**Question:**

Monochromatic light of wavelength 589 nm is incident from air on a water surface. What are the wavelength, frequency and speed of (a) reflected, and (b) refracted light? Refractive index of water is 1.33.

**Solution:**

Wavelength of incident monochromatic light,

λ = 589 nm = 589 × 10−9 m

Speed of light in air, *c* = 3 × 108 m/s

Refractive index of water, *μ* = 1.33

(a) The ray will reflect back in the same medium as that of incident ray. Hence, the wavelength, speed, and frequency of the reflected ray will be thesame as that of the incident ray.

Frequency of light is given by the relation,

$v=\frac{c}{\lambda}$

$=\frac{3 \times 10^{8}}{589 \times 10^{-9}}$

$=5.09 \times 10^{14} \mathrm{~Hz}$

Hence, the speed, frequency, and wavelength of the reflected light are 3 × 108 m/s, 5.09 ×1014 Hz, and 589 nm respectively.

(b) Frequency of light does not depend on the property of the medium in which it is travelling. Hence, the frequency of the refracted ray in water will be equal to the frequency of the incident or reflected light in air.

$\therefore$ Refracted frequency, $v=5.09 \times 10^{14} \mathrm{~Hz}$

Speed of light in water is related to the refractive index of water as:

$v=\frac{c}{\mu}$

$v=\frac{3 \times 10^{8}}{1.33}=2.26 \times 10^{8} \mathrm{~m} / \mathrm{s}$

Wavelength of light in water is given by the relation,

$\lambda=\frac{v}{v}$

$=\frac{2.26 \times 10^{8}}{5.09 \times 10^{14}}$

$=444.007 \times 10^{-9} \mathrm{~m}$

$=444.01 \mathrm{~nm}$

Hence, the speed, frequency, and wavelength of refracted light are 2.26 ×108 m/s, 444.01nm, and 5.09 × 1014 Hz respectively.

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