# To measure the wavelength of light by a simple diffraction grating experiment

To measure the wavelength of light by a simple diffraction grating experiment

Fig. 26.18 shows how the ordinary type of ray-box used in elementary laboratories may be used in conjunction with a diffraction grating and a second cylindrical lens to form a spectrum of white light and to measure the wavelength of any particular colour in it. The cellulose acetate grating mentioned earlier is very suitable for the purpose and gives good results.

The ray-box itself consists of a vertical line filament electric lamp which can be adjusted in the usual way to give a parallel beam of light from the cylindrical lens Li. The diffraction grating is then set up in front of the lens with a second lens L2 immediately in front of it. The whole arrangement is placed on a sheet of paper as shown. If a small white screen is placed on the axis of the lenses and at a distance from L2 equal to its own focal length, f, a sharp white image of the line filament will be formed on it. This arises from the fact that the direct or zero order diffracted wavefronts emerging from the grating are all parallel to one another for all wavelengths, and consequently all colours come to a focus in the same direction.

On either side of the axis two positions can be found for which a sharp spectrum is focused on the screen, formed in the manner described in the previous section. Suppose we wish to measure the wavelength of yellow light. The position of this is marked in pencil on the paper for both spectra in turn. The position, C, of the centre of the lens L2 is also marked. Having removed the ray-box, the pencil marks are then joined to form an angle YiCY2• Clearly this angle = 28 where 8 is the required angle for substitution in the equation },= d sin e The number of lines on the grating, N per millimetre, is supplied by the makers, so that the value of d is equal to

When doing this experiment it is important to observe that, owing to its longer wavelength, the red of the spectrum is diffracted through a larger angle than the blue. This is the exact opposite of what we see with a spectrum formed by a glass prism where the blue light is refracted through a larger angle than the red.