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## 15 March 2010

### Using Red AND Green Lasers

As soon as we get back from spring break, I will be discussing "physical optics" -- double slits, diffraction gratings, thin films, and so on.  I always start with the double slit -- why light through a double slit produces a diffraction pattern, and the equation for the location of the minima and maxima.

Here the best demonstration, I think, is to shine a red laser through a diffraction grating.  (No, I don't start with a real double slit... a diffraction grating produces sharp maxima which don't invite arguments about whether we're really seeing bright and dark spots; and, the mathematics for diffraction gratings are identical to those of double slits.  Later, after the class is comfortable predicting the location of the bright spots, I explain the qualitative differences between diffraction gratings, double slits, and single slits.)

This demonstration can start off quantitatively.  Using the known slit spacing of the diffraction grating, the wavelength of the laser (printed on there somewhere), and the distance to the screen, predict the distance between the first two bright spots using dsinθ = mλ.

Next, ask the qualitative question: if the red laser is replaced by a green laser, what happens to the distance between bright spots?  Let the class argue it out amongst themselves:  the wavelength of green light is smaller than the wavelength of red light.  (Yes, you have to know that fact for the AP exam.)  By the above equation, reducing the wavelength while keeping d and m constant reduces sin θ as well.  As the sine of an angle decreases, the angle itself decreases.  So, the angle to the bright spot decreases, and the bright spots will be closer together.

Note that it is legitimate to argue using the small angle approximation equation x = mλL/d.  You'd find that reducing the wavelength reduces x, the distance from the central maximum to the mth spot.

Then, if you have different diffraction gratings, you can ask how the distance between spots will change using these other gratings.

"But I don't have a green laser," you say.  I bought one a few years ago for \$200.  But now both green and red lasers have come way down in price.  Search around.  I just bought a pack of twelve keychain red lasers for about \$2 each; I found green lasers for about \$10 each.  Considering its other uses in geometric optics (for ray tracing in an aquarium, say) or in an astronomy unit (to point out stars in a nighttime observing session), the \$10 is worth it.