Question

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

• A. \( 3 \times 10^8 \, \text{ms}^{-1} \)
• B. \( 2 \times 10^8 \, \text{ms}^{-1} \)
• C. \( \sqrt{3} \times 10^8 \, \text{ms}^{-1} \)
• D. \( \frac{3}{2} \times 10^8 \, \text{ms}^{-1} \)

Answer 1

The Correct Option is C

The refractive index \( n \) of a medium is defined as the ratio of the speed of light in vacuum ( \( c \) ) to the speed of light in the medium ( \( v \) ):
\( n = \frac{c}{v} \)

In this case, for an equilateral prism, the refractive index \( n \) is \( \sqrt{3} \) based on the angle of minimum deviation being equal to the angle of the prism. 
Therefore, the speed of light inside the prism is given by:\( v = \frac{c}{n} = \frac{3 \times 10^8}{\sqrt{3}} = \sqrt{3} \times 10^8 \, \text{ms}^{-1} \)