How Is the Diffraction Angle Calculated for Different Wavelengths?

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SUMMARY

The discussion focuses on calculating the diffraction angle for different wavelengths using a grating. The key equation utilized is dsinθ = mλ, where d represents the distance between slits, θ is the diffraction angle, m is the order of the spectrum, and λ is the wavelength. The example provided involves a wavelength of 681 nm at 12 degrees in first order, leading to the calculation of the angle for a wavelength of 439 nm in second order. Participants emphasize the similarity in approach between grating diffraction and double slit diffraction.

PREREQUISITES
  • Understanding of diffraction principles, specifically grating diffraction.
  • Familiarity with the equation dsinθ = mλ.
  • Knowledge of spectral lines and their corresponding wavelengths.
  • Basic grasp of angular measurements in physics.
NEXT STEPS
  • Study the derivation and applications of the grating equation dsinθ = mλ.
  • Learn how to calculate diffraction angles for multiple wavelengths using different orders.
  • Explore the differences between single slit and double slit diffraction patterns.
  • Investigate the Rayleigh criterion and its implications for resolving power in diffraction.
USEFUL FOR

Students studying optics, physics educators, and anyone interested in understanding diffraction patterns and their calculations using gratings.

MarcL
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Homework Statement



A grating places a spectral line of wavelength 681 nm at 12 degrees in first order. At what angle is a line of wavelength 439 nm observed in second order?

Homework Equations



I believe dsinθ= mλ


The Attempt at a Solution



This is where I get lost, I can solve for every problem in difraction ( We did Rayleigh's criterion, double slit / single slit difraction) but I can't seem to be able to start a problem that involves grating, any pointers on how to start would be nice ^^ I just want to know how to approach the problem! :)
 
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As far as finding the angles for the bright fringes, there is no difference between a grating and a double slit.

One approach to this problem would be to use the information about the 681 nm line to determine the distance d between two slits in the grating.
 
Ah, it worked. Thanks a lot ^^ Just a little question, if you don't mind answering it of course. If ever it asked me to look for the distance between the two waves, would I need to compare the equations or something?
 
MarcL said:
Ah, it worked.
Good!

MarcL said:
If ever it asked me to look for the distance between the two waves, would I need to compare the equations or something?

I'm not sure what you mean by "distance between the two waves". Can you clarify that?
 
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