Explanation

(d) If you divide the original slit into $N$ strips and represents the light from each strip, when it reaches the screen, by a phasor, then at the central maximum in the diffraction pattern you add $N$ phasors, all in the same direction and each with the same amplitude. The intensity is therefore $N^{2}$. If you double the slit width, you need $2N$ phasors, if they are each to have the amplitude of the phasors you used for the narrow slit. The intensity at the central maximum is proportional to $(2N)^{2}$ and is, therefore, four times the intensity for the narrow slit