Double slit and grating

What is it about?

Laser light passing through two narrow slits gives a whole series of bright and dark fringes on a distant screen – explained by the wave model of light: each slit sends out a circular wave (Huygens), and the waves interfere. In direction $\alpha$ neighbouring slits have the path difference $\Delta s = g \cdot \sin\alpha$, so principal maxima appear at

More slits make the maxima sharper, with $N - 2$ weak secondary maxima in between. A grating (e.g. $500$ lines per mm, $g = 2\,\mu\text{m}$) gives sharp lines at large angles. In the picture the slits are greatly enlarged; the slit width in the model is $b = \frac{g}{6}$.

Try it

1. Drag the measuring mark to the first maximum and compare with $\frac{\lambda a}{g}$. Load example
2. Increase the number of slits. Five slits
3. Switch to the grating. Grating
4. Try a single slit. Single slit

Tasks

Task 1: Red laser

$\lambda = 650\,\text{nm}$, $g = 0.10\,\text{mm}$, $a = 2.0\,\text{m}$. Find the distance between neighbouring maxima. Load task

Task 2: Grating

$500$ lines per mm, $\lambda = 500\,\text{nm}$, $a = 1.0\,\text{m}$. Find $\alpha_1$, $x_1$ and the highest visible order. Load task

Task 3: More slits

What changes with five instead of two slits (same $g$)?

Ideas for the classroom

• Predict here first, then measure with a real laser, double slit and grating.
• Common stumbling blocks:
  • “Larger slit spacing, larger fringe spacing.” – The opposite: $\Delta x \sim \frac{1}{g}$.
  • The small-angle approximation is often used for gratings without checking.