# Measuring the wavelength of light

##### Class Practical

A simple and elegant experiment to measure the wavelength of light using a fine diffraction grating.

#### Apparatus and materials

Fine diffraction grating (about 300 lines/mm)

Metre rules, 2

Lamp in holder, 12V 36W

Green filter

Power supply, low voltage, variable, able to supply 6A

#### Health & Safety and Technical notes

Each student pair will need fine diffraction grating, and 2 metre rules.

#### Procedure

Set up the 12-V 36-W line-filament lamp high at one end of the laboratory, so that students can see it clearly. Place a green filter in front of the lamp. If necessary, increase the applied voltage to 14 or 15 V so there is enough light.

a Hold a metre rule straight out in front of you towards the lamp, with the near end of the rule at your face. Hold the diffraction grating against the near end of the metre rule and look at the lamp through it.

b Ask your partner to place another metre rule, at 90° to your metre rule at its far end (see the sketch).

c Your partner should hold a pencil vertically above their metre rule and move it along until you see it in the green region of your bright spectrum. Note the distance, x, along your partner's ruler from the pencil to the far end of your ruler.

d When you have made your observation, record it and change places with your partner so that he or she can take their turn.

e Divide your measurement x by the length of your ruler, 100 cm. This gives you tan A, where A is the angle between the line of direct white light and the light to the green in the spectrum marked by the pencil. From tan A, use your calculator to find the angle A, and from this find sin A

f Use the formula d sin A = wavelength to calculate the wavelength of green light. You will need the value of d, spacing, i.e. distance from one ruling to the next. If the grating has 300 lines / mm then the spacing is 1 / 300,000m.

#### Teaching notes

You must judge whether this experiment is appropriate for your students. If it is likely to represent a burden of strange geometry and unsure measurements, omit it. If they are able to cope, this experiment has the potential to give them a sense of delight and insight. It is a real achievement to make such a small measurement using fairly crude equipment.

For a large class, set up a lamp at each end of the room, so that half the class can work facing one way, with half facing the other way, each pair as far as possible from their lamp.

Students may need help with the trigonometry and/or with the calculation of wavelength. To avoid the use of tanA, students could do a scale drawing and find sinA from x / t, as in this diagram.

Then wavelength = sinA x d, where d is the grating spacing.

If you supply the value of d, explain where it came from, and make it clear that a mechanical counting during manufacture can supply it.

If suitable microscopes are available, students could use them to look at their piece of grating and at the graduations on a finely divided ruler. Although students may not be able to measure the grating space, they will certainly see that a direct measurement could be made.

This experiment was safety-checked in February 2006