The correct answer is option C: the resultant amplitude in interference with two coherent sources depends on both intensity and phase difference.

To understand why, let's break down the concept of interference and coherent sources.

Interference:
Interference occurs when two or more waves overlap and combine with each other. In the case of light waves, interference can result in the formation of bright and dark regions known as interference fringes. Interference can be constructive, where the waves reinforce each other and result in a larger amplitude, or destructive, where the waves cancel each other out and result in a smaller amplitude.

Coherent Sources:
Coherent sources are sources that emit waves with a constant phase relationship. In other words, the waves emitted by coherent sources have a fixed phase difference between them. This phase difference determines how the waves will interfere with each other.

Explanation:

Intensity:
The intensity of a wave is the power carried by the wave per unit area. In the case of interference, the intensity of the resultant wave is directly related to the amplitude of the wave. When two waves interfere constructively, their amplitudes add up, resulting in a higher intensity. Conversely, when two waves interfere destructively, their amplitudes subtract, resulting in a lower intensity.

Phase Difference:
The phase difference between two waves determines the nature of their interference. When two coherent waves have a phase difference of an integer multiple of the wavelength (e.g., 0, λ, 2λ, etc.), they are said to be in phase and interfere constructively. This results in maximum constructive interference and a larger amplitude.

On the other hand, when the phase difference between two coherent waves is an odd multiple of half the wavelength (e.g., λ/2, 3λ/2, etc.), they are said to be out of phase and interfere destructively. This results in maximum destructive interference and a smaller amplitude.

Combining Intensity and Phase Difference:
The resultant amplitude in interference depends on both the intensity and the phase difference. If two waves with large amplitudes interfere constructively, the resultant amplitude will be larger. Conversely, if two waves with large amplitudes interfere destructively, the resultant amplitude will be smaller.

Similarly, if two waves with small amplitudes interfere constructively, the resultant amplitude will still be small. And if two waves with small amplitudes interfere destructively, the resultant amplitude will be even smaller.

Therefore, to determine the resultant amplitude in interference, both the intensity and the phase difference between the waves must be taken into account. Hence, the correct answer is option C: the resultant amplitude in interference with two coherent sources depends on both intensity and phase difference.