AP Physics 2 Labs & Investigations
Use experiments to connect a physical model to measurable evidence. Every investigation follows the same student workflow: research question, experiment plan, manual or automatic data collection, apparatus operation, accepted trials, model-appropriate graphing, uncertainty, results, discussion and conclusion. Automatic datasets are clearly labeled and never replace the manual experiment.
What should an AP Physics 2 laboratory investigation include?
A useful physics lab identifies a testable model, independent and dependent variables, controls, a repeatable measurement procedure, an appropriate graph or transformation, uncertainty, and a conclusion that uses data as evidence. The graph must be chosen from the physics model—not merely because every dataset is expected to have a straight-line fit.
AP Physics 2 courses require a minimum of 25% of instructional time in hands-on laboratory investigations. Current course requirements allow virtual labs or simulations when circumstances prevent onsite access, provided the investigation is supervised by a science educator and includes student data collection, analysis, and a maintained lab record. These interactive investigations are designed to support that evidence cycle; a teacher determines how they fit a course laboratory program.
Use the same evidence cycle in every lab
The apparatus changes, but the reasoning sequence stays consistent so the experiment can be written up as a defensible physics investigation.
Determine the Pressure–Temperature Relationship of a Fixed-Volume Gas
Research question: For a fixed amount of gas in a rigid sealed vessel, how does absolute pressure depend on absolute temperature?
Physical procedure
- Seal a fixed amount of gas in a rigid vessel and connect an absolute-pressure sensor.
- Immerse the vessel in a controllable temperature bath and allow the gas to reach thermal equilibrium before each reading.
- Record temperature in kelvins and absolute pressure only after both readings are stable.
- Use at least five well-spaced temperatures while keeping the gas amount and vessel volume fixed.
- Plot P against T. Compare the measured slope with nR/V and inspect whether the intercept is physically plausible within uncertainty.
In a physical classroom version, use a rated rigid vessel and remain within the pressure and temperature limits of the apparatus. The virtual apparatus practices the same measurement sequence without pressurizing real equipment.
Model and evidence
For a fixed amount of dilute gas in a rigid container, the ideal-gas model gives
A P-versus-T graph should therefore be approximately linear. Its slope is nR/V. A substantial nonzero intercept, curvature or drifting slope should trigger a check of sensor zero, thermal equilibrium, fixed volume and model limits.
The proportional model requires absolute temperature in kelvins. A Celsius graph can look linear but its intercept has a different meaning and cannot represent P ∝ T through the origin.
Operate the experiment
Hold n = 0.015 mol and V = 350 mL fixed. Only bath temperature should change between accepted trials. Use absolute pressure and kelvin.
| Trial | Bath / gas T (K) | Absolute P (kPa) | n (mol) | V (mL) | Source |
|---|---|---|---|---|---|
| No readings recorded. Manipulate the apparatus and perform Trial 1. | |||||
The graph begins with your recorded scatter only. A best-fit line is added only when requested. Final analysis unlocks after five accepted trials.
No analysis yet.
Uncertainty & limitations
Pressure-sensor resolution, temperature equilibration and small departures from perfectly fixed volume can shift the fitted slope or intercept. Use the spread about the P–T trend to judge random scatter and the intercept/slope bias to discuss systematic effects.
Write-up rule: distinguish random scatter from a systematic effect and explain how each one changes the strength or value of the final claim.
Discussion
Evaluate linearity, slope agreement, intercept, temperature span, measurement scatter and the most important systematic uncertainty.
Conclusion
State whether the five-trial evidence supports the pressure–temperature model.
Lab feedback
- Complete the experiment to receive evidence-based feedback.
Determine the Specific Heat of an Unknown Metal by Calorimetry
Research question: Can an energy-balance experiment identify the specific heat of an unknown metal from measured masses and temperatures?
Physical procedure
- Dry and weigh the metal sample. Measure the water mass in the insulated calorimeter.
- Measure the water's initial temperature. Heat the metal in a hot-water bath long enough for the metal to approach the bath temperature.
- Transfer the hot metal rapidly into the calorimeter, cover it, stir gently, and watch the temperature probe.
- Record a stable final temperature. The final temperature must lie between the initial metal and water temperatures.
- Repeat the full mixing procedure with the same unknown metal. Calculate one specific-heat estimate per trial, then summarize the five-trial mean and scatter.
Hot metal, hot water and steam can burn skin. Use tongs, eye protection and a stable insulated calorimeter. The virtual apparatus below is for practicing the measurement logic.
