In a certain part of the North America Nebula, the amount of interstellar extinction in the visual wavelength band is 1.1 magnitudes. The thickness of the nebula is estimated to be 20 pc and it is located 700 pc from Earth. Suppose that a B spectral class main-sequence star is observed in the direction of the nebula and that the absolute visual magnitude of the star is known to be M(V)=-1.1 from spectroscopic data. Neglect any other sources of extinction between the observer and the nebula. Show all your work, assumptions, equations, and units.
1. Find the apparent visual magnitude of the star if it is lying just in front of the nebula.
2. Find the apparent visual magnitude of the star if it is lying just behind the nebula.
3. Without taking the existence of the nebula into consideration, based on its apparent magnitude, how far away does the star in part (b) appear to be? What would the percentage error be in determining the distance if interstellar extinction were neglected?