Two narrow slits with a center-to-center distance of 0.48 mm are illuminated with coherent light

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Two narrow slits with a center-to-center distance of 0.48 mm...

Two narrow slits with a center-to-center distance of $0.48 \mathrm{mm}$ are illuminated with coherent light at normal incidence. The intensity of the light falling on a screen $5.0 \mathrm{m}$ away is shown in the figure, where $x$ is the distance from the central maximum on the screen. Sketch a graph of the intensity versus $x$ if only one slit were open.

Two narrow slits with a center-to-center distance of $0.48 \mathrm{mm}$ are illuminated with coherent light at normal incidence. The intensity of the light falling on a screen $5.0 \mathrm{m}$ away is shown in the figure, where $x$ is the distance from the central maximum on the screen.
Sketch a graph of the intensity versus $x$ if only one slit were open.

Key Concepts

Single-Slit Diffraction

This is the phenomenon where light spread occurs when passing through a narrow opening. The light waves emerging from different parts of the slit interfere with each other, creating a pattern on a distant screen that features a central maximum of brightness with diminishing side maxima. The intensity distribution follows a characteristic envelope where the central peak is the brightest, and the light intensity falls off away from the center.

Fraunhofer Diffraction

In the far-field regime, where the screen is placed at a distance much larger than the slit width, the diffraction pattern can be analyzed using Fraunhofer diffraction. This theory simplifies the mathematics and shows that the observed intensity pattern is proportional to the square of the Fourier transform of the aperture function, which in the case of a single slit produces a predictable central maximum and secondary fringes.

Interference versus Diffraction

When multiple slits are used, interference between the waves from each slit creates fine fringes that are modulated by the broader single-slit diffraction envelope. In contrast, with only one slit open, the resulting pattern is solely due to diffraction effects. Understanding this distinction is critical when analyzing or sketching intensity distributions, as the removal of interference fine structure leaves only the diffraction envelope behind.

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