Light scattering homework question (rayleign scattering)

AI Thread Summary
Infrared telescopes can observe deeper into star-forming regions due to less scattering of infrared light compared to visible light. The homework question involves calculating the wavelength of light where scattering is only 2% of that at 490nm. The correct approach involves using the formula I(490)/IR=(lambda/490nm)^4 and equating it to 0.02 to solve for lambda. A misunderstanding in calculations led to an incorrect result, highlighting the importance of proper equation manipulation. The discussion emphasizes the significance of infrared wavelengths, which range from 700nm to 1mm.
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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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