Energy accounting
If the calorimeter starts at the same temperature as the water, use
with cw = 4186 J·kg⁻¹·K⁻¹ and the virtual calorimeter heat capacity fixed at 18 J/K.
Why two answers are shown
The table reports a simple two-object estimate that ignores the cup and a calorimeter-corrected estimate. In a hot-metal/cool-water experiment, ignoring a cup that absorbs energy usually biases the metal's calculated specific heat low.
Operate the experiment
Keep the same unknown metal and calorimeter for one five-trial data set. The hot bath is fixed at 95.0 °C and Ccal = 18 J/K.
| Trial | mm (g) | mw (g) | Tm,i (°C) | Tw,i (°C) | Tf (°C) | c simple | c corrected | Source |
|---|---|---|---|---|---|---|---|---|
| No readings recorded. Operate the calorimetry apparatus and perform Trial 1. | ||||||||
Trial number is a repeated-measurement label, not a physical independent variable. Do not force a regression. Compare the corrected trial estimates, their mean and spread, and the bias from neglecting the calorimeter.
No analysis yet.
Uncertainty & limitations
Mass, initial-temperature and equilibrium-temperature measurements all propagate into the calculated specific heat. Heat exchanged with the cup and surroundings is a systematic effect; repeated-trial scatter is not the same thing as that systematic bias.
Write-up rule: distinguish random scatter from a systematic effect and explain how each one changes the strength or value of the final claim.
Discussion
Compare the simple and corrected models, trial scatter, heat loss and the direction of systematic bias.
Conclusion
Report the corrected five-trial mean with appropriate uncertainty and decide whether the unknown metal is identified consistently.
Lab feedback
- Complete the five-trial experiment to receive evidence-based feedback.
Compare Work Along Two P–V Paths with the Same Endpoints
Research question: If a gas starts and ends at the same thermodynamic states, does the work done by the gas depend on the process path?
Physical procedure
- Use a low-friction piston or gas syringe connected to an absolute pressure sensor and a calibrated volume scale.
- Choose one initial state (P1, V1) and one final state (P2, V2) for both processes.
- For Path A, change pressure and volume gradually together. For Path B, change pressure first at nearly fixed volume, then change volume at nearly constant final pressure.
- At each of five ordered checkpoints, measure both paths without reordering the data. The order is part of the process.
- Plot P versus V and estimate work with the trapezoid rule. Use 1 kPa·L = 1 J.
This lab reports work done by the gas. Expansion gives positive Wby; compression gives negative Wby. Work on the gas has the opposite sign.
Prediction before measuring
Both paths have the same endpoints, so the state change is the same. The area under the P–V curve can still differ because work is a path/process quantity.
First-law connection
Using ΔU = Q − Wby, the same ΔU with different Wby requires different heat transfer Q.
Uncertainty
Pressure resolution, volume-scale reading, piston friction and failure to pause at a quasi-static state all affect the area estimate. Five well-spaced ordered checkpoints are more useful than many rushed readings.
Operate the experiment
Use the same P1, V1, P2, V2 for both paths. The five ordered checkpoints are 0%, 25%, 50%, 75%, 100%.
| Checkpoint | Path A V (L) | Path A P (kPa) | Path B V (L) | Path B P (kPa) | Source |
|---|---|---|---|---|---|
| No paired checkpoints recorded. Prepare the apparatus and perform the 0% checkpoint. | |||||
Use the five checkpoints in recorded order. The vertical constant-volume portion of Path B contributes approximately zero work because ΔV ≈ 0. The graph is P versus V, so signed area has units kPa·L = J.
No analysis yet.
Uncertainty & limitations
Pressure and volume sensor resolution, finite checkpoint spacing and imperfect reproduction of the same endpoints affect the numerical P–V areas. The comparison is strongest when both paths share the same measured start and end states.
Write-up rule: distinguish random scatter from a systematic effect and explain how each one changes the strength or value of the final claim.
Discussion
Compare the two measured areas, endpoint consistency, finite checkpoint spacing, and the effect of pressure/volume uncertainty.
Conclusion
Use the measured work values to decide whether work is path dependent even though the initial and final thermodynamic states are unchanged.
Lab feedback
- Complete five paired checkpoints to receive evidence-based feedback.
Map Electric Potential and Infer the Electric Field
Research question: Do measured potential values between fixed parallel electrodes support the model of an approximately uniform electric field in the central region?
