Diffraction Gratings

A diffraction grating consists of many equally-spaced slits placed extremely close together, e.g., 300 lines per millimetre. Light is diffracted through each slit, causing constructive and destructive interference. Monochromatic light (light of a single colour, and hence one frequency/wavelength) or white light can be used.The formula for Path difference (seen previously) can still be used, with one main change. With such a small slit separation, measuring path difference directly is not possible. However, using geometry, it can be shown that:-

Path Difference = mλ = dsinθ (for maxima)

or

Path Difference = (m + ½)λ = dsinθ (for minima)

Where:-

m = number of maxima out from centre

λ = wavelength of wave (m)

d = separation between each slit

θ = angle between central maxima and maxima in question


Slit Separation and the problems it causes - exam tip

The Slit separation (d) is the biggest source of mistakes in understanding diffraction gratings. Do NOT be tempted to use the number of lines per mm, this is wrong.

The following calculation shows the method for converting lines per mm into d:-

Step 1 - convert into lines per m

Step 2 - Divide 1 by (number per m) to find separation (d)


For example,

Diffraction grating marked as "200 lines per mm"

200 x 1000 = 200,000 lines per m

d = 1 / 200,000 = 5x10-6 m


Changing the distance between Maxima

By changing the subject of the grating equation to sinθ, we can clearly see what changes can cause a larger angle, and therefore a more spread out diffraction pattern.

We can increase the distance between maxima by:-

1. Use a Longer Wavelength of light

2. Decrease the value of d (use more lines per mm)

3. Move further from the screen

The video below gives a detailed summary of diffraction gratings.

Polychromatic Light

So far in this section, we have referred only to monochromatic light (light of one Wavelength), which gives a diffraction pattern such as seen below:-

This pattern looks the same for all monochromatic light, although with different separations depending on Wavelength. If a polychromatic (white light) source is used, however, a combination of all the patterns of each Wavelength is formed on the screen:-

The resulting pattern gives a white central maximum, with spectra forming at each maxima.

The central maximum is white as the path difference is zero, so all colours arrive in phase and recombine to give white light.

Following the grating equation, red light has the longest wavelength and so is deviated the most, with violet deviated the least, giving a spectrum at each maxima.


Spectra from Diffraction and Refraction

The following diagram shows how the spectra from both the diffraction grating and a triangular prism compare to each other:-

As can be seen, both produce a spectrum, but the order of colours is reversed between them.

1. For a prism, red is deviated the least, violet the most.

2. For a diffraction grating, red is deviated the most, violet the least.