If the width of the slit is made double the original width in a single slit diffraction experiment, the size of the central diffraction band will become half of the original value.

Since, we have the first minima occurs at

b sinθ = nλ

If we take n = 1, for the central maxima

Where,

θ is the angle between the wave ray at the point on the screen and the normal at the centre of the slit.

The space between the first minimums contains the central maxima.

If we increase the width will thus decrease.

The intensity depends on the amplitude as

I ∝ A²

Thus, when we double the size of the slit we double the amplitude and hence, the intensity becomes four times that of original intensity.

When central maxima are reduced to half, logically the same light has to be distributed in a smaller region. Increasing the intensity of central band maxima will make the intensity four times that of the original intensity.