First-Order Spectrum Width for Diffraction Grating

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SUMMARY

The discussion centers on calculating the width of the first-order spectrum produced by a diffraction grating with 7510 lines/cm when illuminated by white light with wavelengths ranging from 405 nm to 760 nm. The calculations involve using the sine function to determine the angles for each wavelength, leading to the locations of the first-order maxima. The final width of the spectrum is determined by subtracting the two maxima locations, yielding a definitive width measurement. The confusion regarding the multiplication by two stems from the interpretation of large angle approximations in diffraction theory.

PREREQUISITES
  • Understanding of diffraction grating principles
  • Familiarity with trigonometric functions in physics
  • Knowledge of wavelength measurements in nanometers
  • Ability to perform calculations involving angles and distances
NEXT STEPS
  • Study the principles of diffraction grating and its applications
  • Learn how to apply the diffraction grating formula: d sin θ = nλ
  • Explore the concept of maxima and minima in wave optics
  • Investigate the effects of large angles on diffraction calculations
USEFUL FOR

Students and professionals in physics, optical engineering, and anyone involved in wave optics or diffraction analysis will benefit from this discussion.

lovelylm1980
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White light containing wavelengths from 405 nm to 760 nm falls on a grating with 7510 lines/ cm. How wide is the first-order spectrum on a screen 2.29 m away?

Is this correct

sin theta= (1)*(4.05e-7m)/(1.33e-6m)= 0.305 theta=17.8
location= 2x(tan 17.8)= (2*2.29)*0.321=1.47m

sin theta= (1)*(7.60e-7m)/(1.33e-6m)= 0.571 theta=34.8
location= 2x(tan 34.8)= (2*2.29)*0.695= 3.18m

so then should the answer to the question be
3.18m+1.47m/2= 2.33m
 
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lovelylm1980 said:
location= 2x(tan 17.8)= (2*2.29)*0.321=1.47m
Why did you multiply by 2?
 
so then should i multiply the angle by 2
 
Why are you multiplying anything by 2??
 
because the book states that with large angles you should multiply by two either way I don't get the correct answer based on the formula i used. Whether I multiply by 2 or not the answer still seems to be wrong. Am I not supposed to add at the end then divide by two for the answer?
 
lovelylm1980 said:
because the book states that with large angles you should multiply by two either way I don't get the correct answer based on the formula i used. Whether I multiply by 2 or not the answer still seems to be wrong. Am I not supposed to add at the end then divide by two for the answer?
That makes no sense.

Find the location of the first order maxima for each wavelength. Subtract those two numbers and you'll have the width of the first order spectrum.
 

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