In standard Young's double-slit experiment when sources of light are coherent, then intensity at the centre of the screen is found to be `I_1` and when sources are incoherent, then intensity at the centre is found to be `I_2`. Calculate `I_1//I_2`.
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Explanation

To solve the problem of calculating the ratio \( \frac{I_1}{I_2} \) in Young's double-slit experiment, we will analyze the situation for both coherent and incoherent light sources.

### Step-by-Step Solution:

1. **Understanding the Setup**:
In Young's double-slit experiment, we have two slits (S1 and S2) illuminated by a coherent light source. The light waves from these slits interfere with each other, creating a pattern of bright and dark fringes on a screen.

2. **Intensity with Coherent Sources**:
When the sources are coherent, the intensity at the center of the screen (where the path difference is zero) is given by:
\[ I_1 = 4I \]
Here, \( I \) is the intensity of light from each slit. The factor of 4 comes from the constructive interference of the two coherent waves.

3. **Intensity with Incoherent Sources**:
When the sources are incoherent, the light from the two slits does not interfere in the same way. Instead, the intensities simply add up:
\[ I_2 = I + I = 2I \]

4. **Calculating the Ratio**:
Now, we can find the ratio \( \frac{I_1}{I_2} \):
\[ \frac{I_1}{I_2} = \frac{4I}{2I} = 2 \]

### Final Answer:
Thus, the ratio \( \frac{I_1}{I_2} \) is:
\[ \frac{I_1}{I_2} = 2 \]