To solve the problem of how the image of a pinhole of width \(10^3 \, \text{Å}\) (angstroms) appears on a screen when sunlight is incident on it, we can follow these steps:
### Step-by-Step Solution:
1. **Convert the Width of the Pinhole**:
The width of the pinhole is given as \(10^3 \, \text{Å}\).
\[
1 \, \text{Å} = 10^{-10} \, \text{m} \implies 10^3 \, \text{Å} = 10^3 \times 10^{-10} \, \text{m} = 10^{-7} \, \text{m}
\]
**Hint**: Always convert units to standard SI units for calculations.
2. **Understand the Wavelength of Sunlight**:
The wavelength of sunlight ranges from approximately \(400 \, \text{nm}\) to \(700 \, \text{nm}\).
\[
400 \, \text{nm} = 4 \times 10^{-7} \, \text{m} \quad \text{and} \quad 700 \, \text{nm} = 7 \times 10^{-7} \, \text{m}
\]
**Hint**: Knowing the range of wavelengths helps in understanding diffraction effects.
3. **Compare Pinhole Width and Wavelength**:
The width of the pinhole \(10^{-7} \, \text{m}\) is comparable to the wavelengths of sunlight, which range from \(4 \times 10^{-7} \, \text{m}\) to \(7 \times 10^{-7} \, \text{m}\). This indicates that diffraction will occur since the width of the slit is less than or equal to the wavelength of light.
**Hint**: Diffraction occurs when the size of the aperture is on the order of the wavelength of the light.
4. **Describe the Diffraction Pattern**:
When light passes through the pinhole, it will diffract. The central spot will appear white due to the combination of all colors of light, while the edges will show a spectrum of colors due to the different wavelengths bending at different angles.
**Hint**: The central spot is a result of constructive interference, while the colors around it result from the varying degrees of diffraction.
5. **Conclusion on the Image**:
The image on the screen will consist of a diffuse central white spot surrounded by colored regions. The central spot is white because it is the result of all colors combining, and the surrounding colors are due to the diffraction of different wavelengths.
**Hint**: Remember that the image formed is not a sharp geometrical image but a result of wave phenomena.
### Final Answer:
The image of the pinhole will be a diffuse central white spot with colored regions surrounding it, confirming that the correct options are:
- A diffuse central spot (white in color)
- Diffused colored regions around the sharp central spot.
