It is shown that the backward-scattered interference pattern of an unclad optical fibre can be adequately described by Airy's rainbow theory. A formula is derived from which the diameter of the fibre may be calculated if the position of the rainbow maximum is measured from the scattered pattern. The error involved in this method is less than 3%. Comparison between this method and Marcuse's method is also made, and it is found that the present method can lead to a more reliable result.