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.