The apparent magnitude (how bright an object appears to the observer) is given by

Question

The apparent magnitude (how bright an object appears to the observer) is given by M=(5/2)log(b0/b) where b is the brightness of the object and b0 is a positive constant. A particular telescope is capable of viewing cosmic objects with apparent magnitude 23. An inferior telescope can view cosmic objects having at most apparent magnitude 17. What is the ratio of brightness detected by the first telescope compared to the second?

The first telescope can view objects  times as bright.

(Your answer should be a positive decimal less than 1, since the first telescope should be able to detect dimmer objects than the second)

Answer 1

M = (5/2)log(b₀ / b)

23 = (5/2)log(b₀ / b)

9.2 = log(b₀ / b) So, b₀ / b = 10^9.2. b = 10^-9.2 b₀

17 = (5/2)log(b₀ / b)

6.8 = log(b₀ / b) So, b₀ / b = 10^6.8. b = 10^-6.8b₀

10^-9.2b₀ / (10^-6.8b₀) = 10^-9.2 / 10^-6.8 = 10^-2.4 ≈ 0.00398