Write your name, section, and today's date in the cell below:¶

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Synopsis¶

In this lab, we will explore diffraction, refraction, and polarization of light. There are a couple warnings for this lab: - There are lasers in this lab. Don't look into the aperture. - The glass tubes can get quite hot. Don't touch them while they are on (or for some time after they turn off).

Polarization¶

You have a red laser and three linear polarizers. Hold the polarizer in the path of the beam and rotate the polarizer. Is the laser light polarized? - Give answer here Take two polarizers and hold them at a right angle in the path of the beam. What fraction of the light passes through the beam? - Give answer here Hold a third polarizer at a 45 $^\circ$ angle with respect to the second polarizer (in terms of their orientation with respect to the first polarizer, the angles of the three polarizers should be $0^\circ,90^\circ,45^\circ$ ). What fraction of the light passes through the third polarizer? - Give answer here Rearrange the three polarizers so that the angles are $0^\circ,45^\circ,90^\circ$ . How much light passes through the third polarizer? Is this different from the previous question? Can you explain this behavior? - Give answer here

Diffraction¶

Introduction¶

The light emitted by discharge tubes will be at fixed wavelengths. These wavelengths correspond to the energies emitted when an electron in an atom drops from a higher to lower energy level. By precisely measuring these wavelengths, we can potentially probe low-level quantum effects. In this part of the lab, we will look at the spectra of tubes containing either hydrogen or mercury. As an introduction, look at the overhead lights with the cardboard spectrometer. You should see some strong lines on top of a dimmer continuum. At what wavelengths do you see the lines? - Give answer here

Equipment¶

Take some time to get to know the spectrometer (the metal one). It has one fixed arm with a slit at the end, which will face the gas tube. It has another arm you will look through, which swivels. between the arms, there is a circular pad where you will place either a diffraction grating or a prism, which can be fixed in place with the metal clip (it can be pulled up and lowered down to clip something in place). The pad can itself also rotate, separately from the arm. There are multiple knobs, controlling different pieces: - There is a knob on the fixed arm to change the width of the slit - There is a knob on the swivel arm to control the angle more finely than can be done by manually rotating the arm. - There is a knob to allow the scale to move relative to the swivel arm (the lowest knob; tighten the knob to fix in place) - There is a knob to allow the swivel arm to move (tighten the knob to fix in place) - There is a knob to allow the pad to rotate relative to the arm (tighten the knob to fix in place)

There are metal pieces that will be placed on top of the pad to shield it from external light, but you'll need to remove and replace the pieces whenever you need to modify what's on the pad, so they don't need to be placed yet. For future reference, one piece fits on top of the swivel arm and will rotate when you rotate the arm. The other piece fits around it on the other side, with the hole facing the fixed arm. Once the metal piece is in place, the fixed arm has a piece that can be pulled out and latches onto the metal piece (ask for help if you have trouble with this).

Setup the lamp with the hydgrogen tube, and orient it so that the center of the tube is right outside the slit. Place the diffraction grating onto the center of the pad, and clip it in place. Cover the pad with the metal pieces.

Calibration¶

Look straight through the the swivel arm toward the slit, such that the angle is approximately set to $0^\circ$ . The light should be as bright as possible. Shift the lamp slightly until the light is maximized (i.e. such that the light is right at the slit), and shift the eyepiece as needed to put it into focus. When you widen or narrow the slit, one side is fixed and one side shifts. Which side is fixed?

Give answer here

You should see a vertical line through the eyepiece. Orient the eyepiece so that the line is vertical, and line it up with the side of the side of the slit that is fixed. What reading does the spectrometer give for the angle? Rotate the scale relative to the movable arm (loosening the lowest knob allows for moving the scale relative to the arm) such that the angle is 0 when everything is aligned as described. - Give answer here For future measurements, you'll want to adjust the slit width as needed. In general, you'll want to narrow the slit to make measurements and potentially widen the slit as needed to find the general location of lines. It can be easier to find spectral lines when the slit is wide, just because it allows more light, but narrowing the slit allows for more precise measurements.

Spectral lines¶

A diffraction grating is effectively a series of slits with a periodic structure (i.e. N slits/mm). As a result, light of a particular wavelength that shines through a grating diffracts at a particular angle (dependent on wavelength). By measuring the angle at which light diffracts, we can measure the wavelength of the light. For light that shines directly through a grating, the angle is given by $sin(\theta)=n\lambda/d$ , where d is the distance between slits, and n is an integer greater than or equal to 0.

Find at least three spectral lines (for n=1). At what angles do you see them? Measure this as precisely as possible (use the knob on the swivel arm to finely control the position of the arm). - Give answer here The lines you see are all in the Balmer series, where electrons drop from a higher energy level to the second energy level (not taking into account more complex quantum effects), and we can use the angles to measure the wavelengths. However, we do not know the value of d, the distance between slits, and the first step is to determine the value of d based on a known value of $\lambda$ . For this calculation, we will use H-alpha, the lowest energy visible line (the red line). It is at 656.3 nm. Use this value to calculate the value of d. - Give answer here Based on this calculation, at what wavelengths do you see the other spectral lines (using the previously-given equation)? - Give answer here Replace the tube with mercury (since the tubes are hot and take time to cool off, and since there are multiple lamps available, just use a new lamp). As before, find as many spectral lines as you can. At what angles do you see these lines? - Give answer here Using the equation, at what wavelengths do you see the lines? - Give answer here Are the locations of the spectral lines of mercury unexpected? - Give answer here

Refraction¶

Similarly to a diffraction grating, a prism bends light, and because different wavelengths bend different amounts, a prism separates light into its component wavelengths. For this part of the lab, you will determine the index of refraction of the given prism. The index depends on wavelength, so you will measure it at the wavelengths corresponding to the hydrogen lines.

In general, light that shines on one side of the prism will bend and then pass through another side. The exact angle at which the light diverts after passing through the prism depends on the exact orientation of the prism. However, there is a particular orientation that minimizes the angle at which the light is diverted. The derivation of the equation for this angle is annoying, so for this lab we'll just use the equation directly: $\theta=2\textrm{sin}^{-1}(n\textrm{sin}(\alpha/2))-\alpha$ $\alpha$ is the angle of the prism, which can be measured with a protractor (one side of the prism isn't transparent; the angle is the angle between the two transparent sides). What is the angle $\alpha$ ? - Give answer here Now, replace the grating with the prism. It can be a little tricky to orient the prism correctly, so keep the metal piece in place that goes over the rotating arm but not the piece that goes over the fixed arm. For a particular orientation of the prism, find H-alpha. After finding H-alpha, carefully rotate the prism by hand and follow H-alpha with the eye-piece (I'd suggest one person rotates the prism and one looks through the tube). Find the minimum angle where H-alpha can exist (if you keep rotating the prism in one direction, the refraction angle will keep decreasing until it reaches a minimum value, and then it will start increasing again). What is the minimum angle? Measure the minimum angle for each hydrogen spectral line. - Give answers here Solving for n for each spectral line, what is the index of refraction n at each wavelength? - Give answers here Based on the above, does the index decrease or increase with wavelength? - Give answer here