Question

When a ray of light of frequency $6\times {10}^{14}\text{Hz}$ travels from water of refractive index $\frac{4}{3}$ to glass of refractive index $\frac{8}{5}$, its

• A. $\text{frequency becomes}\frac{5}{6}th\text{of its initial value}.$
• B. $\text{speed becomes}\frac{5}{6}th\text{of its initial value}.$
• C. $\text{wavelength becomes}\frac{6}{5}th\text{of its initial value}.$
• D. $\text{speed becomes}\frac{6}{5}th\text{of its initial value}.$

Answer 1

The correct option is B $\text{speed becomes}\frac{5}{6}th\text{of its initial value}.$

Frequency of the wave doesn't change but speed and wavelength do.

$\frac{v_{water}}{v_{glass}}=\frac{n_{glass}}{n_{water}}$
$\Rightarrow v_{\text{glass}}=v_{\text{water}}\times \frac{4/3}{8/5}$
$\Rightarrow v_{\text{glass}}=\frac{5}{6}{v}_{\text{water}}$

Since, $v=f\lambda$ and $f$ is constant,
$\Rightarrow {\lambda }_{\text{glass}}=\frac{5}{6}{\lambda }_{\text{water}}$

Hence, option (b) is correct.