Consider sunlight incident on a slit of width `10^(4) Å` . The image seen through the slit shall

Options

A. be a fine sharp slit white in colour at the centre
B. a bright slit white at the centre diffusing to zero intensities at the edges
C. a bright slit white at the centre diffusing to regions of different colours
D. only be a diffused slit white in colour

Answer

To solve the problem, we need to analyze the situation of sunlight passing through a slit of width \(10^4 \, \text{Å}\) (angstroms).

### Step-by-Step Solution:

1. **Identify the Width of the Slit**:
The width of the slit is given as \(10^4 \, \text{Å}\). Converting this to a more manageable unit:
\[ 10^4 \, \text{Å} = 10,000 \, \text{Å} \]

2. **Understand the Visible Light Range**:
The visible spectrum of light ranges approximately from \(3900 \, \text{Å}\) to \(7000 \, \text{Å}\). This means that the light we can see falls within this range.

3. **Compare the Slit Width with the Visible Light Range**:
Since the width of the slit \(10,000 \, \text{Å}\) is much larger than the maximum wavelength of visible light (\(7000 \, \text{Å}\)), we can conclude:
\[ \text{Width of slit} \gg \text{Wavelength of visible light} \]

4. **Determine the Effect of the Slit Width**:
When the slit width is significantly larger than the wavelength of light, diffraction effects are negligible. This means that light will pass through the slit without spreading out significantly.

5. **Analyze the Resulting Image**:
Since sunlight is composed of all colors (white light), and there is no significant diffraction, the light will appear as a sharp image. Thus, the image seen through the slit will be:
\[ \text{A fine sharp white light at the center} \]

6. **Select the Correct Option**:
Based on our analysis, the correct description of the image seen through the slit is:
- A fine sharp slit white in color at the center.

### Conclusion:
The correct answer is the first option: "A fine sharp slit white in color at the center."