Laser Safety
- We use low-power lasers, but:
- Keep the lasers aimed horizontally.
- Keep them below eye-level.
- Turn them off when you’re not using them.
- Do not look directly into the beam or its reflections from polished surfaces.
Setting Up
- This Lab is best done in the dark. You will need a desk lamp, flashlight, or other portable source of light that you can turn off and on as you perform the experiment. You will also need a flat, smooth surface upon which to set up your “optical bench”. You will be shining your laser through a slide from your optical desk towards a “screen” that should be approximately 1.5 to 2 meters away from your “optical bench”. Thus you will need 1.5 to 2 meters worth of unimpeded space between your optical bench and the screen.
- Now that you have a portable source of light and an area to set up your optical bench, watch the “Setting Up an Optical Bench for Interference Patterns Video” available on Blackboard. Set up your “optical bench” as instructed in the video.
- Examine the slide provided so you know the location of the slits.
- Position the laser and the slide (use the 0.075 mm slit) on your lab bench so that a diffraction pattern appears on your paper screen.
Observations of Single-Slit Diffraction
- Direct the laser beam through the single-slit labeled 0.075 mm and make a sketch of the pattern at the top of a page in your Write-up Template. The sketch does not have to be to scale. (The patterns are best observed at the paper screen, not from your bench – just make sure that you’re looking at the paper, not the laser!) Record the slit width to the right of the sketch. Repeat this procedure with the single-slit labeled 0.15 mm and sketch its pattern directly beneath the 0.075 mm slit’s pattern while aligning the middle of the central maximum of its pattern with the middle of the central maximum of the 0.075 mm pattern (Sketch the pattern relative in scale to the 0.075 mm slit pattern that you drew). The patterns do not need to be perfect but should reflect the change in center-to-center distances of the minima. Now repeat this procedure with the single-slit labeled 0.4 mm and sketch its pattern directly beneath the 0.15 mm slit’s pattern while aligning the middle of the central maximum of the two. (Again, sketch the pattern relative in scale to the two previous patterns).
- Record observations and note any trends in the distance between minima as the slit width increases.
- Now re-direct the laser beam through the single-slit labeled 0.075 mm onto the paper screen (this is the pattern that you will use for the quantitative analysis later). Carefully mark on the screen the center of the pattern (the middle of the central maximum) and the centers of three diffraction minima to the immediate right and left of the central maximum.
- Be sure to draw a clear picture of your experimental setup. Make sure to measure and record the distance D (distance from the slide to the screen) with uncertainty.
- Complete the rest of the day’s observations before starting the quantitative analysis.
Observations of Double-Slit Interference
- Direct the laser beam through the double-slits and make a sketch of the pattern (Again, the patterns are best observed at the paper screen – just make sure that you’re looking at the paper, not the laser!) Note that the double slit-pattern is comprised of the tiny “beads” of light.
- How does the double-slit pattern differ from the single-slit patterns?
- Notice that the single-slit pattern is imposed on the double-slit interference pattern. Why do you think this is happening?
Determining the Width of a Single Slit from a Diffraction Pattern
For a wavelength \(\lambda\) and nonzero integer \(m\), the \(m^{th}\) minimum of a single-slit diffraction pattern is at an angle \(\theta_{m}\) away from the center of the pattern when the slit is of width \(a\) and $$ a \sin\theta_{m} = m\lambda.$$ It is hard to measure \(\theta_{m}\) directly when it is small, but it is easy to measure \(y_{m}\), the position along the screen of the \(m^{th}\) minimum, relative to the center of the pattern.
- If you have not done so already, make a sketch similar to the one on the chalk board that I used in the “Interference of Light From a Laser Video”. A copy of this chalk board is in Blackboard. Show just the first minimum to the right of the central maximum in your sketch. Looking at this sketch, use the single-slit equation above to derive a linear equation for \(y_{m}\) in terms of the order of diffraction \(m\), \(D\), \(\lambda\), and \(a\). (Hint: Look for the similar triangles and determine the relationship between \(y_{m}\), \(D\), and \(\theta_{m}\) knowing that \(\theta_{m}\) is a very, very small angle.)
- Using the single-slit pattern that you marked earlier, measure the positions \(y_{m}\) relative to the middle of the central maximum of the single-slit pattern minima and record them in a table along with their uncertainties.
- Negative \(m\) values should correspond to negative \(y_{m}\) values.
- Plot the minima positions \(y_{m}\) vs. the order of diffraction \(m\), including error bars. Include a point at \((0,0)\), but note in your table that this point is not the location of a diffraction pattern minimum – it’s the location of the central maximum. Thus force your plot through \((0,0)\) by setting the y-intercept to \(0\) in Excel.
- Use straight-line analysis and the known wavelength of your diode laser to find the slit width \(a\) with uncertainty.
- Compare to the expected value.
