# Two-dimensional diffraction grating

##### Class practical

Some students may have looked at a line source of light through an ordinary grating. Here they look at a point source of light through two identical gratings. They can try crossed gratings or rotating gratings, to get an idea of the pattern that they produce.

#### Apparatus and materials

For each student or group of students

Coarse diffraction gratings, 2

Finely woven cloth, 2 pieces

Rotating devices, 1 (if available)

Sheet of plastic grating replica (if available)

Compact light source and power supply

#### Health & Safety and Technical notes

The compact light source is now known to be a source of UV radiation. Do not allow students to approach nearer than 1.5 m. If this is a possibility, set up a 6 mm-thick sheet of glass as a UV filter.

The microscope slide of pieces of grating is a model of a crystal with grains in various directions. You can show pictures of what happens when X-rays fall onto a single crystal of potassium alum and powdered potassium alum. These pictures are evidence for the diffraction of X-rays by planes of atoms in a crystal.

If you can get a sheet of plastic grating replica, you can make a composite grating on a microscopic slide. This is an analogue of a crystal. Cut the grating replica into small pieces, a few millimetres across. Stick these onto a 5 cm glass slide, jigsaw fashion, with double sided sellotape so that the rulings are in random directions. Put a second slide over the top to cover the pieces.

#### Procedure

a Set up the compact light source at one end of the laboratory; put it fairly high up so that everyone can see it. From a distance, it should behave like a point source of light.

b Students hold a grating near to one eye and look through it at the distant light source.

c They then look at the same source holding a tightly stretched piece of finely woven cloth near their eye. A piece of silk or fine cotton should work. This acts as a two-dimensional grating.

d They can try placing a second grating on top of the first one so that the two sets of slits are at right angles.

e Ask the students what they would see if the woven cloth were rotated. They can try the special rotating device if it is available.

f Put the composite grating in the beam of light and note the diffraction pattern on a screen.

#### Teaching notes

1 Looking through a single grating at a point source produces multiple images of that source; they are coloured if the source is white. The result from two crossed gratings is surprising: rather than two sets of diffraction patterns at right angles, there are more ‘spots’ to be seen. Altering the angle between the gratings changes the pattern.

2 Discuss the shape of a diffraction pattern from a single grating. (Multiple 'images' of the light source; coloured if the source is white.) Ask students to predict what they expect to see from crossed gratings.

Bring out the fact that instead of two diffraction patterns at right angles, the crossed gratings produce a more complex pattern with more 'spots' than the two single gratings.

3 The crossed gratings produce a pattern similar to the piece of cloth, which is like a two-dimensional grating.

4 The composite grating has multiple, randomly placed pieces of grating. This is like a crystal – with randomly oriented domains. The result is a circular diffraction pattern. Discuss how this is produced by the addition of the diffraction patterns in each direction. They are overlaid on each other.

5 If a crossed grating is rotated in a holder, than an image of concentric circles is produced (by persistence of vision), modelling powder photographs of crystals or looking at street lights through steamed up windows.

6 This is useful preparation for seeing the diffraction pattern from a crystal – as with the Electron diffraction experiment.

This experiment was safety-tested in May 2006