Q.Consider a point at the focal point of a convergent lens. Another convergent lens of short focal length is placed on the other side. What is the nature of the wavefronts emerging from the final image?

Frequency Invariance

When a light wave crosses from one medium into another — on reflection or on refraction — one property never changes: its frequency. Everything else about the wave (its speed, its wavelength) can change, but the frequency is fixed the moment the wave leaves its source.

Why frequency is set by the source, not the medium

A wave's frequency is the rate at which its source oscillates. Think of shaking one end of a rope: if you shake it 5 times a second, exactly 5 crests leave your hand every second. If that rope changes into a heavier rope partway along, the wave travels slower in the heavier section, but the number of crests arriving per second at the join must still equal 5 — a crest cannot be created or destroyed at the boundary. The same logic applies to light: whatever surface it meets, the boundary condition (continuity of the oscillating electric and magnetic fields) forces the reflected and refracted waves to oscillate at exactly the incident frequency.

What changes instead: speed and wavelength

In a medium of refractive index $n$, light slows to $v = c/n$. Since frequency $f$ is unchanged and $v = f\lambda$, the wavelength inside the medium must shrink:

For reflection, the ray stays in the original medium, so speed, wavelength, and frequency are all unchanged. For refraction, the frequency still matches the incident wave, but speed and wavelength both scale by $1/n$.

Does slowing down mean losing energy?

No. The energy of light is carried by its photons, each of energy $E = hf$ — a quantity that depends only on frequency. Since frequency doesn't change on entering a denser medium, the energy per photon is unchanged too; only the wave's speed and wavelength are affected. (The wave's amplitude does adjust at the boundary so that energy is properly split between the reflected and transmitted beams — but frequency, and hence photon energy, is untouched.)

Worked example

Light of $\lambda_0 = 589\ \text{nm}$ in air strikes water ($n = 1.33$). The frequency is …