# Homework # 1, due 10 Feb = 1 magnitude leads to ```Homework # 1, due 10 Feb
1. Show that an extinction of Aλ = 1 magnitude leads to
a flux Fλ decrease to 40% of its original value.
2. Assuming dust grains are 0.1&micro; m in radius, that the
gas density in the ISM is nH = 1 cm−3, and the number density of dust grains is nd = 10−12 cm−3 and
uniformly distribued, find the column density NH of
hydrogen to be expected along a line of sight in which
a source is observed to have an extinction AV = 1 magnitude. What is the mean free path of light along this
line of sight? What is the distance to the source?
3. Assume a star cluster has 200 F5 stars at the main
sequence turnoff and 20 K0III giant stars. Determine
the quantities MV and B − V for each type of star
singly and also for the cluster. Suppose the cluster is
at a distance of 2 kpc. What is mV for the cluster?
4. In a galaxy at a distance of d Mpc, what would be
mB⊙? In this galaxy, what length does 1 arcsec correspond to? If the surface brightness of this galaxy is
IB = 27 mag arsec−2, show that the brightness of this
galaxy is equivalent to 0.99 LB⊙ pc−2. Why doesn’t
this quantity depend on the distance?
```