#### 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 1

Wavelength of incident monochromatic light,

λ = 589 nm = 589 × 10^{−9} m

Speed of light in air, *c* = 3 × 10^{8} 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 the same as that of the incident ray.

Frequency of light is given by the relation,

`v = c/lambda`

`= (3 xx10^8)/(589 xx 10^(-9))`

Hence, the speed, frequency, and wavelength of the reflected light are 3 × 10^{8} m/s, 5.09 ×10^{14} 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.

∴ Refracted frequency, *ν* = 5.09 ×10^{14} Hz

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

`v = c/mu`

`v = (3xx 10^8)/1.33 = 2.26 xx 10^8 "m/s"`

Wavelength of light in water is given by the relation,

`lambda = v/v`

`= (2.26 xx 10^8)/(5.09 xx 10^(14))`

`= 444.007 xx 10^(-9) m`

= 444.01 nm

Hence, the speed, frequency, and wavelength of refracted light are 2.26 ×10^{8} m/s, 444.01nm, and 5.09 × 10^{14} Hz respectively.

#### Solution 2

Wave length of incident monochromatic light

`lambda = 589 nm = 589 xx 10^(-9)`

Speed of light in air `c =3 xx 10^8 "m/s"`

Refractive index of water, `mu = 1.33`

a) The ray will reflect back in the same medium as that of indient ray. Hence the wavelength, speed and frquency of the ray will be same as that of the incient ray.

Frequency of light is given by the realtion

`v = c/lambda`

`= (3xx10^8)/(589xx10^(-9))`

`= 5.09 xx 10^14 Hz`

Hence the speed, frequency and wavelength of the reflected light are `3 xx 10^8 "m/s"` `5.09 xx 10^14 "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

:. Refracted frequency, v = `5.09 xx 10^14 Hz`

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

`v = v/mu`

`v = (3xx10^8)/1.33 = 2.66 xx 10^8 "m/s"`

Wavelength of light in water is given by the relation

`lambda = v/v`

`= (2.26 xx 10^8)/(5.09 xx 10^(14))`

`= 444.007 xx 10^(-9) m`

= 444.01 nm

Hence the speed, frequency , and wavelength f refracted light are `2.26 xx 10^8 "m/s"`, 444.01 nm, and `5.09 xx 10^14` Hz respectively