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

Explanation

To solve the problem of how sunlight incident on a slit of width \(10^4 \, \text{Å}\) will appear, we can follow these steps:

### Step 1: Understand the given parameters
We are given a slit width \(A = 10^4 \, \text{Å}\). We need to convert this to meters for better understanding:
\[ 1 \, \text{Å} = 10^{-10} \, \text{m} \]
Thus,
\[ A = 10^4 \, \text{Å} = 10^4 \times 10^{-10} \, \text{m} = 10^{-6} \, \text{m} = 1 \, \mu\text{m} \]

### Step 2: Determine the wavelength of sunlight
Sunlight is composed of visible light, which has a wavelength range approximately between \(4000 \, \text{Å}\) to \(8000 \, \text{Å}\):
\[ 4000 \, \text{Å} = 4 \times 10^{-7} \, \text{m} \quad \text{and} \quad 8000 \, \text{Å} = 8 \times 10^{-7} \, \text{m} \]

### Step 3: Compare the slit width with the wavelength
Now, we compare the width of the slit \(A\) with the wavelengths of sunlight:
- The slit width \(A = 1 \, \mu\text{m} = 10^{-6} \, \text{m}\)
- The wavelength of sunlight ranges from \(4 \times 10^{-7} \, \text{m}\) to \(8 \times 10^{-7} \, \text{m}\)

Since \(10^{-6} \, \text{m} > 8 \times 10^{-7} \, \text{m}\), we conclude that the slit width is greater than the wavelength of sunlight.

### Step 4: Analyze the diffraction condition
According to the principles of wave optics, diffraction effects become significant when the slit width is comparable to or smaller than the wavelength of light. In this case, since the slit width is greater than the wavelength, diffraction will not occur.

### Step 5: Determine the appearance of the image
Because there is no diffraction, the image formed on the screen will be a sharp and clear representation of the slit itself. The light passing through the slit will not spread out, and thus the image will be a fine, sharp slit.

### Conclusion
The image seen through the slit will be a sharp white line at the center of the screen.

### Final Answer
The image seen through the slit shall be a sharp white line at the center.

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