LabMouse Physics AS | Waves | Diffraction
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Instead of getting a dull pattern from two sources using double slits, we can use a diffraction grating. A diffraction grating is a series of slits, possibly many thousand to the centimetre if you are experimenting with light, and this ensures a brighter, sharper pattern. Diffraction gratings can be used with any wave source but we shall be concentrating on their use with light.
Light that we receive from the sun is called white light. It consists of a complete range of colours of light, each of a different wavelength, superimposed on each other so that it gives the appearance of being white. A sodium street light also emits a range of colours, but not so diverse, and we can use a diffraction grating to analyse the wavelengths of this light.
We can use the following equation (which you don't need to prove) to find the wavelength of each colour.
`"d"\ sin theta = "n"\ λ`
Where: d = distance between each slit in m θ = angle at which the particular wavelength is visible in ° λ = wavelength of the light in m n = order of the maximum (a whole number)
So
`λ = ("d"\ sin theta) / "n"`
This equation tells us that each individual wavelength of the light that makes up the initial complete light can only be seen at a specific angle. If we measure the angle, we can work out the wavelength.
The diagram below shows the spectrum of sodium vapour when it has passed through a diffraction grating.
To keep the explanation simple we shall consider the light coming from just two slits. (The directions of the waves are shown in blue.) If the diagram is showing an interference maximum at α, then the two waves, each originating from a different slit, must be in phase. If they were not then the waves would destructively interfere.
This means they must be a whole number of wavelengths apart, i.e. the distance PQ, shown in red must be a complete number of wavelengths, nλ.
Using trigonometry: d sin θ = PQ n λ = d sin θ
Note this diagram is not to scale. In practice, point α is a long distance from the slits, making θ very small, and the angle at Q virtually a right angle.
