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:

• Circular apertures produce central bright circles

• First bright ring of radius=$$2.44λf/D$$, where:

• λ is the wavelength of light.

• f is the focal length of the lens.

• D is the diameter of the circular aperture.

• 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,…).