**Two-slit interference**

The prototypical example of interference is the two-slit experiment. Consider monochromatic (single wavelength) light incident on two narrow slits as shown.

Wave crests leaving the upper and lower
slits at a given instant of time are indicated by the violet and green lines.
In the directions shown by the blue lines, the violet and green waves rise and fall
together, giving **constructive interference** in those directions.
Midway between those directions, the two contributions are 180 degrees out of
phase, so they tend to cancel one another. The result is that if a screen is placed to
the right, an **interference pattern** is seen: there are peaks in the
brightness in the direction of the blue arrows, with dark bands in between.

To solve for the angular position of the maxima, consider two rays emited at an angle
q from each of the slits.
The screen is assumed to be very far away (in comparison to the distance between the slits),
so the rays from to the two slits to any given point on the screen are nearly parallel.
If the distance
**D****x**
is an integer number * m* of wavelengths, a bright maximum
will appear on the screen. The formula for the positions of those maxima is

where * m* = 0,1,2,3,...

A second formula is needed to relate the positions on the screen to the angle q. The screen, the center line, and the line to an arbitrary point on the screen form a right triangle, leading to the formula

**tan** **q**
** = y / L**

where ** L** is the distance from the slits to the screen and

**How bright are the maxima** you may ask? -- Equal contributions
from each of two slits makes the *E* and *B* fields twice as
large as they would have been with only one slit open. The light *intensity*
(measured in W/m^2) is proportional to
*E ^{2}* and