Physical procedure
- Connect two parallel electrodes to a DC source and keep the electrode spacing fixed.
- Use a high-resistance voltmeter so the probe does not substantially disturb the electric field.
- Measure potential at five well-spaced positions along the central line between the electrodes.
- Keep the applied potential difference and electrode geometry unchanged during the run.
- Plot V against x. The slope estimates dV/dx, so the electric-field component is the negative slope.
Use only a low-voltage classroom DC source. Do not short the electrodes with the probe or a conductor. The virtual apparatus below practices the same measurement logic.
What the model predicts
For ideal parallel electrodes, the central field is approximately uniform. If potential rises toward +x, then the x-component of the field is negative:
The field points from higher electric potential toward lower electric potential. Equipotential lines are perpendicular to the field direction.
Finite electrodes produce edge/fringing effects. This experiment deliberately samples the central region and does not claim a perfectly uniform field everywhere.
Student controls
| Point | x (cm) | x/d | Measured V (V) | Source |
|---|---|---|---|---|
| No field-map points recorded. Prepare the apparatus and perform the 10% target. | ||||
Do not infer the electric field from a single point. Use the slope of the complete V-versus-x dataset and include its sign.
No analysis yet.
Uncertainty & limitations
Probe position and voltmeter resolution create random scatter, while fringing fields and probe disturbance can create systematic departures from a uniform-field model. Treat central-region linearity as evidence, not proof of uniformity everywhere.
Write-up rule: distinguish random scatter from a systematic effect and explain how each one changes the strength or value of the final claim.
Discussion
Compare the measured slope with ΔV/d and discuss meter resolution, position uncertainty and edge effects.
Conclusion
Use the complete dataset to decide whether the central field is approximately uniform.
Lab feedback
- Complete five recorded points to receive evidence-based feedback.
Test the Parallel-Plate Capacitance Model
Research question: How does capacitance depend on plate overlap area, plate separation, or dielectric constant when the other two quantities are held fixed?
Physical procedure
- Connect a parallel-plate capacitor to a capacitance meter and zero the meter before collecting data.
- Choose exactly one independent variable: overlap area A, separation d, or dielectric constant κ.
- Keep the other two quantities fixed for all five measurements.
- For the separation experiment, transform the horizontal axis to 1/d because the model predicts C ∝ 1/d.
- Use slope agreement, R², measurement uncertainty, and a nonzero intercept to judge the model rather than declaring agreement from one point.
What the slope should mean
- Vary A: slope = κε0/d, expressed here in pF per cm².
- Vary d: plot C against 1/d; slope = κε0A, in pF per m⁻¹.
- Vary κ: slope = ε0A/d, in pF per unit κ.
The ideal parallel-plate expression assumes plates are parallel and edge/fringing effects are small. Parasitic capacitance and plate misalignment can produce a nonzero intercept or weaker agreement.
Operate the experiment
The two control variables and meter precision must remain fixed during a five-trial series. Only the chosen independent variable may change after preparation.
| Trial | Design | A (cm²) | d (mm) | κ | Graph x | C (pF) | Source |
|---|---|---|---|---|---|---|---|
| No capacitance measurements recorded. Prepare the apparatus and perform Trial 1. | |||||||
Use the graph required by the chosen model. For Design d, plot C against 1/d rather than against d itself.
No analysis yet.
Uncertainty & limitations
Plate spacing and area measurements directly affect the predicted capacitance. Stray capacitance and edge effects create systematic offsets, especially at small separations or for finite plates.
Write-up rule: distinguish random scatter from a systematic effect and explain how each one changes the strength or value of the final claim.
Discussion
Compare the measured slope with the model prediction and discuss meter precision, geometry control, plate alignment, parasitic capacitance and edge effects.
Conclusion
Use all five measurements to decide whether the selected one-variable dependence is supported over the measured range.
Lab feedback
- Complete five recorded trials to receive evidence-based feedback.
Test Electric Potential Energy → Kinetic Energy
Research question: When a positive test charge is released from rest through a known electric potential drop, does its measured kinetic-energy gain equal the decrease in electric potential energy, qΔVdrop?
Physical procedure
- Use a positively charged test particle released from rest at the higher-potential side of the apparatus.
- Keep the charge and mass fixed while changing only the electric potential drop.
- Measure the final speed with the photogate after the particle crosses the acceleration region.
- Calculate K = ½mv² from the measured speed and calculate qΔV from the electrical settings.
- Plot measured K against qΔV. Energy conservation predicts a slope of 1 and an intercept near zero.
