Which of the following phenomena can not be explained by wave theory of light?

We need to identify which phenomenon cannot be explained by the wave theory of light.

Wave theory explains:

- Reflection: When a wave hits a boundary, part of it bounces back. Wave theory successfully explains the law of reflection (angle of incidence = angle of reflection).

- Refraction: Wave theory explains refraction using Huygens' principle, showing how wavelets travel at different speeds in different media, causing the wavefront to bend.

- Diffraction: The bending of light around obstacles and through narrow slits is a purely wave phenomenon, well explained by Huygens' construction.

What wave theory cannot explain: The Compton Effect.

The Compton effect is the phenomenon where X-rays scattered by electrons show an increase in wavelength (wavelength shift). This was observed by Arthur Compton in 1923.

Why wave theory fails: According to wave theory, scattered radiation should have the same frequency as the incident radiation. However, Compton observed a shift in wavelength that depends on the scattering angle. This shift can only be explained by treating light as particles (photons) that collide with electrons, transferring momentum and energy like billiard balls. The scattered photon has less energy and hence a longer wavelength.

The Compton scattering formula $$\Delta\lambda = \frac{h}{m_e c}(1 - \cos\phi)$$ requires the particle (photon) nature of light.

The correct answer is Option A: Compton effect.