Question

Monochromatic light of wavelength 589 nm is incident from air to a water surface. What are the wavelength, frequency and speed of reflected and refracted light

Answer 1

Answer:

For reflected light,

Frequency = 5.09 × 10^14 Hz

Speed = 3 × 10^8 m/s

Wavelength = 589 nm

For refracted light,

Frequency = 5.09 × 10^14 Hz

Speed = 2.26 × 10^8 m/s

Wavelength = 444.01 nm

Explanation:

Refer the attached picture.

Answer 2

➨Given:-

￫ Wavelength of incident monochromic light, λ = 589 nm = 589 × 10^-9

￫ Speed of the light in air c = 3 × 10^8 m/s

￫ Refractive index of water μ = 1.33

➨To Prove:-

The wavelength, frequency and speed of reflected and refracted light = ?

➨Solution:-

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

Frequency of the light is given by the relation,

• v = c/λ

• v = 3 × 10^8/ 589 × 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 the light does not depend upon the property of the medium in which it is travelling.

Hence the frequency of the retracted ray in water will be equal to the frequency of the incident or reflected light in the air

Refracted Frequency,

v = 5.09 × 10^14 Hz !

Speed of the light in water is realated to the refractive index of the water as

• v = c/μ

• v = ( 3 × 10^8 )/ 1.33

• v = 2.26 × 10^8 m/s

Wavelength of light in the water is given by the relation,

• λ = v/v

• λ = 2.26 × 10^8/5.09 × 10^14

• λ = 444.007 × 10^-9 m

• λ = 444.01 nm

Hence,

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

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