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PBL: Single slit diffraction

Sticks and Hoses

Take about 2 meters of plastic hose pipe and stretch it straight.

  • Start curving it into a circle.

  • Derive an equation for the distance between the ends as a function of the angle between the ends of the pipe (The angle being defined such that it is 0 radians when the hose is straight).
  • Plot the function in Geogebra.
  • Do a simple experiment to test you model.

You can build this in Algodoo by putting motors between lots of sticks, see if you can build one like mine.

Plot the PE in the spring that joins the ends.

You can also try building this in Geogebra (a bit more tricky).

Measure the intensity of the light diffracted through a single slit as you scan a sensor across the pattern

With reference to Huygen's construction explain why the Algodoo graph is the same as the single slit diffraction pattern.

  • Why is the length graph not quite right?
  • Are there any other differences between the prediction and reality?
  • What is the ratio between the intensity of the principal max and the first max? Does this agree with the prediction? Does it agree with the Algodoo model?
  • Try fitting the single slit diffraction equation to you data.

In the IB you will only be asked about the position of the first minima.

  • What is the angle between the ends of the pipe at the first minima?
  • What is the phase difference between the waves represented by the pipe ends?
  • Show that the 1st minima occurs at an angle given by dsinθ = λ

This Geogebra applet shows how the Intensity varies at different angles from the central maximum

Extension

Throughout this example we have assumed that the rays are parallel. How would you modify the model if the rays were not parallel?

In Geogebra you can base the colour of the dots on a value. See if you can produce a diffraction pattern.
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