Question

A monochromatic light of wavelength 589 nm is incident from air onto water surface. The refractive index of water is 1.33. What is the wavelength and speed of refracted light?

• A. $589nm,2.256\times {10}^{8}m{s}^{-1}$
• B. $443nm,2.256\times {10}^{8}m{s}^{-1}$
• C. $632nm,3\times {10}^{8}m{s}^{-1}$
• D. $726nm,3\times {10}^{8}m{s}^{-1}$

Answer 1

Answer: (B)

$443nm,2.256\times {10}^{8}m{s}^{-1}$

On refraction, $\lambda$ of light changes but frequency remains unchanged.
$\therefore \nu =5.1\times {10}^{14}Hz$
$v_w=\frac{c}{\mu }=\frac{3\times {10}^8}{1.33}=2.256\times {10}^{8}m{s}^{-1}$.
Also,
${\lambda }_w=\frac{v_w}{\nu }=\frac{2.256\times {10}^8}{5.1\times {10}^{14}}=443\times {10}^{-9}m=443nm$