If I were to look at a 10th magnitude star with a big enough telescope, would I be blinded?

Not by a long shot!

According to my handbook, a 0th magnitude star produces a radiant intensity of 2.5 x 10^-10 lumens/square centimeter. 1 lumen is 0.0014 watts of energy. So the Sun, which has a visual magnitude of -27.0 is worth 12.7 lumens/square centimeter, which is enough to permanently damage your eye.

The pupil has a diameter of about 5 millimeters. So, for a 10th magnitude star to produce as bright an image as the sun, we have to amplify its light by a factor of 12.7/2.5 x 10^-10 = 50 billion times. Since the aperture of the eye is 5 millimeters across, this means we need a telescope with a mirror some 5 mm x (5 x 10^10)^1/2 = 1100 meters in diameter if I have done the calculation correctly.

You are not likely to get such an optical telescope anywhere. Note, the Palomar mirror is about 5 meters across and would make a 10th magnitude star appear (5 meters/5 millimeters)^2 = 1 million times brighter. Since there are 5 magnitudes for every factor of 100, this means the 10th magnitude star, at the eyepiece, would look about as bright as a naked eye star with a magnitude of +10 - 15 = -5.0. A little brighter than Venus at its brightest.

Copyright 1997 Dr. Sten Odenwald