Lectures on Physics has been derived from Benjamin Crowell's Light and Matter series of free introductory textbooks on physics. See the editorial for more information....

Spacing of the fringes at small angles

At small angles, we can use the approximation sin θ ≈ θ , which is valid if θ is measured in radians. The equation for double-slit diffraction becomes simply

which can be solved for θ to give

The difference in angle between successive fringes is the change in θ that results from changing m by plus or minus one,

For example, if we write θ7 for the angle of the seventh bright fringe on one side of the central maximum and θ8 for the neighboring one, we have

and similarly for any other neighboring pair of fringes.

Last Update: 2010-11-11