Question

Monochromatic light of wavelength 589 nm is incident from air on awater surface. What are the wavelength, frequency and speed of(a) reflected, and (b) refracted light? Refractive index of water is1.33.

Answer 1

Given,

Wavelength of light λ=589 nm

Speed of light in air, c=3× 10 8   ms -1

Reflective index of water, μ=1.33

(a)

Since the reflected ray will reflect back to the same medium as that of incident ray. Thus, the wavelength, speed, and frequency of the reflected ray will be same as of incident ray.

Let ν be the frequency of the light,

Then,

ν= c λ

Substitute the values in above expression.

ν= 3× 10 8 589× 10 −9

ν=5.09× 10 14  Hz

(b)

Since, the frequency of light doesn’t depend on the property of the medium. Thus, the frequency of the refracted ray in water will be same as in air

Hence, refracted frequency will be ν=5.09× 10 14  Hz.

Let v be the velocity of light in water.

Thus, the expression for velocity of light is,

v= c μ

Substitute the values in above expression.

v= 3× 10 8 1.33 =2.25× 10 8   ms -1

Hence, wavelength of light in water is,

λ= v ν = 2.25× 10 8 5.09× 10 14 =4.44× 10 −7  m =444 nm