Question

A thin prism has an angle of \(8^{\circ}\) and a minimum deviation of \(6^{\circ}\). Find the speed of light in the prism.

• A. \(1.71\times10^{8}\,m/s,\)
• B. \(2.0\times10^{8}\,m/s\)
• C. \(2.5\times10^{8}\,m/s\)
• D. \(3.0\times10^{8}\,m/s\)

Hint:

For a thin prism, always remember: \[ \boxed{\mu=1+\frac{\delta_m}{A}} \] where both \(A\) and \(\delta_m\) must be in the same unit (degrees or radians). The speed of light inside the prism is \[ \boxed{v=\frac{c}{\mu}}. \]

Answer 1

The Correct Option is A

At minimum deviation the refractive index is $\mu = \sin\frac{A+D_m}{2}/\sin\frac{A}{2}$. Substituting $A = 8°$ and $D_m = 6°$ gives $\mu = \sin 7°/\sin 4° \approx 1.75$.