In Young's double slit experiment, if the two slits are illuminated with separate sources, no interference pattern is observed because

Options

A. there will be no constant phase difference between the two waves
B. the wavelength are not equal
C. the amplitudes are not equal
D. none of the above

Answer

### Step-by-Step Solution:

1. **Understanding Young's Double Slit Experiment**: In this experiment, light from a coherent source passes through two closely spaced slits (S1 and S2) to produce an interference pattern on a screen. The key to observing this pattern is that the light waves from both slits must be coherent.

2. **Definition of Coherent Sources**: Coherent sources are those that emit waves with a constant phase difference, the same frequency, and the same wavelength. This ensures that the waves can interfere constructively (creating bright fringes) and destructively (creating dark fringes).

3. **Separate Sources and Coherence**: If the two slits are illuminated by separate light sources, these sources may not maintain a constant phase relationship. This lack of coherence means that the light waves from the two slits will have varying phase differences over time.

4. **Resulting Interference Pattern**: Because of the varying phase differences, the condition for constructive and destructive interference will not be consistently met. As a result, no stable interference pattern (i.e., no distinct bright and dark fringes) will be observed on the screen.

5. **Conclusion**: Therefore, the reason no interference pattern is observed when the two slits are illuminated by separate sources is that the light waves from these sources are not coherent, leading to a lack of a constant phase difference.

### Final Answer:
In Young's double slit experiment, if the two slits are illuminated with separate sources, no interference pattern is observed because the light waves from the two sources are not coherent, resulting in a varying phase difference.

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