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25.31
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12.66
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79
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25.31
mm
12.66
mm
79
The Single Slit Diffraction Calculator computes the positions of dark fringes (minima) produced when monochromatic light passes through a narrow slit. Using the condition a sin θ = mλ for destructive interference, it finds the diffraction angle, slit width, or wavelength and calculates the angular and linear width of the central maximum on a distant screen.
Single-slit diffraction is a foundational phenomenon in wave optics that demonstrates the wave nature of light. Unlike the sharp geometric shadow predicted by ray optics, a slit of width comparable to the wavelength produces a characteristic pattern of bright and dark bands. The central maximum is twice as wide as all other maxima and contains about 84% of the total transmitted intensity.
When a plane wave of wavelength λ passes through a slit of width a, each point across the aperture acts as a source of secondary wavelets (Huygens' principle). These wavelets interfere destructively at angles where:
$$a\sin\theta = m\lambda, \quad m = \pm1, \pm2, \pm3, \ldots$$
This condition gives the positions of the dark fringes (minima). The integer m is the order of the minimum — there is no m = 0 minimum because zero-order corresponds to the central bright maximum.
The central maximum extends between the first minima on either side:
$$\text{Angular half-width} = \arcsin\left(\frac{\lambda}{a}\right)$$
On a screen at distance L, the width of the central maximum is:
$$W = 2L\tan\left(\arcsin\frac{\lambda}{a}\right)$$
The intensity distribution follows the sinc-squared function:
$$I(\theta) = I_0 \left(\frac{\sin\beta}{\beta}\right)^2, \quad \beta = \frac{\pi a \sin\theta}{\lambda}$$
The ratio a/λ controls the overall pattern: when a >> λ, diffraction is negligible and the pattern approaches a geometric shadow. When a ≈ λ, the light spreads broadly. If a < λ, the first minimum does not exist and the slit acts as a point source radiating in all forward directions.
The position of the m-th minimum on the screen tells you where dark bands appear. Between consecutive minima lie secondary maxima of decreasing intensity. If the computed angle approaches 90°, the minimum barely exists — you are near the limit where mλ/a = 1. The a/λ ratio indicates the diffraction regime: values above 100 mean minimal spreading; values near 1 mean strong diffraction; values below 1 mean the slit is too narrow for minima to form.
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A 632.8 nm HeNe laser through a 50 μm slit produces first minima at ±0.725°. On a screen 1 m away, the central bright band is about 25.3 mm wide — far larger than the 50 μm slit, demonstrating clear diffraction.
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If the second-order minimum appears at 2.5° with 550 nm light, the slit width is about 25.2 μm. This technique is commonly used in optics labs to measure aperture dimensions.
When light passes through a slit whose width is comparable to its wavelength, different parts of the wavefront interfere with each other. Points across the slit act as coherent secondary sources (Huygens' principle), and their wavelets add constructively or destructively depending on the observation angle, creating the characteristic pattern of bright and dark bands.
The central maximum spans from the m = −1 to m = +1 minima, covering an angular range of 2 arcsin(λ/a). Higher-order maxima sit between consecutive minima separated by only arcsin((m+1)λ/a) − arcsin(mλ/a), which is approximately half the central width for small angles.
When a >> λ, the diffraction angles become very small and the pattern collapses to a narrow central peak — essentially a geometric shadow. Diffraction effects become negligible when a/λ > 1000.
When a < λ, the condition a sin θ = λ has no solution because sin θ cannot exceed 1. No minima exist and the slit radiates light nearly uniformly in the forward hemisphere, behaving like a cylindrical point source.
Single-slit diffraction produces a broad envelope pattern from one aperture. Double-slit interference produces closely spaced fringes from two coherent sources. In a real double-slit experiment, both effects combine: the interference fringes are modulated by the single-slit diffraction envelope.
The first secondary maximum (between m = 1 and m = 2 minima) has about 4.7% of the central peak intensity. The second has about 1.7%, and they decrease roughly as 1/(mπ)² for higher orders.
Roboculator Team
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