Diffraction Gratings: Many Slits, Sharper Peaks

1 · Predict

A diffraction grating has hundreds of tightly-spaced parallel slits (measured in lines per millimeter). Does a grating with MORE lines per millimeter diffract light to a larger or smaller angle for the first bright peak?

• Larger angle — more lines per mm means a smaller spacing between slits, which spreads the diffraction pattern to a wider angle.
• A denser grating gives a smaller diffraction angle.
• The diffraction angle doesn't depend on lines per mm.

2 · Set Up

1. Open the grating preset and press Reset. Light wavelength is 500 nm.
2. Enable the first-order diffraction angle readout.
3. Set the grating's line density for each trial and record the first-order bright-fringe angle.

3 · Collect Data

Plot sin θ (y-axis) against lines per mm (x-axis) for your three trials. Is the line straight through the origin?

4 · Analyze

1. For one trial, compute the slit spacing d = 1/(lines per mm) in mm, then solve d·sin θ = λ for θ, using λ = 500 nm (converting units carefully). Compare to the table.
2. Explain why a HIGHER line density (more lines per mm) means a SMALLER slit spacing d, which — since d·sinθ = λ — requires a LARGER angle θ to satisfy the same wavelength condition.

5 · Extend

1. Diffraction gratings are the heart of most spectrometers: different wavelengths diffract to different angles from the same grating, spatially separating a light source's spectrum for analysis. Explain why a denser grating (more lines per mm) gives BETTER wavelength resolution — it spreads a given wavelength range over a wider angular range.
2. The colorful rainbow you see reflecting off a CD or DVD is diffraction grating behavior — the disc's closely-spaced data tracks act like a reflection grating. Explain why tilting a CD at different angles reveals different colors most brightly.

The Physics Behind This Experiment

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