Physics

Single-slit diffraction depends on the competition between the slit width $a$ and the wavelength $\lambda$. The position of dark fringes is determined by the condition $a \sin\theta = m\lambda$, which tells you where destructive interference occurs. When you double the slit width, the angle $\theta$ at which this condition is satisfied must shrink by half to compensate—so the dark fringe moves closer to the center. The distance on the screen scales directly with the angle, meaning the first dark fringe moves to half its original distance.

Single-slit diffraction depends on the competition between the slit width $a$ and the wavelength $\lambda$. The position of dark fringes is determined by the condition $a \sin\theta = m\lambda$, which tells you where destructive interference occurs. When you double the slit width, the angle $\theta$ at which this condition is satisfied must shrink by half to compensate—so the dark fringe moves closer to the center. The distance on the screen scales directly with the angle, meaning the first dark fringe moves to half its original distance.