Do you know a formula to calculate the virtual distance of a star when viewed through a telescope?

Question

I want to figure out the difference in light years between a star viewed with the naked eye and it's 'virtual' distance when viewed with a telescope.

Answer 1

You are talking about magnification I think. If you magnify it, then it looks bigger. The usual way something looks bigger is if you are closer. For very distant objects that are much, much smaller than the distance, cutting the distance in half doubles the size. So double the magnification is like cutting the distance in half. Magnifying 100 times is like seeing it from 100 times closer. So a planet 100 million miles away, when magnified 100 times in a telescope, looks like it would from only 1 million miles away. But if you get too close, that simple relationship breaks down. Lucky for us, nothing in space is close enough to worry much about that. Except maybe the Moon.

Answer 2

There isn't a term "virtual distance" in astronomy.
But you may be referring to "magnitude" - the brightness of the star.

Absolute magnitude is the brightness of a star calculated if the star were 10 parsecs away.
Apparent magnitude is the brightness of a star as it appears to us on earth (naked eye).
Many telescopes include in their specs the apparent magnitude of stars the telescope can resolve (perfect vision on a completely clear night with no clouds can see stars of about magnitude 7 (the higher the number, the dimmer the star appears).
A more powerful the telescope can resolve dimmer stars than a smaller less powerful scope.