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Wize University Physics Textbook (Master) > Wave Optics

Single Slit Diffraction

Double Slit Diffraction Modified Previous Section
Realistic Double Slit diffractionNext Section
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Diffraction as the Spreading of Light


Diffraction is the spreading out of light as it passes through a small opening.

But why does this happen? Why does light "spread" in the first place?


According to Huygen's Principle, waves can be modeled as a bunch of little wavelets. That is, every point on a wave front can be considered a point source, generating secondary waves spreading away from it. As a wave spreads out, each wavelet is spreading out and interfering with all the others.




→\to Actually, light can be described as either waves, or as particles called photons.

→\to The fact that light can be accurately described either way is why we talk about the wave-particle duality.



Wize Concept
It turns out that this duality is true for all matter as well. Electrons behave like waves, and fundamentally, everything else does, too!

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.

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?