# Diffraction

Diffraction occurs “when waves pass through small openings, around obstacles, or past sharp edges. When an opaque object is placed between a point source of light and a screen, no sharp boundary exists on the screen between a shadowed region and an illuminated region. The illuminated region above the shadow of the object contains alternating light and dark fringes. Such a display is called a diffraction pattern.” [1]

## Young's Double Slit Experiment

Consider two slits a distance  apart and a screen a distance  from the slits. To find the positions of the maxima (brightest points) on the screen, the path difference from each of the slits,  must be an integer number of wavelengths . The the angle between a ray of light from one slit and the normal of that slit is , then for constructive interference:



If  is the distance from the centre of the screen to a maxima, then .

If we assume the screen is much further away than the slits, such that  then using the small angle approximation, , rearranging gives:



where

 is the distance on the screen to the nth maxima
 is the wavelength

For destructive interference, the path difference must be . This gives:



for the nth minima.

## References

1. Halliday, Resnik, Walker: Fundamentals of Physics, 8th edition. p. 1200