That double slit experiment is not without reason one of the key experiments in physics. With this experiment, Thomas Young succeeded in 1802 in experimentally proving the wave properties of light for the first time.
In quantum mechanics, too, the interference at the double slit serves as evidence for the existence of matter waves.
In this explanation you will find out exactly what the experiment and the interference are all about.
Double slit experiment simply explained
At the center of the double-slit experiment is the wave property of light. In the process, light waves fall, which in the most common case are from one laser be generated on one double slit. This one is two narrow, parallel fissures.
An important property of light used in the experiment is coherence.
Two waves are coherentif their speed and frequency are the same. They can only differ in which section within a period the wave is located, i.e. the phase.
You can find more about the coherence of waves in the corresponding explanation.
Light is for example not coherentif two waves with different wavelengths to be viewed as. For this reason, in the double-slit experiment monochromatic lighti.e. light with one wavelength is used.
Interference at the double slit – experimental setup
With help of a lasers is now on the double slit coherent light blasted. Some distance behind the double slit becomes a umbrella placed.
On this screen, if done correctly, will be a Pattern of light and dark areas visible.
But what exactly is that and how does it come about?
Interference at the double slit – observation
Exactly this pattern of light and dark areas, which can be seen on the screen, becomes interference pattern called. The reason for the emergence of this pattern lies in the Huygens’ principle.
That Huygens’ principle States that every pointwhich is reached by a wavefront, again starting point for one new, spherical elementary wave is.
More to Huygens’ principle you can find out in the accompanying declaration.
In relation to the experimental setup in the double-slit experiment, the both column sources of circular waves dar, who overlay be able.
This overlaywhich is shown in Figure 2, is in physics as interference known. differed will between two types of interference, constructive and destructive interference.
Constructive interference at the double slit
to describe the interference crests and troughs considered, so the maxima and minimums a wave.
Interference describes the superimposition of waves. A distinction is made between more constructive and destructive interference.
at constructive interference meeting two crests or two troughs on each other. That means the waves strengthen each other.
the destructive interference describes the opposite: meet here Wave crest and wave trough on each other. there weaknesses the waves or Clear from.
So the is considered amplitude a resultant wave that varies depending on the type of interference bigger or smaller is called the amplitudes of the incoming waves.
On the screen, the constructive interference corresponds to one bright stripesso one maximumwhile the destructive interference as dark stripe one minimum is equivalent to.
The location of the maxima and minima depends on the wavelength of light from and can based geometric considerations be calculated. You can even use this method any formulas for the double slit derive
Interference at the double slit – formula
To calculate the maxima and minima, it is helpful to use a geometric sketch of the experimental setup. From this, on closer inspection, conclusions can be drawn about the Ratios of different system sizes to be pulled. These are outlined in the figure below.
d corresponds to this gap spacingα dem angle between the ray axis and the distance to the observed point on the screen, L dem Distance from double slit and screen, x the position of the considered minimum or maximum starting from the beam axis and Δs dem path difference
Of the path differencealso path length called, is the path difference two coherent waves. He dictates where to go constructive and destructive interference comes.
If the path difference one integer multiples of the wavelength corresponds, it comes to more constructive interference and with it one maximumSo if
,
where is the wavelength of light and is a natural number.
Destructive InterferenceSo a minimumoccurs when the path difference a half-integer multiple of the wavelength is
.
The n gives the in both cases Order of the minimum or maximum.
For the angle considering Figure 3, it holds that
.
This follows from the fact that the sine of an angle is Quotient of opposite side and hypotenuse is equivalent to. For example, the Wavelength of the light used be calculated when the remaining quantities are known.
Task:
A slit-spaced double slit is illuminated with a green laser. One is considered maximum first Order, so with . For the angle, the experimenters find a .
Determine the wavelength of the light used.
Solution:
The formula for the is used Path difference for maxima. With applies
This expression can now be used in the formula for Angle. Finally it is reshaped.
You now get the wavelength Deploy known sizes
This corresponds to the typical wavelength for green light.
However, in many cases it is complexthe angle exactly to determine why another expression must be sought for this.
Other system parameters are used to help, namely the Distance of the gap to the screen and the position of the maximum or minimum relative to the beam axis.
This is done via the small-angle approximation. But how exactly does that work?
Small angle approximation double slit
About quantities such as the wavelength of the light or the aisle width regardless of the angle represent α, the Distance L and the position x of the minimum/maximum.
The following relationship can be derived from this sketch and the identity of the tangent (opposite/adjacent).
This is where the small-angle approximation comes into play, which allows tan(α) and sin(α) in the experiment to equate.
the small-angle approximation describes one mathematical approximation for small angles. If these are sufficiently small, you can use the following relationship
.
Since the Angles in the double slit experiment usually very small are, the approximation can be carried out without any problems. The expression for the tangent of the angle can thus be equated with the sine, from which follows a formula that no longer depends on α.
This formula is generally validbut can still be specified for minima and maxima.
For maxima is valid in the double-slit experiment
,
while for minimums is applicable
.
Is the known wavelength of light and can x and L measure become, so you can, for example, the gap width to calculate. You will find out exactly how this works in the next section.
Calculate double gap gap width
The calculation of the gap width of the double gap is done by Rearranging the known formulas for minima and maxima after d.
Becomes a maximum viewed on the screen at a distance x from the beam axis, it follows for the slit width d
.
For minimums is applicable
.
Using these expressions, the gap spacing can now be calculated if the known to other sizes are.
task:
Red light falls through a double slit with the wavelength λ=650 nm. On the 3.2 m distant screen becomes a Distance between the zeroth and first maximum measured by 4 mm.
Calculate the gap width of the double slit used.
solution:
notes First, find out all the quantities that are mentioned in the text so that you can use them correctly in the formula later. It makes sense to do this directly in rewrite meters.
Since here the Distance between two maxima is considered is the formula for the Slit spacing at maxima to use. The known sizes can now be inserted into these.
Although in many double-slit experiments light is used as a shaft, it is also possible other forms of coherent waves to use, such as matter waves or even electrons.
But isn’t the electron actually a particle?
electron double slit
Electrons are true in the classical sense particlebut point just like light wave properties on.
That could Claus Jonsson in the year 1961 demonstrated experimentally for the first time.
In doing so, he left – quite analogous to the double-slit experiment with light – Electrons on the double slit meet and watched on the screen the familiar interference pattern.
With the classical physics was this phenomenon not to explain. Jönsson concluded from this that electrons are quantum objects acts.
quantum objects are objects in physics that are experiments either particle and wave properties exhibit.
This peculiarity is as Wave-particle duality known.
The experiment was after this observation for electrons for many other particles repeatedsuch as neutrons or atoms. Also with these was a interference pattern to recognize what the wave property of matter was occupied.
In particular, with it matter one wavelength be assigned. This is as De Broglie wavelength known.
The double-slit experiment is not limited to the field of optics, but forms a basic building block quantum mechanics and particle physics.