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.
Given:
Wavelength of incident light (λ) = 589 nm
Refractive Index of water = 1.33
λ = Wavelength of light
c = Speed of light in vacuum/ air = 3 × 108 m/s
f = Frequency of light
Figure showing reflection and refraction of a light ray
(a) In case of Reflection:
Explanation: Wavelength and frequency of light do not change in case of reflection as the speed of light remains constant because the reflected light is in the same medium as that of incident light.
Wavelength of reflected light (λ1) = 589 nm
Frequency of reflected light (f1) = 
= 
= 5.093 × 1014 Hz
Speed of reflected light (c1) = f1λ1 = 3 × 108 m/s
Wavelength, frequency and speed of reflected light are 589nm, 5.093 × 1014Hz and 3 × 108 m/s respectively.
(b) In case of Refraction:
Explanation: In refraction velocity of light changes as it enters another medium. As a result its wavelength changes but frequency remains constant.
v = Velocity of light in a particular medium
μ = Refractive index of medium = 
So, μ = 
⇒ 
⇒ v2 = 2.25 × 108 m/s.
We know that f2 = f1 = 5.093 × 1014 Hz
⇒ 
Or λ = 442.8nm
Wavelength, frequency and speed of refracted light are 442.8nm, 5.093 × 1014 Hz and 2.25 × 108 m/s respectively.