What counts as evidence?
- A straight K-versus-qΔV trend across all five accepted measurements.
- A best-fit slope close to 1 rather than agreement at only one voltage.
- An intercept small compared with the measured energy range.
- Acknowledgment that photogate precision, stray forces and nonuniform/fringing fields can shift the measured energy.
This lab uses ΔVdrop = Vstart − Vend > 0 for a positive charge. The electric potential energy decreases by qΔVdrop, while kinetic energy increases by the same amount in the ideal model.
Student controls
| Trial | Source | q (µC) | m (g) | ΔV (V) | v (m/s) | K (mJ) | qΔV (mJ) |
|---|---|---|---|---|---|---|---|
| No electric-energy trials recorded. | |||||||
Use all five accepted measurements. The central test is whether measured K is proportional to qΔV with slope near 1.
No analysis yet.
Uncertainty & limitations
Voltage and speed/kinetic-energy measurement uncertainties propagate into the energy comparison. Field nonuniformity, friction or unmodeled energy transfer can produce a systematic energy deficit.
Write-up rule: distinguish random scatter from a systematic effect and explain how each one changes the strength or value of the final claim.
Discussion
Compare the measured slope with 1 and discuss photogate precision, fringing fields, stray forces and any nonzero energy intercept.
Conclusion
Use the complete dataset to decide whether the measured kinetic-energy gain supports electric-energy conservation.
Lab feedback
- Complete five recorded trials to receive evidence-based feedback.
Ohmic Resistor vs Filament Lamp I–V Investigation
Research question: When the applied potential difference is changed, does current remain proportional to voltage for an ohmic resistor, and how does the response change for a self-heating filament lamp?
Physical procedure
- Connect the ammeter in series with the test element and the voltmeter in parallel across it.
- Keep one element and the same wiring for the complete five-point voltage series.
- At each target voltage, close the switch and wait for the reading to stabilize before capturing V and I.
- Calculate the operating resistance from R = V/I and power from P = VI for every accepted measurement.
- For the resistor, test whether I versus V is linear. For the lamp, use the changing V/I values and curved I–V trend as evidence instead of forcing a straight-line model.
What counts as evidence?
- Ohmic resistor: nearly constant V/I and a high-quality straight-line I–V trend whose slope is about 1/R.
- Filament lamp: V/I rises as voltage and filament temperature increase, while current grows less than proportionally.
- All five points must come from one fixed element and one fixed nominal setup.
- Meter resolution, lead/contact resistance, source internal resistance and thermal lag must be considered when interpreting small deviations.
A poor straight-line fit for the lamp is not automatically experimental error. The nonlinearity is the physical behavior being investigated.
Student controls
| Trial | Source | Element | V (V) | I (mA) | V/I (Ω) | P (W) |
|---|---|---|---|---|---|---|
| No I–V measurements recorded. | ||||||
Use all five accepted measurements. A resistor may justify a best-fit line; a filament lamp should be interpreted through curvature and changing V/I resistance.
No analysis yet.
Uncertainty & limitations
Voltage and current resolution set the scatter in the I–V graph. Resistor heating or lamp-filament temperature changes are physical changes in the component, not merely measurement error, and should be discussed as part of the model.
Write-up rule: distinguish random scatter from a systematic effect and explain how each one changes the strength or value of the final claim.
Discussion
Use the graph shape, resistance trend, meter precision and thermal behavior to explain whether the element is ohmic over the tested range.
Conclusion
Classify the selected element from the five-point evidence, not from its name.
Lab feedback
- Complete five recorded trials to receive evidence-based feedback.
Kirchhoff Junction & Loop Verification
Research question: When a fixed resistor network is driven at several source voltages, do the measured branch currents satisfy charge conservation at the junction and do the measured potential changes sum to zero around each loop?
Physical procedure
- Wire R₁ in series with a junction that splits into parallel branches R₂ and R₃.
- Measure I₁ before the junction and I₂, I₃ in the two branches. Measure V₁ across R₁ and V₂, V₃ across the parallel resistors.
- Keep the same resistor network for all five source voltages.
- At each source setting, test the junction rule with I₁ − I₂ − I₃ and the two loop rules with Vbat − V₁ − V₂ and Vbat − V₁ − V₃.
- Use the complete five-point series to decide whether the conservation residuals are small compared with measurement uncertainty.
What counts as evidence?
- The I₁ versus I₂+I₃ graph should have slope near 1 and intercept near 0.
