Page:TolmanEmission.djvu/5

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Consider now a source of light approaching the slit with the velocity v. If τ' is the period of the source which now produces a bright line at D and Δt' the time interval between departure from the source of two light impulses which now arrive simultaneously at D, we evidently have the relation

i\tau'=\Delta t'=\frac{L'-L_{2}+v\Delta t'}{c+v}+\frac{L_{2}}{c+v_{3}}-\frac{L_{4}}{c+v_{4}}, (4)

where c+v[1] in accordance with the Stewart theory is the velocity of the light before reflection and L_{3} and L_{4} are the components which must be added to c to give the velocity of light along the paths BD=L_{3} and CD=L_{4} after its reflection.

According to the Stewart theory v_{3} and v_{4} will be equal to the components in the direction BD and CD of the velocities of the mirror images of the original source. An idea of the size of these components is most easily obtained graphically. Considering, for example, the point of reflection C as a portion of a plane mirror EF which is tangent to the concave mirror at C, the position of the image I_2 can be found by the usual construction, the line AI_2 connecting source and image being perpendicular to EF and the distances AE and EI_2 equal. Both the original source and the image will evidently be moving towards the point F with the same velocity v. By a similar construction, which has been omitted to avoid confusion, the image I_1 produced by reflection from B is found to be located as shown, and moves also with the velocity v in the direction of the corresponding arrow.

It can be seen from the construction that in the arrangement shown the motion of the image I_1 and the corresponding reflected ray BD are

  1. See note I. p. 138.