Solving Diffraction Grating Homework: Max Wavelength at 11°

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SUMMARY

The discussion focuses on calculating the maximum visible wavelengths produced by a diffraction grating with 105 lines/m at an angle of 11°. The relevant equation used is d*sinθ = m*λ, where d is the grating spacing (1 x 10-5 m). The participants determined that for m values of 3 and 4, the corresponding wavelengths are 636 nm and 477 nm, respectively, indicating multiple solutions for visible wavelengths.

PREREQUISITES
  • Understanding of diffraction grating principles
  • Familiarity with the equation d*sinθ = m*λ
  • Knowledge of visible light wavelengths
  • Basic trigonometry for angle calculations
NEXT STEPS
  • Research the properties of diffraction gratings and their applications
  • Learn about the relationship between angle, wavelength, and order of diffraction
  • Explore the concept of grating spacing and its effect on diffraction patterns
  • Investigate the calculation of maximum wavelengths for different m values
USEFUL FOR

Students studying optics, physics educators, and anyone interested in understanding diffraction phenomena and wavelength calculations in optical systems.

Swan
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Homework Statement


A monochromatic plane wave is normally incident on a diffraction grating with 105 lines/m. For what visible wavelengths would this grating produce a maximum at 11°.

Homework Equations


d*sinθ = m*λ


The Attempt at a Solution


d = 1 x 10-5 m

I don't get how to actually solve it because i don't know what the m for this situation would be.
 
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Hi Swan! :smile:
Swan said:
For what visible wavelengths would this grating produce a maximum at 11°.

I don't get how to actually solve it because i don't know what the m for this situation would be.

(we usually use "n", not "m")

it can be any whole number …

there may be more than one value for which there is a solution :wink:
 
tiny-tim said:
Hi Swan! :smile:


(we usually use "n", not "m")

it can be any whole number …

there may be more than one value for which there is a solution :wink:

Hello tiny-tim. Thank You for replying. How would i go about solving this question?
 
by using your equation …

what do you get? :smile:
 
tiny-tim said:
by using your equation …

what do you get? :smile:

I got at m = 3 and m = 4 the diffraction grating would produce a maximum at 11° at visible wavelengths of 636 nm, 477 nm respectively to m = 3, m = 4.
 
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