Huygen's wave theory, proposed by Dutch physicist Christiaan Huygens in the 17th century, was an important milestone in understanding the nature of light. However, there are certain phenomena that Huygen's wave theory could not adequately explain. Let's discuss each of these phenomena in detail:

1. Reflection:
- Reflection occurs when light waves strike a surface and bounce back.
- According to Huygen's wave theory, each point on a wavefront acts as a source of secondary wavelets that propagate in all directions.
- However, this theory could not explain why light waves always obey the law of reflection, which states that the angle of incidence is equal to the angle of reflection.
- Later, the particle nature of light was introduced by the photoelectric effect and explained reflection based on the behavior of photons.

2. Refraction:
- Refraction is the bending of light as it passes from one medium to another with a different refractive index.
- Huygen's wave theory suggested that the speed of light changes when it enters a different medium, causing a change in direction.
- However, it failed to explain why light waves bend towards the normal when entering a denser medium and away from the normal when entering a less dense medium.
- The particle nature of light, combined with the wave nature, was later used to explain refraction using the concept of photons and their interaction with the atoms in the medium.

3. Diffraction:
- Diffraction refers to the bending or spreading of light waves around obstacles or through narrow openings.
- Huygen's wave theory could not provide a satisfactory explanation for diffraction phenomena.
- It assumed that light waves only traveled in straight lines and did not account for their ability to bend around obstacles or spread out after passing through narrow slits.
- Later, the wave nature of light was further explored by Thomas Young's double-slit experiment, which provided strong evidence for the wave-like behavior of light and explained diffraction.

4. Polarization:
- Polarization refers to the orientation of the electric field vector of a light wave.
- Huygen's wave theory could not explain the phenomenon of polarization.
- It assumed that light waves oscillate in all possible directions perpendicular to the direction of propagation.
- However, polarized light waves have their electric field vectors oscillating in a specific plane.
- The concept of polarization was later explained by the wave theory of light through the superposition of multiple waves and their interactions.

In summary, while Huygen's wave theory was a significant advancement in understanding the nature of light, it could not fully explain certain phenomena such as reflection, refraction, diffraction, and polarization. Later developments in the understanding of light, including the particle-wave duality and the concept of photons, helped provide a more comprehensive explanation for these phenomena.