Calculating Width of Single Slit Diffraction Pattern

In summary, the central bright fringe in a single slit diffraction pattern from light of wavelength 412 nm is 1.9 cm wide on a screen that is 1.05 m from the slit. To find the width of the slit, use the equation tanθ=h/D, with h being the distance from the central maximum and D being the distance to the screen. Remember to use the small angle approximation for this equation. Also, note that in the diffraction equation, "h" is measured from the central maximum. When using the equation .5asintheta=.5wavelength, the .5 should not be included. For more information, refer to the link provided.
  • #1
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Homework Statement



The central bright fringe in a single slit diffraction pattern from light of wavelength 412 nm is 1.9 cm wide on a screen that is 1.05 m from the slit.

How wide is the slit?

Homework Equations



i keep trying the equation .5asintheta=.5wavelength
I can't seem to get the right answer but I am sure its easy

The Attempt at a Solution

 
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  • #2
Express sinθ in terms of pattern position and distance to screen. (Use a small angle approximation.)
 
  • #3
is it the eq. tantheta=h/D?
 
  • #4
phy112 said:
is it the eq. tantheta=h/D?
Yes, and for small angles tanθ ≈ sinθ.
 
  • #5
do you use h=1.9 cm and D=1.05m?
 
  • #6
phy112 said:
do you use h=1.9 cm and D=1.05m?
Not exactly. Note that in the diffraction equation, "h" is measured from the central maximum.

Also, when you wrote ".5asintheta=.5wavelength" why do you have .5 in there?

Read this: http://hyperphysics.phy-astr.gsu.edu/HBASE/PHYOPT/sinslit.html" [Broken]
 
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1. How do you calculate the width of a single slit diffraction pattern?

The width of a single slit diffraction pattern can be calculated by using the equation: w = λL/d, where w is the width of the diffraction pattern, λ is the wavelength of the light, L is the distance between the slit and the screen, and d is the width of the slit.

2. What is the significance of the width of a single slit diffraction pattern?

The width of a single slit diffraction pattern is significant because it determines the resolution of the diffraction pattern and the amount of diffraction that occurs. A wider slit will result in a broader diffraction pattern with less resolution, while a narrower slit will result in a sharper pattern with more resolution.

3. How does the width of a single slit affect the diffraction pattern?

The width of a single slit directly affects the diffraction pattern. A wider slit allows more light to pass through, resulting in a broader diffraction pattern with less contrast. A narrower slit allows less light to pass through, resulting in a sharper diffraction pattern with more contrast.

4. What is the relationship between the width of a single slit and the distance between the slit and the screen?

The width of a single slit and the distance between the slit and the screen have an inverse relationship. As the distance between the slit and the screen increases, the width of the diffraction pattern decreases. This is because the light rays spread out more as they travel a longer distance, resulting in a narrower pattern.

5. Can the width of a single slit diffraction pattern be adjusted?

Yes, the width of a single slit diffraction pattern can be adjusted by changing the width of the slit or the distance between the slit and the screen. A narrower slit or a longer distance will result in a narrower pattern, while a wider slit or a shorter distance will result in a wider pattern.

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