Question

When monochromatic light is incident on a surface separating two media, the refracted and reflected light both have the same frequency as the incident frequency but the wavelength of refracted light is different. Explain why.

Answer 1

Why Frequency Remains Same but Wavelength Changes During Refraction
When monochromatic light is incident on a boundary separating two different media, part of it is reflected and part is refracted.

1. Why Frequency Remains the Same
- The frequency of light is determined by the source that produces it.
- When light passes from one medium to another, the oscillations of the electric field must remain continuous across the boundary.
- Therefore, the frequency of the reflected and refracted waves remains equal to the frequency of the incident wave.
- Hence:
f_incident = f_reflected = f_refracted

2. Why Wavelength Changes in the Refracted Light
The speed of light depends on the medium.
In vacuum:
c = f λ₀
In a medium of refractive index n:
v = f λ
where v = c / n
Since frequency f remains constant and the speed changes in the new medium, the wavelength must change accordingly.
From v = f λ:
λ = v / f
Substituting v = c / n:
λ = (c / n) / f
But c = f λ₀, so:
λ = λ₀ / n
Thus, the wavelength in the medium becomes smaller if n > 1.

Conclusion:
- Frequency does not change because it is fixed by the source and must remain continuous across the boundary.
- Wavelength changes because the speed of light changes in different media.
- Therefore, refracted light has the same frequency but different wavelength compared to incident light.