We know that we can see objects because of the light reflected by them. But if an object reflects light of wavelengths undetectable by our eyes, will it be invisible?
I think if you think of glass instead of thinking of table, then your problem will be immediately solved.
Most prescription glasses for spectacles are opaque to Ultraviolet light. But they remain transpaerent to the visible light.
So you can actually see through glasses (in other words not see them). But let's say only you could see Ultra violet light, and you called that color "CRAZYBLUE". Then a transpaerent glass to me, would appear absolutely "CRAZYBLUE" to you.
If the object only reflected light that was undetectable to our eyes then it wouldn't be visible (to our eyes) but it could be discoverable. Objects depending on their temp can reflect or emit wavelengths across the whole spectrum. Most undetectable to our eyes. Even though an object reflects light undetectable, we could still see it even if a small part of the light was visible.
We see objects not only because of reflected, but also due to transmitted, scattered and refracted light.
A glass sphere for example reflects and absorbs very little visible light, but instead transmits most of it. Light rays are refracted so that the image of the background is distorted - something that our brain can convert into spatial information.
If no visible light is reflected, it can be due to two reasons: visible light is completely absorbed or transmitted. If the light is absorbed, the object just appears black. If all light is transmitted, it appears transparent, and depending on its shape might actually look nearly invisible indeed. For this reason we put bird stickers on large window panes.
Apart from this there are also sources of light, which obviously are visible even without reflecting anything. Here are a variety of effects, which for example absorb some invisible light wave and re-emit visible light (fluorescence).
Let's understand it this way
human eye is a camera or a sensor that detects the light.
Actually the light coming from outside world form an image on retina of our eye. (Refer this for more details - https://www.myvmc.com/anatomy/the-eye-and-vision/)
thus we can only see the object if it emits or reflects light that can be detected by our eye.
Now Can there be a table which we can't see?
yes of course - the best example would be people walking on water. Actually they are not walking on water but on a table of glass that has same refractive index as that of water and thus it is not visible. https://youtu.be/pMHUMxSfn3I