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Diffraction

As you have learned in this TLP, diffraction patterns are formed from constructively interfering rays of scattered waves. Consider the diagram on the left.

The scattered rays will be in phase if the optical path difference (o.p.d.) is an integer number of wavelengths,
which can be written as:

nλ = s sinθ.

s θ θ θ o.p.d. o.p.d. - optical path difference

Spacing
A diffraction pattern can be observed if a screen is placed in the optical path, as shown below:




L diffraction slit spacing, s screen laser θ x

If θ is small, then we can approximate sinθ ≈ tanθ such that
  λ/s≈x/L

  

Layer 2 0.8 0.6 0.4 0.2 0 /m screen face laser screen refraction slit spacing, s Vertical spacing of spots on the screen is given by, x = λL / s x can also be found using similar triangles. Sorry, your browser does not support inline SVG.
Colour



Slit spacing, s
5 μm
Screen distance, L
2 m
Please select a colour, slit spacing and screen distance

  

Layer 2 screen face 0.8 0.6 0.4 0.2 0 /m laser screen refraction slit spacing, s
Q1 Calculate the slit width (s) given that

wavelength of light (λ) = 600 nm
distance to screen (L) = 1.75 m
Enter your answer for slit width / μm



  

Select quiz



Image formation
u v f Object(diffraction grating) Lens Back focal plane(diffraction pattern) Magnified Image(slits resolved) +θ −θ

Interestingly the diffraction pattern we would have seen without the lens is reformed by the lens at the “back focal plane”. The distance from the lens to this plane is characteristic of the lens, and is called the focal length.

  

Examine the set up


 
          
  Diffraction grating s

Diffraction grating

  

Back focal plane


screen face 7
Observation
on the screen
Adjust screen distance from the lens
5.5cm

  
Forming an image


Using the focal length of 5.5 cm, and setting the distance from the grating to the lens (u) to be 20 cm, use the lens equation (1/f = 1/u + 1/v) to calculate where the screen should be in order to see the image (i.e. the distance v).
An image is formed on the screen but the distance must be adjusted to get a focussed image.

Adjust image focus
Diffraction grating image

Selected Area Diffraction
It is possible to use an aperture to form an image from only some of the beams that pass through the back focal plane. This is known as selected area imaging. If the image includes the straight through beam that was not diffracted it is called bright field imaging because this is the most intense beam. If the straight through beam is excluded, then it is known as dark field imaging.

Diffraction grating

Grating

Bright field

Dark field

apertures

Diffraction
pattern

  


What image is shown by introducing an aperture?
Use the radio buttons to change the size of the moveable dot.
Move the grey dot around by dragging to see the image for
each part of the diffraction pattern..

Bright field image
apertures
Select aperture size and display