Waves

The Diffraction Grating

A diffraction grating has thousands of narrow apertures. Consider a typical grating having 500linesmm^-1. The situation can be analysed in the same way as Young’s two slit experiment.

If distance b–c is l then waves from a and b will interfere constructively at a point in a direction q to the normal.

However, if b–c is l then d–e will be 2l, f–g will be 3l and so on. Therefore, waves from hundreds of slits will interfere constructively, producing a well defined maximum of the diffraction pattern, called a diffraction image.

Other maxima will occur when b–c = 2l, 3l etc.

The width of the apertures is only 1/500mm so the fringe spacing is much wider than in Young’s experiment which means that the angles q are not small angles.

Therefore, to find the angular positions of the maxima, we use the equation

where n (= 1, 2, 3 etc) is now called the order of the image of the diffraction pattern.

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