COMEDK · Physics · 25. Ray Optics

When angle of incidence on one face of the equilateral glass prism is $3 / 4^{\text {th }}$ of the angle of prism, the ray of light undergoes minimum deviation. If the velocity of light in vacuum is '$c$' then the velocity of light in the glass is :

A $\dfrac{c}{\sqrt{2}}$
B $\dfrac{c^2}{\sqrt{2}}$
C $\dfrac{3 c}{4}$$
D $\sqrt{2} c$

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Correct Answer

(A) $\dfrac{c}{\sqrt{2}}$

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Detailed explanation

For an equilateral prism, the angle of prism $A = 60^{\circ}$. The condition for minimum deviation is given by $i = e$ and $r_1 = r_2 = r = A/2$. Given that the angle of incidence $i = \dfrac{3}{4} A$, we have $i = \dfrac{3}{4} \times 60^{\circ} = 45^{\circ}$. Since…

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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When angle of incidence on one face of the equilateral glass prism is \(3 / 4^{\text {th }}\) of the angle of prism, the ray of light undergoes minimum deviation. If the velocity of light in vacuum is '\(c\)' then the velocity of light in the glass is :

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