If I shone a a powerful, non-burning laser light into into a telescope and pointed it at a star, would anyone there be able to detect it?
No, but let's see why. What we'll discover is that it would be slightly better (but still quite hopeless) to ditch the telescope and simply shine the laser directly at the star.
I'm not sure a telescope works if you use it backwards.
It does! A telescope works by taking in parallel beams of light through the aperture, focusing them, and projecting them out of the eyepiece to form a magnified and brightened image for your eye. If we instead shine parallel beams of light (a laser) into the eyepiece, they will be expanded and projected out of the aperture.
You can try this experiment yourself with a (preferably weak) laser pointer and aiming the telescope at a wall. You'll see an expanded laser dot, similar in size to the size of the telescope's aperture. The spot will have a lower surface brightness because the same amount of light was spread over a larger area.
So why can't we just aim this bigger spot at a distant star and have someone there see it?
The problem is not the telescope, but the nature of light. Light has a wave-like behavior, and the waves spread apart a little bit as they travel. So even though we usually think of a laser as a perfectly parallel beam of light, it still gets wider as it travels. This is the real problem. The minimum possible divergence angle depends on the wavelength of the light and the radius of the laser beam at its narrowest point. The narrower the beam and the larger the wavelength of light, the more the beam must diverge. For typical visible-light handheld laser pointers this angle is about 1.2 milliradians or 0.069 degrees.
Let's imagine taking a 5mW green (532nm) handheld laser pointer (beam radius a little less than 1mm) and shine it through an 8" (20cm) aperture telescope. This immediately expands the laser beam to a width of 20cm. Let's aim the telescope to shine it at the nearest star system, Alpha Centuari, 4.2 light years away. The divergence of the beam remains 1.2 milliradians, which means that for every kilometer it travels, the beam spreads out by another 1.2 meters.
When the beam reaches Alpha Centuari, it will be more than 600 AU across.
Let's do a little calculation. The intensity of our laser beam at the source is 5mW spread over a spot about 1mm in radius, which is about 500 watts per square meter. This is about half the intensity of sunlight at Earth's surface. After being expanded by the telescope, the intensity is about 0.16 watts per square meter. Still bright enough to see if in the dark. But when arriving at Alpha Centuari and being spread over the whole star system, the intensity is a mere 10^-31 watts per square meter. There is little hope in anyone being able to detect it, even if the astronomers there could filter out the light of Sol, or even the rest of the light coming from Earth.
If we imagine you leave the laser shining at Alpha Centuari forever, and someone there keeps a similar 20cm diameter telescope aimed at Earth, they need to wait on average half a million years to receive a single photon of your laser! (Which would be swamped by all sorts of other photons in the meantime. For perspective the laser altogether is emitting about 10^16 photons per second!)
Ditching the telescope and pointing the laser directly at Alpha Centuari would give us roughly the same result. The difference is that it would take out the first 20cm of beam expansion by the telescope, equivalent to removing about 200 meters of beam divergence out of the 4.2 light years to Alpha Centuari. (Woohoo?) We'd also prevent a little bit of the laser light from being absorbed by the mirrors or lenses, since no mirror or lens is perfect.
So, little hope of signaling other star systems with a handheld laser, and if we want to do it anyway then we may as well not use telescopes. But is signaling with lasers completely hopeless?
What if we use a better laser?
To optimize our chances, we should maximize the amount of light we throw out, and minimize how rapidly the beam spreads out. So we should use a more powerful laser, a shorter wavelength of light (maybe violet, since anything shorter will be scattered or absorbed too much by the atmosphere), and a larger initial beam diameter. The shorter wavelength of light and larger beam diameter both allow us to reduce the beam divergence, achieving a smaller spot at the target star. (This is an unintuitive thing about lasers: a
larger beam can be made to spread apart more slowly, which over large distances allows us achieve a smaller spot size!)
If we were to shine a 1
megawatt violet (400nm) beam with a 1 meter initial diameter, then we could theoretically achieve a spot size at Alpha Centuari of just 10 million kilometers, or about 33 light seconds diameter. A huge improvement. We also have more light in the beam altogether, and the intensity of the beam at Alpha Centauri would be about 10^-15 watts per square meter. Very weak, but at least now it's in the realm of "detectable with a lot of effort". A 10m wide telescope would expect to receive hundreds of thousands of photons of the laser beam per second. Detectable if the light of Sol were excluded (could be blocked with an occulting disk in their telescope), and it would be a few times stronger signal than the light of Earth itself.