Diffraction grating problems

  • Thread starter bigsaucy
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  • #1
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A diffraction grating with 600 lines/mm is illuminated with light of wavelength 500nm. A very wide viewing screen is 2.0m behind the grating.

b.) How many bright fringes can be seen on the screen.

MY ATTEMPT:

i worked out the angular separation between bright fringes to be 0.305 rad (i know this is right because i got the answer to part a right). So then the screen has a total angle of 180 degrees or pi rad. therefore i reasoned that the number of fringes is pi rad/0.305 rad. But since there won't be any bright fringe at 0 rad or pi rad, the final solution must be pi (rad/0.305 rad - 2)

Is this reasoning correct or am I completely off? (Note, the answer is 7 fringes)
 

Answers and Replies

  • #2
Doc Al
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Hint: What's the highest order fringe visible on the screen?
 
  • #3
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Yeah... still not hitting any switches, sorry, lol.
How are we meant to find the number of orders?
 
  • #4
Doc Al
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What equation tells you the angle that a bright fringe makes?
 
  • #5
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d sin theta = m lambda?
 
  • #6
Doc Al
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d sin theta = m lambda?
Exactly. Use that to find the greatest value of m that can appear on screen.
 
  • #7
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I don;t get it? How am I meant to solve for something that has two unknown variables? the theta and the m value?
 
  • #8
Doc Al
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I don;t get it? How am I meant to solve for something that has two unknown variables? the theta and the m value?
Ah, but theta is not an unknown. What's the largest angle that a fringe could make and still be visible on the screen? (For all practical purposes.)
 

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