http://www.ck12.org Chapter 15. Diffraction and Interference of Light
In the early 1800s, light was assumed to be a particle. There was a significant amount of evidence to point to
that conclusion, and famous scientist Isaac Newton’s calculations all support the particle theory. In 1803, however,
Thomas Young performed his famous Double Slit Experiment to prove that light was a wave. Young shined a light
onto the side of a sealed box with two slits in it, creating an interference pattern on the inside of the box opposite
the slits. As seen above, interference patterns are characterized by alternating bright and dark lines. The bright lines
are a result of constructive interference, while the dark lines are a result of destructive interference. By creating this
interference pattern, Young proved light is a wave and changed the course of physics.
Calculating Wavelength from Double Slit Pattern
Using the characteristics of the double slit interference pattern, it is possible to calculate the wavelength of light
used to produce the interference. To complete this calculation, it is only necessary to measure a few distances. As
can be seen below, five distances are measured. In the sketch,Lis the distance from the two slits to the back wall
where the interference pattern can be seen.dis the distance between the two slits. To understandx, look again at the
interference pattern shown above. The middle line, which is the brightest, is called thecentral line. The remaining
lines are calledfringes. The lines on either side of the central line are called the first order fringes, the next lines are
called the second order fringes, and so on.xis the distance from the central line to the first order fringe.
r 1 andr 2 are the distances from the slits to the first order fringe. We know that the fringes are a result of constructive
interference, and that the fringe is a result of the crest of two waves interfering. If we assume thatr 2 is a whole
number of wavelengths (confirm for yourself that this is a logical assumption), thenr 1 must be one more wavelength.
This is becauser 1 andr 2 are the distances to the first order fringe. Mathematically, we can let
r 2 =nλandr 1 =nλ+λ, whereλis the wavelength andnis a constant.
Using this relationship, we determine thatr 1 −r 2 =λ.
Looking again at the diagram, the red and blue triangles are similar, which means that the ratios of corresponding
sides are the same. The ratio ofxtoLin the red triangle is equal to the ratio ofλtodin the blue triangle. For
proof of this, visit http://www.physicsclassroom.com/class/light/u12l3c.cfm. From this, we can determine that the
wavelength is dependent onx, d,andL: