Measurement of wavelength from Young’s experiment
Fig. 26.14 shows the ray geometry for the first bright fringe next to the central one. For clarity the vertical scale of this diagram has, like the others, been greatly exaggerated: actually the fringe spacing x is only about one six-hundredth of the distance D.
We saw in the previous section that the distance S2A is one wavelength longer than SIA. Thus, if we drop a perpendicular S]N on to the line S2A it will cut off a length S2N = A. Bearing in mind the smallness of the distance a between slits and the fringe spacing x we may, to a very close approximation, regard the two rightangled triangles S2NS] and ACM as equiangular and therefore similar. Hence A x a D or A = ax D
The fringes are all effectively equidistant and so we take the fringe spacing x as equal to the average spacing of as many fringes as can be seen and measured. It has already been explained how this may be done either with a micrometer eyepiece or, more roughly with a half-millimetre scale used in conjunction with a magnifying glass.
The distance a between the slits may also be measured with the half-millimetre scale, though more accurate results are obtained with a travelling microscope. This microscope is fitted with a crosswire on which the slits are focused in turn. The consequent movement a of the microscope carriage is measured by a vernier or micrometer screw. Owing to the smaller percentage error involved, it is sufficiently accurate to measure the distance D with an ordinary millimetre scale.