How Wide Must a Narrow Slit Be for First Diffraction Minimum?

Understanding Diffraction and Slit Width

Diffraction: Diffraction is a phenomenon where waves spread out as they encounter obstacles or openings. In the case of light, it results in patterns of light and dark areas when light passes through a narrow slit.

Calculating the Slit Width

The formula for calculating the slit width in a diffraction pattern is inversely related to the central maximum width. This means that as the slit width decreases, the central maximum widens, and vice versa.

Given that the diffraction minimum occurs at ±12° with a laser light of 633 nm, the width of the narrow slit is 3 μm. This can be derived from the diffraction formula and the observed angular width of the central maximum.

Behavior of Light in Diffraction Patterns

As we move farther from the central maximum in a single-slit diffraction pattern, both the width and intensity decrease compared to a double-slit diffraction pattern. This behavior can be attributed to the bending of light as the aperture's size decreases.

Implications for Monochromatic Light

When monochromatic light is passed through a single slit, a diffraction pattern similar to the double-slit experiment is observed. By analyzing the diffraction patterns, we can determine the slit width required for different diffraction phenomena.

Therefore, in the case of a narrow slit producing the first diffraction minimum at ±12° with laser light of 633 nm, the width of the slit needs to be 3 μm to achieve this specific diffraction pattern.