The angle of an equilateral prism is 60^o. Wh | vedclass

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(B) For a ray to be parallel to the base inside an equilateral prism,the prism must be in the position of minimum deviation.In this case,the angle of

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$\sqrt{3}$

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(B) For a ray to be parallel to the base inside an equilateral prism,the prism must be in the position of minimum deviation.In this case,the angle of incidence $i$ is equal to the angle of emergence $e$,and the angle of refraction $r_1 = r_2 = r = A/2$.Given the prism is equilateral,the prism angle $A = 60^o$.Therefore,the angle of refraction is $r = 60^o / 2 = 30^o$.According to Snell's law at the first surface,$\mu = \frac{\sin i}{\sin r}$.For minimum deviation,the ray inside is parallel to the base,which implies $i = e = (A + \delta_m) / 2$.However,a simpler way to find the refractive index $\mu$ when the ray is parallel to the base is using the relation $\mu = \frac{\sin i}{\sin r}$.Since the ray is parallel to the base,the angle of incidence $i$ must satisfy $\sin i = \mu \sin 30^o$.For an equilateral prism,the condition for the ray to be parallel to the base is $i = 60^o$.Thus,$\mu = \frac{\sin 60^o}{\sin 30^o} = \frac{\sqrt{3}/2}{1/2} = \sqrt{3}$.

The angle of an equilateral prism is $60^o$. What should be the refractive index of the prism so that the ray is parallel to the base inside the prism?

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