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Non-physicist asking.

Note: I see that there are similar questions but none that I can find that addresses this specific query.

Exaggerated diagram

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Question

If the two beams of light leave the source at the same time, what happens?

(a) they arrive simultaneously at the viewer with the wavelength shifted

(b) they arrive at different times with the original wavelength

(c) something else

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The light which came by the straight line (in the image ) will take less time to reach the object, this is because the speed of light doesn't change, but the distance covered is different. I am not sure about the wavelength, however I don't see any reason for a change in wavelength.

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    $\begingroup$ The only reason is that the "diverted" beam will interact with the potential well of the massive body, to some extent (it will be a very small effect, and the two effects will cancel out overall). Its frequency will increase (blue shift) on approach and decrease (red shift) as it moves away from the body. $\endgroup$
    – m4r35n357
    Jul 21, 2020 at 9:28
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There is a simple gedankenexperiment to envisioned that the amounts of time will be different. Imagine that the massive body is actually a very compact object that can bend strongly the light rays grazing it. Put this object far far away. Much further away than the source is from the viewer, such that the gravitational field of the massive body becomes negligible in the majority of the path. So the path passing closer to the massive body clearly will takes longer.

Diagram

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