Question

The time taken by a monochromatic light ray to travel a certain distance in air is 9 x 10${}^{-6}$ sec. The time taken by the light ray to travel the same distance in water of Refractive Index 4/3 is :

• A. $9\mu sec$
• B. $12\mu sec$
• C. $\frac{27}{4}\mu sec$
• D. $\frac{1}{12}\mu sec$

Answer 1

The correct option is B $12\mu sec$

Using the relation $\frac{v_1}{v_2}=\frac{{\mu }_2}{{\mu }_1}$
where $v_1$ and $v_2$ are the respective velocity of light in air and water and ${\mu }_1$ and ${\mu }_2$ are the respective refractive index of air and water.

Given : ${\mu }_2=\frac{4}{3}$ and ${\mu }_1=1$

Time taken by light to travel a distance $x$ in air $9\times {10}^{-6}s$ and that in water be $t$.

$\Rightarrow \frac{\frac{x}{9\times {10}^{-6}}}{\frac{x}{t}}=\frac{\frac{4}{3}}{1}$
Or $\frac{t}{9\times {10}^{-6}}=\frac{4}{3}$

$\Rightarrow t=12\mu sec$