Physics IA · C · Wave behaviour · topic 19 of 30

Single slit: how does the pattern width change with a? · IB Physics IA idea: guide, sample graph and step-by-step plan

beautiful physics, simple graph

A narrower slit makes a wider pattern, which feels backwards. You're going to measure how much wider, and test the rule.

Difficulty●●○ Medium
KitStandard: laser, slit set, tape measure
TimeAbout 10 hours
FitsHL (single-slit diffraction is HL); SL with extra reading
  • ✓ you like optics
  • ✓ you can work carefully in a dim room
  • ✓ you want a result that gives you the laser's wavelength

The big idea

← define the edge FIRST

Light passing through a slit of width a spreads out, and the central bright band has width w ≈ 2λD/a on a screen at distance D. So w is proportional to 1/a, and a graph of w against 1/a is a straight line through the origin whose gradient gives λ. The hard part is measuring w: the edge of a bright spot is not sharp. Decide how you will define the edge, and the rest follows.

Make it yours: pick one twist

Copying a classic won't show your choices. Pick one of these (or invent your own) and your IA becomes yours.

Swipe for more twists →

Change the screen distance instead

Keep a fixed and move the screen.

→ A different graph (w against D); the gradient tells you something new and the measurement of D becomes the main uncertainty.
Use a different colour

Repeat with red and green lasers (check their wavelengths).

→ Two gradients, and a ratio you can compare with the ratio of wavelengths.
Make your own slit

Use two razor blades or slides with a measured gap, and measure the gap under a magnifier.

→ The slit width becomes your largest uncertainty, and the evaluation is rich.
Measure the intensity

Use a light sensor or phone camera to record the intensity profile.

→ A more objective definition of the edge: the first minimum, found from the profile, not by eye.
Check the small-angle approximation

Use a wide pattern (a narrow slit, a short D) and compare 2D tanθ with 2D sinθ.

→ Tests an assumption in your formula; a clear step in the analysis.
Test a double slit

Measure the fringe spacing of a double slit within the single-slit envelope.

→ Brings in two interference effects; harder, but a good stretch.

Your Physics IA research question: run the check

Write your own question first. Then make sure it ticks every box:

  • Names one independent variable and its range (which slit widths, in mm, and how many values).
  • Names one dependent variable and how the edge is defined (width of the central maximum, between which points?).
  • Says what stays fixed: screen distance, the laser, the alignment, how dark the room is.
  • Says what you will compare your result with (the 2λD/a prediction, the stated wavelength, or both).
  • Is narrow enough to finish with at least 6 slit widths, repeats of each measurement, and a safe laser procedure.

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The set-up

One way to set it up. Draw your own version, with your real distances and slit widths, for the Method section.

wDalaser: low power, neverlook into the beamsingle slit of width a:clamped, beam centredscreen: mark the first darkgaps either side, then wtape measure for D,keep it the same

How your Physics IA could be laid out

The usual order for a topic like this, what each part needs to show, and roughly how much of your 3,000 words it takes. The words are all yours.

Research question and context~250
Your question; why diffraction limits cameras, telescopes and microscopes; what you expect and why.
Background physics~450
Diffraction at a single slit and the condition for the first minimum; the formula for the central width and its small-angle assumption; the predicted graph.
Variablestable
Independent, dependent and controlled variables, each with how you set, measure or keep it constant, and why it matters.
Method~400
How you align the laser and slit; how you fix D; how you mark the edges of the pattern; how you measure the slit; repeats.
Safety, ethics, environment~60
Short and specific: laser class, reflections, a dim room, beam stops.
Raw datatable
One table: slit width, then each width reading, with the resolution of the ruler and of the slit width in the headers.
Processing~250
How you find w and its uncertainty; how you get 1/a; how you find the wavelength from the gradient; one worked example each.
Graphs and analysis~350
w against 1/a with error bars; the best-fit line and a worst-fit line; what the gradient gives and whether the line goes through the origin.
Conclusion~450
Answer the question with numbers: how w follows 1/a, and how the wavelength from the gradient compares with the stated value.
Evaluation~650, the biggest part!
Strengths, weaknesses ranked by effect (slit width, edge judgement, laser wavelength, small-angle assumption), and improvements tied to each.
Referencesnot counted
Every source you used, including the laser's data sheet.

