Question

If the angle of minimum deviation is equal to angle of a prism for an equilateral prism, then the speed of light inside the prism is _____

• A. 3x10⁸ ms^-1
• B. \(2\sqrt3\times10^8\) ms^-1
• C. \(\sqrt3\times10^8\) ms^-1
• D. \(\frac{\sqrt3}{2}\times10^8\) ms^-1

Answer 1

The Correct Option is C

Given: - The prism is equilateral, so angle \(A = 60^\circ\) - Angle of minimum deviation \(D_m = A = 60^\circ\) Using the formula for refractive index at minimum deviation: \[ \mu = \frac{\sin\left( \frac{A + D_m}{2} \right)}{\sin\left( \frac{A}{2} \right)} \] Substitute the values: \[ \mu = \frac{\sin\left( \frac{60^\circ + 60^\circ}{2} \right)}{\sin\left( \frac{60^\circ}{2} \right)} = \frac{\sin(60^\circ)}{\sin(30^\circ)} = \frac{\frac{\sqrt{3}}{2}}{\frac{1}{2}} = \sqrt{3} \] Now, use the relation: \[ \mu = \frac{c}{v} \Rightarrow v = \frac{c}{\mu} = \frac{3 \times 10^8}{\sqrt{3}} = \sqrt{3} \times 10^8 \ \text{ms}^{-1} \] Thus, the speed of light inside the prism is \(\sqrt{3} \times 10^8 \ \text{ms}^{-1}\)