HW help (Double Slit, Resolving power etc)

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(a) A double-slit experiment is set up using red light (l = 708 nm). A first order bright fringe is seen at a given location on a screen. What wavelength of visible light (between 380 nm and 750 nm) would produce a dark fringe at the identical location on the screen?
l = nm

All right so i know
d * sin theta = m * Wavelenght

How do i find the Distance and the angle?
 

Answers and Replies

  • #2
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The condition for constructive interference is what you have written down (i.e. peak on peak), but destructive interference happens when you have a trough meet a peak, i.e. there is a half wavelength difference so for destructive interference (dark fringe) [tex]dsin (\theta) = (m + 0.5)\lambda[/tex]. You should be able to go from there.
 
  • #3
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(b) A new experiment is created with the screen at a distance of 1.8 m from the slits (with spacing 0.08 mm). What is the distance between the second order bright fringe of light with l = 691 nm and the third order bright fringe of light with l = 414 nm? (Give the absolute value of the smallest possible distance between these two fringes: the distance between bright fringes on the same side of the central bright fringe.)







Ok so
D sin theta = m * Wavelenght

Distance is 2.2?
I am going to find theta
m = 1
Wavelenght is 698 in one part, and then i do the quation again for 413 right?
 
  • #4
OlderDan
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Alt+F4 said:
(b) A new experiment is created with the screen at a distance of 1.8 m from the slits (with spacing 0.08 mm). What is the distance between the second order bright fringe of light with l = 691 nm and the third order bright fringe of light with l = 414 nm? (Give the absolute value of the smallest possible distance between these two fringes: the distance between bright fringes on the same side of the central bright fringe.)







Ok so
D sin theta = m * Wavelenght

Distance is 2.2?
I am going to find theta
m = 1
Wavelenght is 698 in one part, and then i do the quation again for 413 right?
Don't lose track of the statement about the different orders of the finges. What is m for second order, and for third order?
 
  • #5
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OlderDan said:
Don't lose track of the statement about the different orders of the finges. What is m for second order, and for third order?
2 for second order, and 3 for third order
 
  • #6
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got the answer, thanks
 
Last edited:
  • #7
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You don't actually need to find the distance at all. You will have two equations equal to [tex]dsin (\theta) [/tex], and you just have to solve for the 1 unknown (wavelength).
 
  • #8
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Alt+F4 said:
got the answer, thanks

and that would be?
 
  • #9
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.00315 m
................
 
  • #10
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Yes that's correct for (b). What answer did you get for (a).
 

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