Question

The dust in an interstellar cloud blocks blue light in the following way: For every 1 pc light travels through the cloud, only $90 \%$ of the light continues. Thus, after $2 \mathrm{pc}, 90 \%$ of the remain$\operatorname{ing} 90 \%,$ or $81 \%(0.9 \times 0.9 \times 0.81),$ remains. a. You might initially expect that after $10 \mathrm{pc}$, the ten $10 \%$ reductions would have removed all of the blue light. How much blue light actually remains? b. The same cloud removes about $7 \%$ of the red light every parsec, so after $1 \mathrm{pc}$, the ratio of blue to red has dropped to $90 / 93=97 \%$ of its unreddened value. What is the ratio of blue to red after 5 pc? after 10 pc?

Name: Problem 6, Chapter 72: Pathways to Astronomy
Uploaded: 2020-07-02T19:58:30-08:00
Duration: 4 min 40 s
Channel: Samantha Baker

   The dust in an interstellar cloud blocks blue light in the following way: For every 1 pc light travels through the cloud, only $90 \%$ of the light continues. Thus, after $2 \mathrm{pc}, 90 \%$ of the remain$\operatorname{ing} 90 \%,$ or $81 \%(0.9 \times 0.9 \times 0.81),$ remains.
a. You might initially expect that after $10 \mathrm{pc}$, the ten $10 \%$ reductions would have removed all of the blue light. How much blue light actually remains?
b. The same cloud removes about $7 \%$ of the red light every parsec, so after $1 \mathrm{pc}$, the ratio of blue to red has dropped to $90 / 93=97 \%$ of its unreddened value. What is the ratio of blue to red after 5 pc? after 10 pc?

Pathways to Astronomy

Stephen E. Schneider 2nd Edition

Chapter 72, Problem 6

Instant Answer

Solved by Expert Samantha Baker

07/02/2020

Step 1

After 1 pc, $90\%$ of the blue light remains. After 2 pc, $81\%$ of the remaining blue light remains. After 3 pc, $72.9\%$ of the remaining blue light remains. After 4 pc, $65.61\%$ of the remaining blue light remains. After 5 pc, $59.05\%$ of the remaining blue Show more…

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The dust in an interstellar cloud blocks blue light in the following way: For every 1 pc light travels through the cloud, only $90 \%$ of the light continues. Thus, after $2 \mathrm{pc}, 90 \%$ of the remain$\operatorname{ing} 90 \%,$ or $81 \%(0.9 \times 0.9 \times 0.81),$ remains. a. You might initially expect that after $10 \mathrm{pc}$, the ten $10 \%$ reductions would have removed all of the blue light. How much blue light actually remains? b. The same cloud removes about $7 \%$ of the red light every parsec, so after $1 \mathrm{pc}$, the ratio of blue to red has dropped to $90 / 93=97 \%$ of its unreddened value. What is the ratio of blue to red after 5 pc? after 10 pc?