The wave theory of light can not explain the phenomenon of

Photoelectric effect

The correct answer is Option (4) → Photoelectric effect

The wave theory of light can explain reflection, refraction, and dispersion as they arise from wave properties such as interference and diffraction.

However, the photoelectric effect involves the emission of electrons from a metal surface when light of sufficient frequency falls on it. This requires particle nature (photons with energy $E = \frac{hc}{\lambda}$), which the wave theory cannot explain.

Hence, the wave theory fails to explain the photoelectric effect.