Diffraction Gratings

12PHY - Wave Systems

Finn Le Sueur

2024

Recall: Diffraction

A double slit has only two openings, while a diffraction grating has thousands of equally spaced openings!
This increases the amount of interference that is occurring, which makes the fringes narrower
This is because there is more interference occurring which results more areas of destructive interference.

Here is a double-slit interference pattern.

Here is a diffraction grating interference pattern. Source

And here you can see how the pattern changes progressively as more slits are added to a barrier.

Instead of having two slits, diffraction gratings often have tens, hundreds or thousands
Their spacing is typically extremely small, this means the spacing between fringes is much larger than double-slits
The slits are extremely thin, so the light is diffracted over almost 180 degrees
There are a large number of slits, so interference is predominantly destructive, with small areas of constructive interference.
In the case of white light, within each fringe (n) the individual wavelengths are also split up

We should notice, as mentioned before, red light diffracts the most and blue/purple the least. This means for each fringe red is on the outside and blue/violet on the inside.
For the central white fringe, each different wavelength has arrived in-phase (\(pd=n\lambda\)), therefore their antinodes recombine into white light.

Diffraction gratings cloze. Collect one, glue it in and fill in the blanks.

We can still use our equations from before \(pd = dsin(\theta)\)
However, diffraction gratings are typically described like this: “2000 lines per cm”. We need to calculate \(d\), slit separation, from this number.

Calculate the slit separation for a grating with 2000 lines per cm.

Because there are 2000 lines (gaps) in \(1cm\), we can simply divide them to find the distance between each gap.

\[ \begin{aligned} d &= \frac{1cm}{2000 lines} \newline d &= 5\times10^{-4}cm \newline d &= 5\times10^{-6}m \end{aligned} \]

Calculate the slit separation for a grating with 120,000 lines per \(2.5cm\).

\[ \begin{aligned} d &= \frac{2.5cm}{120000 lines} \newline d &= 2.083\times10^{-5}cm \end{aligned} \]