Why does a single slit diffraction pattern occur?

When light passes through a narrow gap it will diffract (spread out). This means the light reaching the screen could have come from anywhere within the slit. If one wavefront passes through the left of the slit and another through the right, when they meet they will have travelled slightly different distances - these distances are called the path length and the difference between them is the path difference. 

 

As the waves meet, they will interfere (their displacements add together). If the wavefronts are no longer alligned due to the path difference, the waves can begin to cancel out casing dark spots to appear. No light appears on the screen when the two waves meeting are antiphase (peak meets a trough) as the dispacements always sum to zero. This occurs when the path difference is a half-integer number of wavelengths. A bright spot appears when the waves are in phase and the paths difference is equal to an integer multiple of wavelengths.

 

For dark fringes:

a*sin(θ) = nλ      (a is the width of the slit. λ is the wavelenth of the light. n is any integer)

A little note: monochromatic (light of a single wavelengh) is used to make the dark and bright spots clear to see. Look at the equation and think about why light of many colours would make this difficult.