If $I_0$ is the intensity of the principal maximum in the single slit diffraction pattern, then what will be its intensity when the slit width is doubled?

In diffraction, the amplitude $A$ of the central maximum is proportional to the slit width $a$ ($A\propto a$).Since Intensity $I\propto A^2$, then $I\propto a^2$.If the slit width is doubled ($a^{\prime }=2a$):
$$I^{\prime }\propto (2a{)}^2=4a^2=4I_0$$
The intensity of the central maximum increases by a factor of 4.