Page:PlummerAberration.djvu/3

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254
Mr. H. C. Plummer, On the Theory of
LXX. 3,

where A1F1 = f, A1C = b. If we admit a contraction λ-1 which will make CF1 = λ.CF2, the equation of BA2B' becomes

.

This is a real deformation of the figure of the mirror. But if BA3B' is the surface at which the advancing wave-front actually meets the moving mirror

where v is the velocity of the mirror, and the virtual surface on which the wave falls becomes

.

This is still a paraboloid, and the wave BCB' will reach its focus F3 after a time

.

Hence no change of focus will be detected provided F2F3 = vt. Now

so that

which is equal to vt if

or

This is the law of contraction previously obtained, and the result is a complete compensation of the optical effect due to the motion of the mirror.