The refractive index of water is $(\frac{4}{3})$ and that of glass is $(\frac{3}{2})$. If the speed of light in glass is $2 × 10^8 m/s$, the speed of light in water will be
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → $(\frac{9}{4}) × 10^8 m/s$
Refractive index: $n = \frac{c}{v}$
For glass: $n_g = \frac{3}{2}$, speed $v_g = 2 \times 10^8 \, \text{m/s}$
$n_g = \frac{c}{v_g} \;\;\Rightarrow\;\; c = n_g \cdot v_g = \frac{3}{2} \cdot 2 \times 10^8 = 3 \times 10^8 \, \text{m/s}$
For water: $n_w = \frac{4}{3}$
$v_w = \frac{c}{n_w} = \frac{3 \times 10^8}{4/3} = \frac{3 \times 10^8 \cdot 3}{4} = 2.25 \times 10^8 \, \text{m/s}$
Answer: Speed of light in water = $2.25 \times 10^8 \, \text{m/s}$