Question

The dust in an interstellar cloud blocks blue light in the following way: For every 1.00 pc light travels through the cloud, only 90.1% of the light goes through the cloud. Thus, after 2.00 pc, 90.1% of the remaining 90.1% or 81.2% (0.901 × 0.901 = 0.812) remains. a. You might initially expect that after 15 pc, the total of these 9.9% reductions would have removed all of the blue light. How much blue light actually remains? % b. The same cloud removes about 4.2% of the red light every parsec, so after 1.00 pc, the ratio of blue to red has dropped to 90.1/95.8 ≈ 94% of its unreddened value. What is the ratio of blue to red after 5.00 pc? % What is the ratio of blue to red after 10 pc? %

Answer 1

a] Let I_o be the intensity of the light at d = 0 pc

then, from the above relation,

I = I_o(0.901)ⁿ

where n = distance in parsec

so, after 15pc, I/I_o = 0.901¹⁵ = 0.2093 = 20.93%

this is how much blue light remains.

b] For red light:

I = [I_o - I_o0.042]ⁿ = I_o(1 - 0.042)ⁿ

so, at 5pc, I/I_o for red is: 0.80691 = 80.691%

and for blue: I/I_o = 0.59377 = 59.377%

therefore, ratio of blue to red after 5pc is:

r = 59.377/80.691 = 73.58% of its unreddened value (when no red is present).