Interference and diffraction of light

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Homework Help Overview

The problem involves the diffraction of green light with a wavelength of 5000 Å incident on a grating, where the second-order image is observed at an angle of 32 degrees from the normal. The objective is to determine the number of lines per centimeter on the grating.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants attempt to use the equation relating wavelength, slit spacing, and diffraction angle but express confusion over the relationship between slit spacing and the number of lines per centimeter. Questions arise about how to derive the number of lines from the calculated distance between slits.

Discussion Status

Participants are actively discussing the relationship between the distance between slits and the number of lines per centimeter. Some guidance has been provided regarding the conversion of slit spacing to lines per centimeter, but confusion remains about the appropriate equations and calculations to use.

Contextual Notes

There is an ongoing discussion about the definitions of variables and the correct approach to solving for the number of lines per centimeter, with some participants expressing uncertainty about how to proceed with the calculations.

poohead
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Homework Statement


green light of wavelength 5000 A is incident normally on a grating, and the 2nd order image is diffracted 32 degrees from the normal. how many lines/cm are marked on the grating

A=10^-10 n= 2 degree= 32 d=? wavelength- 5000 A

the answer to the question is 5300 lines/cm

Homework Equations



wavelength=d sin degree/ n

The Attempt at a Solution



we tried to solve for d using the following above equation but came out with the wrong answer, need help please i am in a fatal situation here,

 
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poohead said:
we tried to solve for d using the following above equation but came out with the wrong answer, need help please i am in a fatal situation here,
d is the distance between slits, not the number of slits per cm.
 
So then what would I do to get an answer with lines/cm
 
poohead said:
So then what would I do to get an answer with lines/cm
Given the spacing between lines, figure out how many fit into a centimeter.
 
the spacing between lines is X?
 
I don't understand then what equation i am to use to solve for such
 
poohead said:
I don't understand then what equation i am to use to solve for such
Here's an example: If d = 1/100 of a cm, how many lines are there per centimeter?
 
100? but you said that d is the distance between slits, not the number of slits per cm. so what am i trying to find for this situation?
 
poohead said:
100?
Right. If you can do this example, use similar reasoning to solve your problem.
but you said that d is the distance between slits, not the number of slits per cm.
That's true. You use d to calculate the number of slits per cm.
so what am i trying to find for this situation?
Your final answer will be the number of lines per cm. You start by finding d.
 
  • #10
sorry I am still confused on how to get there, what would i possibly do with d?
 
  • #11
poohead said:
sorry I am still confused on how to get there, what would i possibly do with d?
Try this analogy: Along a path there is a tree every 1/4 mile. How many trees per mile?

Here "1/4 mile" plays the same role as "d".
 
  • #12
there would be four, but so i solved for d and i get 1.81x10^-6, so now i convert that into cm?
 
  • #13
poohead said:
so i solved for d and i get 1.81x10^-6,
Careful how you round off.
so now i convert that into cm?
Yes, find d in cm.
 

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