Diffraction Patterns Due To A Single Slit And A Circular Aperture
Concepts to remember on Diffraction Patterns Due to a ‘Single-Slit’ and a ‘Circular Aperture’:
Single-Slit:
- Diffraction is the spread of light when passing through a slit.
- Diffraction produces a pattern of bright and dark bands.
- Central Bright spot is inversely proportional to the slit’s width. $$W=2λL/a$$
- Dark band $$sinθ_n = nλ/a$$ where n=1,2,3,…
- θn is the angle of the nth dark band from the center.
- λ is the wavelength of light.
- a is the width of the slit.
Circular Aperture:
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Circular apertures produce central bright circles
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First bright ring of radius=$$2.44λf/D$$, where:
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λ is the wavelength of light.
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f is the focal length of the lens.
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D is the diameter of the circular aperture.
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Dark rings are located by:
$$J_\alpha(x_\alpha)=0, x_\alpha=k\pi $$
- $$J_\alpha(x_\alpha)$$ is the Bessel function of the first kind of order α.
- $$x_\alpha$$ is the argument of the Bessel function.
- k is an integer (1, 2, 3,…).
