Light scattering homework question (rayleign scattering)

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Homework Help Overview

The discussion revolves around a problem related to light scattering, specifically focusing on Rayleigh scattering in the context of infrared telescopes and their ability to observe star-forming regions in the galaxy. The original poster presents a scenario involving the scattering of light at different wavelengths.

Discussion Character

  • Exploratory, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants discuss the application of a formula relating the intensity of light scattering at different wavelengths. There are attempts to solve for the wavelength where scattering is reduced to 2% of that at 490nm. Questions arise about the calculations and interpretations of the formula.

Discussion Status

Some participants are actively engaging with the calculations and questioning the steps taken by the original poster. There is a recognition of a potential misunderstanding regarding the interpretation of the percentage reduction in scattering. Guidance has been offered to equate the formula to the correct percentage and solve for the unknown wavelength.

Contextual Notes

Participants note the range of infrared wavelengths (700nm to 1mm) as relevant context for the problem. There is an indication that the original poster may not have all the necessary information or clarity regarding the problem setup.

haitianstudent
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Homework Statement


Infrared telescopes, which use special infrared detectors, are able to peer farther into star-forming regions of the galaxy because infrared light is not scattered as strongly as is visible light by the tenuous clouds of hydrogen gas from which new stars are created.


Homework Equations



For what wavelength of light is the scattering only 2.00% that of light with a visible wavelength of 490nm ?

The Attempt at a Solution


the formula is I(490)/IR=(lamda/490nm)^4.
I'm really not sure what I am doing wrong here
 
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Did you solve for lamda? What did you do?
 
I first took lamda and 490 to the 4th power and I got (lamda)^4/5.77*10^10. Then I crossed multiply by 200, I then recived 1.15E13...and I took the fourth root of that and received 1841 but its apparently wrong
 
haitianstudent said:
the formula is I(490)/IR=(lamda/490nm)^4.
2% is not = 1 / 200

The formula is correct. Equate it to 0.02 and solve for the sole unknown, viz., λ

Are you told the correct answer?
 
Note infrared is 700nm to 1mm.
 

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