Young's Double Slit Experiment

Double Slit Experiment

The phenomenon of interference arises in both classical and quantum physics. In everyday life, more general interference effects can be seen, for example, patterns formed on the surface of a body of water when the wakes of two passing ships merge and pass through each other. Mathematically, this effect is due to the addition of corresponding physical quantities, such as wave height in the case of surface waves on water, to produce modulated patterns. These patterns can be made to exhibit clear regularities, particularly in simple situations. This effect has most often been studied by passing light through a pair of slits in a diaphragm, due in particular to an influential experiment in the early nineteenth century performed by Thomas Young in which a double-slitted screen was used to produce an interference pattern. This pattern was readily explained in terms of classical light beams as waves traveling in the classical electromagnetic field. However, there are important differences between quantum interference and the more familiar effect of interference in classical physics. In particular, in quantum mechanical situations there are complex amplitudes, which therefore mathematically involve a phase contribution, that add, giving rise to characteristically quantum behavior, rather than real-valued intensities which are sometimes also referred to as amplitudes which add as in the case of water waves. It is important, from the ontological perspective, to recognize that quantum mechanical quantities do not directly describe substances, unlike in the classical ether theory of Christiaan Huygens, for example.

Important equations

When working on a problem it is important to explain the geometry and the equations that are derived from the geometry

Sinθ = nλ/d (equation 1)

d sinθ = nλ (equation 2)

n = the number of complete waves in the path differance (must be a whole interger)

λ = the wave lenght of the monochromic light

d = the distance between slits

This equation is refering to the path differance in bottom diagram (diagram b)  Sinθ is equal to opposite over hypothenus.  That means that Sinθ is equal to d (which is the distance between the two slits) over the path differeance.  If the path differance is a complete wavelength or a multple of a complete wavelengths (λ is the wavelength and n is a whole interger) then when the two rays meet on the screen it will produce constructive interferance producing what is called a "bright" spot.  As we move away from the center the next bright spot (n = 1) the path differance is one wavelength, the next bright spot (n =2) has a path differance of two wavelenghts, etc.....  We simply move the d to the other side to get the second equation

Sinθ = D/y (equation 3)

D = the distance from the screen with the two slits to screen where the fringes are projected on.

y = the distance from the center bright spot to the next fringe

This equation is not listed as a "needed" equation in most texts when it comes to the double slit experiment.  The equation is included here because it will be needed to related fringe location and distance to the screen to wavelength.  D is the distance to the screen, and y is the distance from the center bright spot to the another bright spot (it doesn't have to the 1st)

y/D = nλ/d (equation 4)

s = λD/d (equation 5)

s = thhe distance from the center bright spot to the first bright spot.

Because the angles in equations 1 and 3 are equal, we can set the second half of equation 1 equal to the second half of equation 3 to get equation four.  This equation is very important because it is the equation for any possable bright spots.

Equation 5 is the expression for a the center bright fringe to the first bright fringe.

y/D = (n +1/2)λ/d

The Last equation aplies all of the geometry and concepts of the frist four equations but instead of looking for a full wavelenght differance, we are now concerned with a one and a half of a wave (hence the n + 1/2).  With the path differance at least a half of a wave it would result in destructive interferance and therefor a dark fringe.