As a result of interference of two coherent sources of light, energy is

Options

A. Increased
B. Redistributed and the distribution does not vary with time
C. Decreased
D. Redistributed and the distribution changes with time

Answer

To solve the question regarding the interference of two coherent sources of light and how it affects energy, we can break it down into the following steps:

### Step 1: Understanding Interference
Interference is the phenomenon that occurs when two coherent light sources superimpose on each other. This results in a redistribution of energy across the interference pattern.

**Hint:** Remember that coherent sources maintain a constant phase difference over time.

### Step 2: Coherent Sources
Coherent sources are those that emit light waves with a constant phase difference. This means that if one source is at a certain phase, the other source will always be at a fixed phase relative to it.

**Hint:** Think about how the phase relationship between the two sources affects the resulting interference pattern.

### Step 3: Superposition Principle
According to the superposition principle, the total intensity (or energy) at any point on the screen where the light waves overlap is the sum of the intensities from both sources. This can be expressed mathematically as:
\[ I = I_1 + I_2 + 2\sqrt{I_1 I_2} \cos(\phi) \]
where \( \phi \) is the phase difference between the two waves.

**Hint:** Consider how the cosine term affects the overall intensity based on the phase difference.

### Step 4: Constant Phase Difference
Since the sources are coherent, the phase difference \( \phi \) remains constant over time. This implies that the term \( \cos(\phi) \) does not change, leading to a constant intensity at any point on the screen.

**Hint:** Reflect on how a constant phase difference influences the stability of the interference pattern.

### Step 5: Energy Distribution
As a result of the constant intensity, the energy distribution across the interference pattern does not vary with time. The energy is redistributed, but the total energy remains constant because the phase difference does not change.

**Hint:** Think about how energy conservation plays a role in the interference of light.

### Conclusion
Thus, the answer to the question is that the energy is redistributed but does not vary with time due to the constant phase difference between the coherent sources.

**Final Answer:** The correct option is that energy is distributed but the distribution does not vary with time.