There are several ways to decide this question, all fairly easy...
We can't tell if a light signal has been reflected or if it is still in its original direction. The same is true about refraction. If we can see the same thing twice then that tells us that one or both of them is reflected or refracted. This is why people think gravitational lensing takes place, because the same object (by accurate measurement of its colour spectrum and other properties) is seen in two places, either side of the direction where the centre of the gravitational lens is thought to be.
There are several ways to decide this question, all fairly easy...
To excellent Ray's answer I would add that if the reflected stellar light passes through an atmosphere, one can detect absorption lines in the spectrum that aren't there in the star spectrum. These lines show for example that the atmosphere temperature is very different from the star surface temperature.
If the iight is reflected from a hard surface, like for the Moon, provided one has the original star spectrum, one can detect a difference of the spectrum overall shape wrt to the star one, because different colours are differently absorbed or diffused by a hard surface.
What you want to look for is some change to the incoming radiation that is effected by the reflector itself. This often means that you must recognize what must be the originating source of the radiation and find that the radiation you see has been altered by the reflector. Unfortunately this is very difficult to determine unequivolcally. You may have to know something about the reflector in advance. For example, we infer that the planets shine by reflected sunlight because they are too small to generate the light and solar spectrum we observe on their own. Thus, reasoning must be employed to infer whether or not a particular source of light originates within the object or is reflected by the object.
With regard to Ray's first point, astronomical reflecting telescopes do a very good job of reflecting starlight including the star's spectrum so that I doubt that one could discern whether one was looking directly at the star through a refracting telescope or viewing reflected starlight from the mirror of a reflecting telescope.
George
And the image in a reflecting telescope will be inverted! With regard to polarized light you don't know a priori the cause of the polarization but you are right it's at least an indicator of reflected light. Thanks for pointing it out!
An interesting question. Analysis of light from distant stars is a key knowledge of other worlds, other planetary systems, exoplanets. Considering current research problems important for science, I think that the question concerns particularly important issues. I believe that research on this topic should be continued. There was an interesting discussion. Greetings
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