Diffraction Grating Maximum Order

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SUMMARY

The maximum order of diffraction for a grating with 1000 lines per mm illuminated by sodium light with a wavelength of 589.3 nm is determined using the equation dsin(θ) = mλ. The slit spacing (d) is calculated as the inverse of the number of lines per mm, resulting in d = 1 mm / 1000 = 1 x 10^-6 m. The maximum order (m) occurs when sin(θ) = 1, leading to m = d/λ, which gives a maximum order of 3.4. Therefore, the highest observable order is 3, as diffraction orders must be whole numbers.

PREREQUISITES
  • Understanding of diffraction principles
  • Familiarity with the grating equation dsin(θ) = mλ
  • Basic knowledge of wavelength and slit spacing calculations
  • Concept of maximum angle limitations in diffraction
NEXT STEPS
  • Study the derivation and applications of the grating equation dsin(θ) = mλ
  • Explore the effects of varying slit spacing on diffraction patterns
  • Investigate the properties of sodium light and its applications in spectroscopy
  • Learn about higher-order diffraction and its implications in optical systems
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Students in physics, optical engineers, and anyone studying wave phenomena and diffraction patterns in light.

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Homework Statement



A grating having 1000 lines per mm is illuminated with sodium light of mean wavelength 589.3 nm. Determine the maximum order of diffraction that can be observed.

Homework Equations



dsin(\theta)=m\lambda

d=slit spacing

The Attempt at a Solution



The order of diffraction is given by m, and m=(dsin\theta)/\lambda, so i figure m takes a maximum value when sin(\theta)=1, or when m=d/\lambda but i am not sure if this is correct.
I'd be grateful for any hints.
 
Last edited:
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Yes, the angle can't be greater than 90 degrees.
So if you put sin = 1 you will get a value for m that could be, for example, 3.4
This means you could get a 3rd order but not a 4th
 
thanks
 

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