How Do You Calculate Unknown Wavelengths Using Diffraction Grating Formulas?

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SUMMARY

The calculation of unknown wavelengths using diffraction grating formulas involves applying the equation nλ = d sin(θ). In the discussion, a known wavelength of 420 nm produces a bright fringe at an angle of 26°, while an unknown wavelength produces a bright fringe at 56° with the same order m. The correct approach requires using the sine of the angles and considering the distance ratios if initial calculations do not yield accurate results. This method is crucial for solving diffraction problems accurately.

PREREQUISITES
  • Understanding of diffraction grating principles
  • Familiarity with the formula nλ = d sin(θ)
  • Basic trigonometry, particularly sine functions
  • Knowledge of bright fringe order in diffraction patterns
NEXT STEPS
  • Research the impact of angle approximation on diffraction calculations
  • Learn about the application of distance ratios in diffraction problems
  • Explore the use of diffraction gratings in optical devices
  • Study advanced diffraction patterns and their mathematical representations
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Students and professionals in physics, optical engineering, and anyone involved in experiments or applications related to diffraction and wavelength calculations.

Laceb04
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For a wavelength of 420 nm, a diffraction grating produces a bright fringe at an angle of 26°. For an unknown wavelength, the same grating produces a bright fringe at an angle of 56°. In both cases the bright fringes are of the same order m. What is the unknown wavelength?
________________nm


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My answers all keep coming out wrong. I don't know what I'm doing!
 
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Laceb04 said:
My answers all keep coming out wrong. I don't know what I'm doing!

It's hard for us to tell what you're doing wrong when you don't post your work. Let's see your attempted solution.
 
According to the short cut formula
n lambda = d sin theta
just set up x sine angle to 420 sine angle ratio.
However, this only works for small angles.
If that does not give right answer, you have to distance ratios
 

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