At any point P on the back screen, there is light from two different sources: the two slits.
The line joining P to the point exactly between the two slits intersects the perpendicular
to the front screen at an angle.
We will assume that the two screens are very far apart—somewhat more precisely, that L
is much bigger than d. For this reason, this analysis is often referred to as the “far-field
approximation.” This approximation allows us to assume that angles and , formed by
the lines connecting each of the slits to P, are both roughly equal to. The light from the
right slit—the bottom slit in our diagram—travels a distance of l = d sin more than the
light from the other slit before it reaches the screen at the point P.
As a result, the two beams of light arrive at P out of phase by d sin. If d sin = (n + 1/2)
, where n is an integer, then the two waves are half a wavelength out of phase and will
destructively interfere. In other words, the two waves cancel each other out, so no light
hits the screen at P. These points are called the minima of the pattern.
On the other hand, if d sin = n , then the two waves are in phase and constructively
interfere, so the most light hits the screen at these points. Accordingly, these points are
called the maxima of the pattern.