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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 0.1µ 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?