The distance from the slit significantly influences the diffraction pattern by modifying both its size and intensity.

Diffraction is a wave phenomenon that occurs when a wave encounters an obstacle or passes through a slit. As the wave interacts with the slit or obstacle, it bends and spreads out, resulting in a characteristic diffraction pattern. This pattern is defined by a central bright fringe (known as the maximum) surrounded by alternating dark and bright fringes (minima and maxima).

The distance from the slit to the screen where the diffraction pattern is observed plays a crucial role in determining the dimensions and intensity of the pattern. As this distance, denoted as $L$, increases, the diffraction pattern expands, causing the fringes to become wider. This expansion occurs because the diffracted waves have more space to spread out and interfere with one another. Consequently, the central maximum widens, and the intensity of the light diminishes as the energy is distributed over a larger area.

Conversely, when the distance from the slit to the screen decreases, the diffraction pattern contracts, and the fringes become narrower. In this case, the central maximum becomes more concentrated, and the light’s intensity increases as the energy is focused within a smaller region.

The relationship between the distance from the slit and the size of the diffraction pattern can be quantified using the formula for single-slit diffraction:

In this formula, $\lambda$ represents the wavelength of the light, $w$ is the width of the central maximum, $L$ is the distance from the slit to the screen, and $d$ is the width of the slit. From this relationship, it is evident that as $L$ increases, the width $w$ also increases, indicating a larger diffraction pattern.

In simpler terms, the distance from the slit to the observation screen affects both the size and brightness of the diffraction pattern. As this distance increases, the pattern spreads out, causing the light fringes to widen and appear less intense. Conversely, a shorter distance results in a tighter and brighter pattern. This phenomenon stems from the interplay of how light waves spread and interfere with one another.