Dispersion by diffraction grating

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Homework Help Overview

The problem involves calculating the width of the first-order spectrum produced by a diffraction grating when white light of varying wavelengths is incident upon it. The context includes specific values for wavelength and grating lines per centimeter.

Discussion Character

  • Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants discuss the application of a specific equation related to diffraction and question its consistency and correctness. There are attempts to clarify the relationship between variables and units, with some participants expressing uncertainty about the equation used.

Discussion Status

There is ongoing exploration of the equation's validity and its application to the problem. Some participants have arrived at similar numerical results, but there is no explicit consensus on the correctness of the approach or the equation itself.

Contextual Notes

Participants mention time constraints, indicating urgency in resolving the problem. There is also a focus on ensuring unit consistency in the calculations.

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Homework Statement



White light containing wavelengths from 396 nm to 756 nm falls on a grating with 7300 lines/cm. How wide is the first-order spectrum on a screen 2.15 m away?

Homework Equations


y=m*L*wavelenth/(d)


The Attempt at a Solution


using the equation I have found y1 to be 62.149 and y2 118.635. I took the difference of the two which gave me 56.486 cm, but that is wrong for some reason. Please help.
 
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Are you sure of that that's the equation for diffraction? Checking the units, it's quite inconsistent... Check the equation again...
 
That's the equation I'm used to. If we assume that the angle is small then sintheta=y/L
dsintheta=m*wavelength
d(y/L)=m*wavelength
m*wavelength*L/(d)=y ? I don't know what's wrong with the equation. For the units I converted everything to cm because 1/7300=d in cm.
 
Please help, I only have a couple of hours left.
 
I got 56.502 cm, using the equation. we seem to get the same answer.
 
Last edited:

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