prism is $A = 60^{\circ}$.When the refracted ray inside the prism is parallel to the base,the condition

Vedclass · Accepted Answer

$1.4$

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(A) For an equilateral prism,the angle of the prism is $A = 60^{\circ}$.When the refracted ray inside the prism is parallel to the base,the condition for minimum deviation is satisfied.In this condition,the angle of incidence $i$ is equal to the angle of emergence $e$,and the angles of refraction are equal,i.e.,$r_{1} = r_{2} = r$.We know that $r_{1} + r_{2} = A$,so $2r = 60^{\circ}$,which gives $r = 30^{\circ}$.Applying Snell's Law at the first surface:$n_{1} \sin i = n_{2} \sin r$$1 	imes \sin 45^{\circ} = \mu 	imes \sin 30^{\circ}$$\frac{1}{\sqrt{2}} = \mu 	imes \frac{1}{2}$$\mu = \frac{2}{\sqrt{2}} = \sqrt{2} \approx 1.414$.Thus,the refractive index is approximately $1.41$.

The angle of incidence for an equilateral prism is $45^{\circ}$. What should be the refractive index of the prism material so that the ray is parallel to the base inside the prism?

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