Question

The difference in speeds of a ray of light in glass and water is $2.5\times {10}^{7}m/s$. If the $R.I$ of glass and water are $\frac{3}{2}$ and $\frac{4}{3}$ respectively, then the velocity of light in air is

• A. $2\times {10}^{8}m/s$
• B. $2.25\times {10}^{8}m/s$
• C. $3\times {10}^{8}m/s$
• D. $2.5\times {10}^{8}m/s$

Answer 1

The correct option is C $3\times {10}^{8}m/s$

$\begin{array}{c}{\mu }_g=\frac{3}{2}\\ {\mu }_{\text{water}}=\frac{4}{3}\end{array}$

$\begin{array}{cc}& v_{\text{glass}}-v_{\text{water}}=2.5\times {10}^{7}m/s-\left(a\right)\\ & \mu =\frac{v\text{(in air)}}{v\text{(in another medium )}}\end{array}$

$\begin{array}{cc}{\mu }_g& =\frac{v_a}{v_g}\\ \frac{3}{2}& =\frac{v_a}{v_g}\\ \frac{3v_g}{2}& =v_a-\left(i\right)\end{array}$

$\begin{array}{c}{\mu }_{\text{water}}=\frac{v_{\text{in air}}}{v_{\text{water}}}\\ \frac{4}{3}\times v_{\text{water}}=v_{\text{air}}-\left(ii\right)\\ \text{Equating (i)}\&\text{(ii)}\end{array}$

$\begin{array}{c}\frac{4}{3}\times v_{\text{water}}=\frac{3}{2}{v}_g\\ \frac{8}{9}{v}_{\text{water}}=v_g-\left(iii\right)\end{array}$

$\text{Putting (iii) in a}$

$\begin{array}{cc}\frac{-8}{9}{v}_{water}+v_{water}& =2.5\times {10}^7\\ \frac{1}{9}{v}_{water}& =2.5\times {10}^7\end{array}$

$v_{\text{water}}=2.25\times {10}^{8}m/s⟹v_{\text{air}}=\frac{4}{3}\times 2.25\times {10}^8=3\times {10}^{8}m/s$