What your Physics IA graph could look like

the gradient gives λ!

Made-up data, to show you the form of a strong graph, not the answer. Yours will look different. example only

05101520253001020304050607080Inverse slit width 1/a / mm⁻¹ (± 0.5)Width of central maximum w / mm (± 1 mm)w = 2λD/a, red laser (650 nm), D = 2.0 msame set-up with a green laser (532 nm)your data, with error barsgradient = 2λD: you can solvefor the wavelength from itILLUSTRATIVE · MADE-UP DATA
  • Axis labels name the quantity and its unit, with the uncertainty of the value you set or read.
  • Error bars on every point. The reading of the spot edge is usually the biggest vertical bar.
  • A second line shows what a different laser would give: the gradient carries the wavelength.
  • Start the axes at zero, because the line should pass through the origin.
  • Another graph to consider: w against D for one slit, to test the proportionality to screen distance.

Which uncertainty matters most?

Rank by the effect on your wavelength found from one point (a = 0.10 mm, w = 26 mm). The slit width on the label is often the weakest number you use.

Slit width (± 0.005 mm of 0.10 mm)5%Edge of the spot (± 1 mm of 26 mm)3.8%Laser wavelength tolerance (± 10 nm)1.5%Screen distance (± 3 mm of 2000 mm)0.15%biggest effect: discuss this first!% uncertainty in λ from one readingILLUSTRATIVE · MADE-UP NUMBERS

Your game plan

laser safety goes in your plan

Tick steps off as you go. We'll remember on this device.

0 of 10 done

  1. Read and predictFind the condition for the first minimum of a single slit and the formula for the central width (this is HL content, so SL students need to read up on it and cite the source). Say what the small-angle approximation assumes and when it fails.
  2. Trial run (1 lesson)Set up in a dim room with a safe laser. Can you see the first minima clearly? Does the pattern move if you bump the table? How will you mark the edges without looking into the beam?
  3. Define the edgeDecide what you will call the edge of the central maximum, such as the first dark gap, and apply it every time. Write this definition in your method.
  4. Check the slit widthsDo not trust the label alone. Can you measure the slit with a microscope or by another diffraction measurement? Decide what uncertainty you will use.
  5. Decide widths, D and repeatsChoose at least 6 slit widths across a wide range, one fixed D, and a number of repeats. Make sure the pattern fits on your screen at every width.
  6. Collect the dataMark the edges on paper taped to the screen, then measure with a ruler. Record units and resolution. Re-align the laser if you knock anything.
  7. ProcessFind w and its uncertainty, calculate 1/a and its uncertainty, and decide how you will combine them in the graph.
  8. Graph and comparePlot w against 1/a with error bars, add best-fit and worst-fit lines, and calculate λ from the gradient with an uncertainty.
  9. EvaluateRank the weaknesses by their effect on λ. Link each improvement to a specific problem.
  10. Write, then checkWrite in the order of the layout above, then run the checklist below before your teacher's draft.

Physics you'll need

Traps to avoid in this Physics IA

  • Looking into the beam, or leaving it uncovered at eye level. Use a low-power (class 2) laser, follow your school's laser rules, keep the beam below eye level and block it beyond the screen.
  • Reading the edge of a bright spot by eye, differently each time, so the scatter looks like a physics effect.
  • Trusting the slit width printed on the card without checking it.
  • A screen distance that changes when you move the slit holder, or is measured from the wrong point.
  • Using the small-angle approximation for a pattern that is far too wide, without testing it.
  • A pattern that runs off the screen at the narrowest slit, so the last points are guesses.

More Physics IA ideas like this

Make sure it's yours

This guide shows how a topic like this is usually approached. It is not an IA. Your question, choices, data, analysis and words must be your own: change something, tell your teacher where the idea came from, and follow your school's rules on outside help.

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