In Young's double-slit experiment (YDSE), when the width of both slits is doubled, the central maximum remains unchanged in terms of its position and intensity. The central maximum refers to the bright central region observed on the screen when light passes through the double slits.
The position of the central maximum is determined by the path length difference between the two slits, which remains the same when the slit widths are doubled. Therefore, the central maximum remains at the same location on the screen.
The intensity of the central maximum is determined by the superposition of the waves from the two slits. When the slit widths are doubled, the amplitudes of the waves passing through each slit also double. However, the intensity is proportional to the square of the amplitude. So, when the amplitudes are doubled, the intensity becomes four times greater. Consequently, the intensity of the central maximum also remains unchanged when the slit widths are doubled.
It's worth noting that the interference pattern beyond the central maximum, consisting of dark and bright fringes, may undergo changes when the slit widths are altered. However, the central maximum remains unaffected.