Question

Suppose you can just barely see a twelfth-magnitude star through an amateur’s 6-inch diameter telescope. What is the magnitude of the dimmest star you can see through a 60-inch diameter telescope?

Answer 1

First we calculate the aperture ratio between the two telescopes.

Diameter of the first telescope, d1 = 6 inch

Diameter of the second telescope, d2 = 60 inch

As we now that the aperture area is proportional to the square of the diameter

Means -

A2/A1 = d2^2 / d1^2 = (60)^2 / 6^2 = 100

So, aperture area of second telescope (A2) is 100 times larger than the first telescope (A1).

So it should be able to detect objects 100 times dimmer.

By definition (look up the Pogson ratio), a 100:1 ratio represents a magnitude change of 5.

Therefore, the larger telescope should be able to detect stars down to about (12+5=)17th magnitude of the dimmest.