Is it possible to bend light without changing its color?

Question

It seems to me that whenever you change the direction of a wave it also affects frequency. Would this not also be true of light waves bending from, for example, gravity?

Answer 1

You are specifically asking about gravitational lensing, that is a distribution of matter between a distand lightsource and the observer, that is capable of bending the light from the source as the light travels towards the observer.

If the (light) source, the massive lensing object, and the observer lie in a straight line, the original light source will appear as a ring around the massive lensing object (provided the lens has circular symmetry).

https://en.wikipedia.org/wiki/Gravitational_lens

Now light in this case follows a geodesic, that is, the world line of a particle, free from all external (non-gravitational) influences follows a geodesic.

In general relativity, a geodesic generalizes the notion of a "straight line" to curved spacetime. Importantly, the world line of a particle free from all external, non-gravitational forces is a particular type of geodesic. In other words, a freely moving or falling particle always moves along a geodesic.

https://en.wikipedia.org/wiki/Geodesics_in_general_relativity

As per GR, light in your case, during gravitational lensing, when gravity bends its path, will retain its frequency unchanged (if there are no other effects), and this means, that the answer to your question about gravity bending light is that in reality this effect does not change lights frequency.

Answer 2

No, it doesn't, as the comments point out. You might possibly be confusing the change in wavelength when the light is inside the "bending material" such as a glass lens. However, upon exiting the lens -- or the localized gravitational field -- the light, now moving in a new direction, retains its vacuum wavelength. The wavelength change is entirely due to the effective index of refraction in the region or medium in question.

You might want to take a peek at the discussion in this physics.SE question.

Answer 3

The frequency of light "in transit" isn't well defined in special or general relativity. You can only define frequency shift for light that travels from an emitter to a receiver, and you get a single frequency ratio for the whole trip; it can't be attributed to any particular part of the trip.

In the case of the bending of light by a massive body like the sun, you can express the frequency shift approximately (but very accurately) as a product of shifts due to the emitter's and receiver's motion relative to the sun, and the quasi-Newtonian gravitational potential at the emitter's and receiver's locations. The bending angle doesn't enter into it, so it seems fair to say that the gravitational bending of the light doesn't affect its frequency.

Answer 4

A prism or lens can cause a separation of beams of different frequency (dispersion or chromatic aberration), but it does not change their frequency. That's way mirrors are used in the larger telescopes.