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Wize High School Grade 12 Physics Textbook > Wave Nature of Light

Single Slit Diffraction

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Single Slit Diffraction



Light passing through a single slit can be viewed as an infinite number of point sources.

The resulting pattern shows a wide central maximum, followed by smaller bright fringes on either side.


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Dark fringes on the screen correspond to destructive interference. The path difference Δl\Delta l is given by:
 wsin⁡θ=nλ \boxed{ \ w\sin\theta=n\lambda \ }
n=±1,±2,…n=\pm1,\pm2,\ldots

where ww is the width of the slit.

Exam Tip
  • This formula is exactly the same as for the double slit, except that here ww is the width of the slit instead of the distance between the two slits dd.
  • Also, n\bf n here labels the dark spots, not the bright spots as the double slit.


Watch Out!
Because nn labels the dark spots on either side, and we have a bright spot at the center, nn cannot be zero.










Bright fringes on the screen correspond to constructive interference. The path difference Δl\Delta l is given by:
 wsin⁡θ=(n+12)λ \boxed{ \ w\sin\theta=\bigg(n+\dfrac{1}{2}\bigg)\lambda \ }
n=±1,±2,…n=\pm1,\pm2,\ldots


Exam Tip
To find the width of the central maximum, you need to find double the distance yy corresponding to the first dark fringe, which has n=1n=1.

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Small Angle Approximation:


For y≪Dy\ll D we can use the small angle approximation, which gives us:

nλw=sin⁡θ ≈ tan⁡θ=yD\dfrac{n\lambda}{w}=\sin\theta \ \approx \ \tan\theta=\dfrac{y}{D}

Therefore we have the angle and position on the screen for dark fringes:

 θ=nλw \boxed{\ \theta=\dfrac{n\lambda}{w} \ } and  y=nλDw \boxed{ \ y=\dfrac{n\lambda D}{w} \ }

for n=±1,±2, ...n=\pm1,\pm2, \ ...

Wize Concept
As the width of the slit ww gets smaller (the slit gets narrower), the patter gets wider.

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Example: Single vs. Double Slit


A two-slit apparatus with slits a distance of 22 mm apart is illuminated by an Argon laser (wavelength454.6454.6nm). Then, in a separate experiment a single slit of width 22 mm is illuminated. The two intensity patterns are shown below. Which one is the single-slit?



The lower one is the single slit because it has a much wider central max.

Practice: Single Slit


You shine light of 480480nm upon a single slit located 0.10.1m away from a screen. On the screen, you measure the distance to the 3rd3^{rd} dark spot to be 0.50.5m.

a) What is the width of the slit?

b) What is the width of the central bright spot?