8.4 The Diffraction Grating

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1. What is a Diffraction Grating?

A diffraction grating is a flat piece of glass (or plastic) that has a very large number of tiny, equally spaced parallel slits (grooves) cut into its surface. These slits are microscopic — far too small to see with the naked eye.

When light hits the diffraction grating, it passes through all these slits at the same time. Each slit diffracts (spreads out) the light, and the waves from all the slits then interfere with each other. This produces a pattern of bright spots (called maxima) and dark regions on a screen placed behind the grating.

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2. The Pattern Produced

When monochromatic light (light of a single colour/wavelength) passes through a diffraction grating, the pattern on the screen shows a series of bright spots.

• The central bright spot is called the zero order (n = 0). This is where light passes straight through without being deflected. It is the brightest spot.
• On either side of the zero order, you get the first order (n = 1), then the second order (n = 2), and so on.
• The bright spots become less intense (dimmer) as you move further from the centre.
• The pattern is symmetric — there is a first order on the left and on the right, a second order on the left and on the right, etc.
• The gap between adjacent bright spots increases as the order number increases (the spots spread further apart as you go outward).

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3. Grating Spacing (d)

The grating spacing, given the symbol d, is the distance between the centres of two adjacent (neighbouring) slits on the grating. Its unit is metres (m).

Diffraction gratings are usually described by how many lines (slits) they have per millimetre or per metre. This is represented by the letter N.

You can calculate d using:

$d = \frac{1}{N}$

• If N is in lines per metre, then d is in metres (m)
• If N is in lines per millimetre, then d is in millimetres (mm) — you would then need to convert to metres

✏️ Example:

A grating has 100 lines per mm. Find d.

$$d = \frac{1}{100 \text{ lines/mm}} = 0.01 \text{ mm} = 1.0 \times 10^{-5} \text{ m}$$