Question

A small coin is resting on the bottom of the beaker filled with a liquid. Aray of light from the coin travels upto the surface of the liquid and moves along the surface (figure). How fast is light travelling in the liquid?

• A. $2.4 \times 10^{8} m / s$
• B. $1.8 \times 10^{8} m / s$
• C. $3.0 \times 10^{8} m / s$
• D. $5.0 \times 10^{5} m / s$

Answer 1

Answer: (B)

From figure, $O A=4 \,cm , A B=3 \,cm$
$\therefore O B=\sqrt{4^{2}+3^{2}}=5\,cm$
Now, $\mu=\frac{1}{\sin C}=\frac{1}{A B / O B}=\frac{O B}{A B}=\frac{5}{3}$
From, $\mu=\frac{C}{C / v}=\frac{C}{\mu}=\frac{3 \times 10^{8}}{5 / 3}$
$=1.8 \times 10^{8} m / s$