The naked eye can detect a stellar object of sixth

The naked eye can detect a stellar object of sixth magnitude in the night sky. With binoculars, we can see an object of the ninth magnitude. The sun’s brightness at Earth is 1400 W/m ² . The Hubble Space Telescope can detect an object of the 30th magnitude, which amounts to a brightness of about 2 × 10 ^{– 20} W/m ² . 

(a) Consider a detector in the Hubble Space Tele-scope with a collection area of 0.30 m ² . If you assume hydrogen light of frequency 486 nm (blue-green), how many photons/s enter the telescope from a 30thmagnitude star? 

(b) An increase of magnitude one represents a decrease in brightness by a factor of 100 ^1/5 . Estimate how many photons/s from a sixth-magnitude star would enter your eye if the diameter of your pupil is 6.5 mm.