Introduction:
The Young's double-slit experiment (YDSE) demonstrates the wave-like nature of light and the phenomenon of interference. In this experiment, light passes through two closely spaced slits and produces an interference pattern on a screen. The width of each slit plays a crucial role in determining the number of maxima observed within the central maximum of the single-slit pattern.

Understanding the problem:
We need to determine the width of each slit to obtain 20 maxima of the double-slit pattern within the central maximum of the single-slit pattern. Let's analyze the factors involved.

Key principles:
1. The number of bright fringes (maxima) observed in the double-slit pattern is determined by the phase difference between the waves from the two slits reaching a particular point on the screen.
2. The phase difference depends on the path difference between the two waves, which is directly related to the width of each slit.

Deriving the formula:
To obtain the formula for determining the width of each slit, we can consider the following:
- Consider a point P on the screen where the interference pattern is observed.
- Let the distance between the two slits be 'd' and the distance from the slits to the screen be 'D'.
- The path difference between the waves from the two slits at point P is given by Δx = d sinθ, where θ is the angle made by the line joining the point P and the central maximum with the normal to the slits.
- For constructive interference (maxima), the path difference should be equal to an integral multiple of the wavelength of light (λ).

Calculating the slit width:
1. For the central maximum of the single-slit pattern, the angle θ is very small, so we can approximate sinθ ≈ θ.
2. The path difference for constructive interference in the double-slit pattern within the central maximum of the single-slit pattern is given by Δx = d sinθ = dθ.
3. For the central maximum, the path difference should be equal to an integral multiple of the wavelength: dθ = mλ, where m is the order of the maximum (m = 0 for the central maximum).
4. Rearranging the equation, we get the relation between the width of each slit (d) and the number of maxima (m): d = mλ/θ.

Applying the formula:
1. We need to obtain 20 maxima within the central maximum, so m = 20.
2. The wavelength of light can vary depending on the source, but let's assume it to be 500 nm (5 x 10^-4 mm) for this example.
3. As mentioned earlier, for the central maximum, sinθ ≈ θ. Therefore, we can consider θ = λ/D, where D is the distance from the slits to the screen.
4. Substituting the values into the formula: d = (20 x 5 x 10^-4 mm) / (5 x 10^-4 mm/D).
5. Simplifying the equation, we find that the width of each slit should be equal to the distance from the slits to the screen (D) in order to obtain 20 maxima within the central maximum of the single-slit