If $I_{0}$ is the intensity of the central diffraction band in the single slit diffraction experiment, then the intensity of the band when the slit width is doubled will be:

$4 I_{0}$

The correct answer is Option (4) → $4 I_{0}$

The intensity of the central diffraction band is proportional to the square of slit width -

$I_0∝a^2$

if slit width is doubled $(a'=2a)$

$I'∝(2a)^2=4a^2$

$∴I'=4I_0$