The refractive indices of glass and water are 3/2 and 4/3, respectively. If the speed of light in water is \( 2.25 \times 10^{8}\,\mathrm{m/s} \), the speed of light in glass will be
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → \( 2 \times 10^{8}\,\mathrm{m/s} \)
The refractive index of a medium is \( n = c/v \), so the speed of light is inversely proportional to the refractive index.
\( \displaystyle n_g v_g = n_w v_w \;\Rightarrow\; v_g = v_w\,\frac{n_w}{n_g} \)
\( \displaystyle v_g = 2.25\times10^{8} \times \frac{4/3}{3/2} = 2.25\times10^{8} \times \frac{8}{9} = 2\times10^{8}\,\mathrm{m/s} \)