Problem

The key insight is that fringe width depends inversely on slit separation—when slits are farther apart, the light waves from each slit diverge less before meeting, so the interference pattern compresses. Specifically, fringe width $\beta = \frac{\lambda D}{d}$, where $d$ is slit separation. If you triple $d$, you're dividing the denominator by 3, so the fringe width becomes one-third its original value.

The key insight is that fringe width depends inversely on slit separation—when slits are farther apart, the light waves from each slit diverge less before meeting, so the interference pattern compresses. Specifically, fringe width $\beta = \frac{\lambda D}{d}$, where $d$ is slit separation. If you triple $d$, you're dividing the denominator by 3, so the fringe width becomes one-third its original value.