How is intensity distribution calculated in single-slit diffraction?

Intensity distribution in single-slit diffraction is calculated using the Fraunhofer diffraction equation.

In single-slit diffraction, light waves passing through a narrow slit interfere with each other, creating a pattern of bright and dark fringes on a screen. The intensity distribution of this pattern can be calculated using the Fraunhofer diffraction equation, which is derived from the principles of wave interference and the Huygens-Fresnel principle.

The Huygens-Fresnel principle states that every point on a wavefront can be considered as a source of secondary wavelets, which spread out in all directions with a speed equal to the speed of propagation of the waves. When light passes through a narrow slit, these secondary wavelets interfere with each other, creating a diffraction pattern. This concept is elaborated in the section discussing wave parameters.

The Fraunhofer diffraction equation is used to calculate the intensity distribution of this pattern. The equation is I(θ) = I0 (sin(β)/β)², where I(θ) is the intensity at an angle θ from the central maximum, I0 is the maximum intensity, and β = πa sin(θ)/λ, where a is the width of the slit and λ is the wavelength of the light. The phenomenon of how these patterns form can further be explored in diffraction patterns.

The equation shows that the intensity of the light decreases as the angle θ increases, creating a central bright fringe surrounded by alternating dark and bright fringes. The width of these fringes depends on the width of the slit and the wavelength of the light.

To calculate the intensity distribution, you would first calculate β for each angle θ, then substitute β into the Fraunhofer diffraction equation to find the intensity at that angle. By doing this for a range of angles, you can create a graph of intensity distribution. Additionally, understanding the principles behind the Young's double slit experiment can complement your knowledge of wave interference and pattern formation.

IB Physics Tutor Summary: In single-slit diffraction, we calculate the spread of light intensity using the Fraunhofer diffraction equation. This is based on the Huygens-Fresnel principle, where each point of a wavefront acts as a source of new waves. The equation helps us understand how light intensity changes at different angles from the central bright spot, showing a pattern of bright and dark bands.