Intensity decreases in diffraction patterns because constructive interference at points away from the central maximum involves contributions from fewer wave sources across the diffracting aperture, resulting in a lower overall amplitude and thus reduced intensity.
Diffraction is a fundamental wave phenomenon where light bends around obstacles or spreads out after passing through narrow openings. When light diffracts through a single slit, it creates a characteristic pattern of bright and dark fringes on a screen. The intensity of these bright fringes is not uniform; it is highest at the center and decreases significantly for the fringes located further away.
Understanding the Diffraction Pattern
A single-slit diffraction pattern consists of:
- A wide, bright central maximum: The most intense part of the pattern, centered directly behind the slit.
- Secondary maxima (or side lobes): Less intense bright fringes located on either side of the central maximum. Their intensity decreases rapidly as you move away from the center.
- Minima (dark fringes): Regions of zero or near-zero intensity separating the maxima.
The Role of Wave Interference
The formation of this pattern and the variation in intensity are explained by the principle of superposition and Huygens' principle. Huygens' principle suggests that every point on a wavefront can be considered a source of secondary spherical wavelets. When these wavelets pass through a slit, they spread out and interfere with each other at various points on a distant screen.
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Central Maximum: At the very center of the screen, the wavelets from all parts of the slit travel approximately the same distance to reach the point. This means they arrive mostly in phase and interfere constructively. The superposition of waves from all parts of the slit results in the maximum possible amplitude, leading to the highest intensity.
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Secondary Maxima: At points away from the center that correspond to secondary maxima, constructive interference still occurs, but in a less efficient way than at the center. The key reason for the lower intensity here is:
Therefore, the intensity of the secondary maxima is less than that of the central maximum because the constructive interference at these points involves contributions from fewer parts of the slit, leading to a lower resultant amplitude and thus lower intensity.
This happens because while some wavelets arrive in phase to build up a bright fringe, contributions from other parts of the slit cancel each other out through destructive interference. The net constructive interference at secondary maxima involves only a portion of the wavelets from the slit, unlike the central maximum where all wavelets contribute constructively. A smaller number of constructively interfering wavelets means a smaller resultant amplitude and, since intensity is proportional to the square of the amplitude, a significantly lower intensity.
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Minima: At the positions of the dark fringes, wavelets from different parts of the slit interfere destructively. This happens when waves arrive out of phase, effectively canceling each other out and resulting in zero or minimal amplitude and intensity.
Factors Affecting Intensity Distribution
While the fundamental reason for decreasing intensity away from the center is the interference mechanism described, the exact distribution depends on factors like:
- Slit width (a): A narrower slit leads to a wider diffraction pattern where light spreads out more.
- Wavelength (λ): Longer wavelengths diffract more, resulting in wider patterns.
- Distance to the screen (D): Affects the spacing of the fringes.
The table below summarizes the key differences in how wavelets interfere at different parts of the pattern:
| Pattern Feature | Interference Type | Contributing Sources | Resultant Amplitude | Intensity |
|---|---|---|---|---|
| Central Maximum | Fully constructive | All parts of slit | Maximum | Highest |
| Secondary Maxima | Partial constructive (with some destructive) | Fewer parts of slit | Reduced | Lower |
| Minima | Destructive (often complete for idealized slit) | Pairs of parts of slit | Minimal/Zero | Lowest/Zero |
In essence, the decrease in intensity as you move from the central peak to the secondary peaks in a diffraction pattern is a direct consequence of how waves originating from different points within the diffracting aperture interfere, with less effective constructive interference occurring further from the center.
