19. Recall [Section 45(B)] that the pressure distribution of an atmosphere can be described by the barometric equation, where the scale height H is the important factor. Analogously, you can relate the number den- sity to height h above the Earth's surface: n(h) = n(0) exp(-h/H) where n() is the density of a particular atmospheric constituent at sea level. Now the optical depth (Sec- tion 87) is proportional to the number of particles in a column through the atmosphere. (a) Write down an expression for the column density N(h) above an altitude h. (b) Looking at the zenith from sea level, the optical depth in the near infrared is about 3. Water vapor contributes most to this opacity; its scale height is about 2 km. Compare the optical depths at ze- nith for infrared telescopes at 2, 4, and 10 km. What do you conclude about the placement of an infrared telescope? of large tele- 19. Recall [Section 45(B)] that the pressure distribution of an atmosphere can be described by the barometric equation, where the scale height H is the important factor. Analogously, you can relate the number den- sity to height h above the Earth's surface: n(h) = n(0) exp(-h/H) where n() is the density of a particular atmospheric constituent at sea level. Now the optical depth (Sec- tion 87) is proportional to the number of particles in a column through the atmosphere. (a) Write down an expression for the column density N(h) above an altitude h. (b) Looking at the zenith from sea level, the optical depth in the near infrared is about 3. Water vapor contributes most to this opacity; its scale height is about 2 km. Compare the optical depths at ze- nith for infrared telescopes at 2, 4, and 10 km. What do you conclude about the placement of an infrared telescope? of large tele