The correct answer is option 'C', which states that the phenomenon of interference is based on the conservation of energy. Interference is a fundamental concept in physics that occurs when two or more waves interact with each other. It is observed in various branches of science, including optics, acoustics, and quantum mechanics.

Interference can be explained using the principle of superposition, which states that when two or more waves meet at a point in space, their amplitudes add up algebraically. This means that the displacement of the medium at that point is the sum of the displacements caused by each individual wave.

To understand why interference is based on the conservation of energy, let's examine the key points:

1. Principle of Superposition:
- When two waves meet, their amplitudes add up algebraically.
- The displacement of the medium at a point is the sum of the displacements caused by each individual wave.

2. Conservation of Energy:
- Energy is a fundamental quantity that cannot be created or destroyed; it can only be transferred or transformed from one form to another.
- In the case of waves, energy is carried by the oscillations of particles or fields in the medium through which the waves propagate.

3. Interference and Energy Conservation:
- When two waves interfere constructively, their amplitudes add up, resulting in a larger displacement of the medium at that point.
- This increase in displacement corresponds to an increase in the energy carried by the waves at that point.
- Similarly, when two waves interfere destructively, their amplitudes cancel out, resulting in a smaller displacement of the medium at that point.
- This decrease in displacement corresponds to a decrease in the energy carried by the waves at that point.

4. Energy Redistribution:
- Interference involves the redistribution of energy between different regions of space.
- When waves interfere constructively, energy is redistributed from regions of lower intensity to regions of higher intensity.
- Conversely, when waves interfere destructively, energy is redistributed from regions of higher intensity to regions of lower intensity.

5. Energy Conservation in Interference:
- The conservation of energy requires that the total energy of the waves before and after interference remains the same.
- This means that the energy redistributed during interference must be balanced by corresponding changes in the energy of the individual waves.

In conclusion, the phenomenon of interference is based on the conservation of energy. When waves interfere, their amplitudes add up or cancel out, resulting in changes in the displacement and energy of the medium at different points. The principle of superposition allows us to understand and analyze these changes, while the conservation of energy ensures that the total energy of the waves remains constant throughout the interference process.