The reflection grating: theory

The ‘grating’ used is a steel ruler. On some parts of the ruler, there are very closely spaced divisions. If one of these areas is illuminated with a laser beam at a very small angle (grazing incidence), the divisions (lines) act as a reflection grating. A vertical series of bright dots appear on the screen. The central dot corresponds to a simple reflection and on either side there are series of dots corresponding to interference maxima.

Figure 1. The experimental set up: laser, diffraction grating and screen.

The experimental set up is shown in Figure 1. The laser beam is diffracted at an angle into the nth order at a distance from the plane of the steel ruler. Consider two rays at A and P respectively. When they have both reached C and R they will have travelled different distances. The path difference between the two rays is given by:

where is the distance between neighbouring divisions on the ruler. Many such pairs of rays may be drawn across the whole grating and these combine to form a bright spot when these rays reinforce i.e. when this path difference is a whole number of wavelengths. Thus, for a maximum we have

from which we deduce

where is an integer which indicates the interference order of the bright spot.

From the figure, it can be seen that:

which for approximates to .

For pure reflection, the angle of incidence equals the angle of reflection

i.e. and , so that

.

From this it follows that

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