If light is incident on a single narrow slit, light is diffracted at the edges of the slit, and interference occurs between light from different parts of the slit. For some angles
from the normal to the slit, destructive interference occurs, with light at the right hand side of the slit having half a wavelength path difference with light at the centre.
If the optical path length of two rays differs by
the two rays interfere destructively. For the waves at the right hand side and centre in the diagram above to be out of phase we need
or
If these two rays interfere destructively, so do rays 2 and 8, 3 and 9, …,, 6 and 12, so that light from one half of the slit interferes destructively with light from the other half. Destructive interference occurs for any angle satisfying
where n=1,2,3,... For any other angle only partial destructive interference occurs. A typical interference pattern is shown below.
When
the equation
has no solution and no dark fringes are produced.