Diffraction gratings - calculating the highest order maximum

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SUMMARY

The discussion focuses on calculating the highest order maximum observable in a diffraction grating scenario involving monochromatic light with a wavelength of 694 nm and a grating with 2192 lines per centimeter. The relevant equation is dsinθ = mλ, where d is the grating spacing, λ is the wavelength, and m is the order of the maximum. The highest order maximum calculated is 6, but concerns were raised regarding the validity of the grating spacing value, suggesting that d must be comparable to the wavelength for diffraction to occur.

PREREQUISITES
  • Understanding of diffraction gratings and their properties
  • Familiarity with the equation dsinθ = mλ
  • Basic knowledge of wave optics and light behavior
  • Ability to perform unit conversions (e.g., cm to m)
NEXT STEPS
  • Research the principles of diffraction and how grating spacing affects light behavior
  • Learn about the physical significance of the order of maxima in diffraction patterns
  • Explore the concept of grating resolution and its dependence on line density
  • Investigate practical applications of diffraction gratings in spectroscopy
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Students studying optics, physics educators, and anyone interested in the practical applications of diffraction gratings in experimental setups.

Marcargo
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Homework Statement


Monochromatic light of wavelength 694. nm is incident on a diffraction grating with 2192 lines per centimetre. What is the highest order maximum that can be observed?



Homework Equations



dsinθ = mλ

The Attempt at a Solution



d = 2192/cm = 21.92/m
λ = 694 x 10 -9m
sinθ = ?

m = dsinθ/λ
= (2192 x sinθ)/(694 x 10-9

I think that this is the equation to use, but I'm not sure what angle to use. I initially tried 90 for θ, but then logically thinking about it, that wouldn't work as light travels only in straight lines. Not sure how to carry on from here. Some insight would help!

Thanks







n.b. Given answer = 6
 
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What is the highest angle possible?

But I don't believe that value for d ... it's 11 orders of magnitude bigger than the wavelength!
You only get diffraction if d is comparable to the wavelength otherwise we'd see baseball diffraction around doorways.
 

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