First-Order Spectrum Width for Diffraction Grating

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Homework Help Overview

The discussion revolves around calculating the width of the first-order spectrum produced by a diffraction grating when white light of varying wavelengths is used. The problem involves understanding the relationship between the angles of diffraction and the distances on a screen from the grating.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants explore the calculations of angles and positions for different wavelengths, questioning the reasoning behind multiplying certain values by two. There is a focus on whether this multiplication is necessary and how it affects the final answer.

Discussion Status

The discussion is active, with participants questioning the validity of their calculations and the application of formulas. Some guidance has been provided regarding the method of finding the width of the spectrum, but there is no clear consensus on the correct approach or final answer.

Contextual Notes

Participants reference a textbook that suggests a specific method for handling large angles, which is under scrutiny. There is uncertainty about the correct application of formulas and the interpretation of the results.

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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