## The Refraction Correction

Astronomical refraction is the apparent displacement of a celestial object due to the bending of the rays of light from the object as they pass through the atmosphere. The angular amount of this displacement is the refraction correction. On account of the greater density of the atmosphere in the lower portion the ray is bent into a curve, which is convex upward, and

more sharply curved in the lower portion. In Fig. 43 the light from the star S is curved from a down to 0, and the observer at O sees the light apparently coming from Salong the line bO. The star seems to him to be higher in the sky than it really is. The difference between the direction of S and the direction of

S' is the correction which must be applied either to the apparent zenith distance or to the apparent altitude to obtain the true zenith distance or the true altitude. A complete formula for the refraction correction for any altitude, any temperature, and any pressure, is rather complicated. For observations with a small transit a simple formula will answer provided its limitations are understood. The simplest method of deriving such a formula is to consider that the refraction takes place at the upper limit of the atmosphere just as it would at the upper surface of a plate of glass. This does not represent the facts but its use may be justified on the ground that the total amount of refraction is the same as though it did happen this way. In Fig. 44 light from the star S is bent at 0' so that it assumes the direction O'O and the observer sees the star apparently at S'. ZO'S (= f') is the true zenith distance, ZO'S' (= f) is the apparent zenith distance, and SO'Sf (= r) is the refraction correction; then, from the figure,

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