- Both signed loop residuals should scatter around 0 V rather than grow systematically with source voltage.
- Do not add absolute voltage drops before deciding a loop traversal direction; Kirchhoff's loop rule uses signed potential changes.
- Small nonzero residuals are expected from meter loading, resistor tolerance, contact resistance and source internal resistance.
Changing R₁, R₂ or R₃ midway creates a different circuit. Reset the lab before collecting a new five-point series.
Student controls
| Trial | Source | Vbat (V) | I₁ (mA) | I₂ (mA) | I₃ (mA) | Junction residual (%) | Loop 2 (V) | Loop 3 (V) |
|---|---|---|---|---|---|---|---|---|
| No Kirchhoff measurements recorded. | ||||||||
Use the current-conservation graph and the signed loop residuals together. A line fit is appropriate for I₁ versus I₂+I₃; the loop residuals should instead remain near zero.
No analysis yet.
Uncertainty & limitations
Meter loading, resistor tolerances and connection resistance affect measured branch currents and potential changes. Compare closure residuals with instrument precision before deciding whether a junction or loop rule is unsupported.
Write-up rule: distinguish random scatter from a systematic effect and explain how each one changes the strength or value of the final claim.
Discussion
Interpret the junction slope, the two loop residuals, meter loading and resistor tolerance separately.
Conclusion
Use both charge-conservation and energy-conservation evidence to decide whether Kirchhoff's rules are supported.
Lab feedback
- Complete five recorded trials to receive evidence-based feedback.
RC Time-Constant Landmark Experiment
Research question: If capacitance and the measurement method are held fixed while resistance changes, does the measured 63% charging or 37% discharging landmark time scale with the circuit time constant RC?
Physical procedure
- Use one capacitor and one source voltage for the entire five-trial series.
- For a charging trial, begin with the capacitor discharged; for a discharging trial, begin with the capacitor charged to the source voltage.
- Change only the resistance between trials. Measure the time required to reach the appropriate landmark voltage.
- Calculate RC for each trial and compare it directly with the measured landmark time.
- Use the slope, intercept and scatter of the five-point graph to decide whether the data support τ = RC.
What counts as evidence?
- At one time constant, a charging capacitor is at about 63% of its final charge/voltage.
- At one time constant, a discharging capacitor is at about 37% of its initial charge/voltage.
- A graph of measured landmark time versus calculated RC should have slope near 1 and intercept near 0.
- Do not fit or require an exponential charging/discharging equation in this lab. Use the landmark and qualitative curve shape.
Changing capacitance, source voltage, transient type or sensor method midway creates a different experiment. Reset before starting a new five-point series.
Student controls
| Trial | Source | Transient | R (kΩ) | C (µF) | RC (s) | Landmark V (V) | Measured t (s) | Difference (%) |
|---|---|---|---|---|---|---|---|---|
| No RC landmark measurements recorded. | ||||||||
Plot measured landmark time against calculated RC. The slope should be near 1. This lab intentionally does not require an exponential fit.
No analysis yet.
Uncertainty & limitations
Timing and voltage resolution affect the extracted time constant. Switch delay, capacitor leakage and meter input resistance can shift the fitted or landmark value systematically.
Write-up rule: distinguish random scatter from a systematic effect and explain how each one changes the strength or value of the final claim.
Discussion
Interpret slope, intercept, timing scatter, component tolerance and the charging/discharging landmark separately.
Conclusion
Use the complete five-point dataset to decide whether the measured landmark time behaves like RC.
Lab feedback
- Complete five recorded trials to receive evidence-based feedback.
Magnetic Force on a Current-Carrying Wire
Research question: When magnetic field strength and the other wire variables are controlled, does the measured force follow F = BIL sinθ as current, active wire length, or angle changes?
Physical procedure
- Place a straight wire segment in a uniform magnetic-field region and connect it to a controlled current source.
- Tare the force sensor before energizing the wire so the reading represents the magnetic force change.
- Change only the selected independent variable. Hold magnetic field and the remaining model factors fixed.
- For angle mode, record the actual angle and use sinθ as the graph variable.
- Compare the experimental slope with the factor predicted by F = BIL sinθ.
What counts as evidence?
- Vary I: slope of F vs I should be BL sinθ.
- Vary L: slope of F vs L should be BI sinθ.
- Vary angle: slope of F vs sinθ should be BIL.
- A small intercept and high R² strengthen the proportional model, but uncertainty and alignment still matter.
Changing more than one model factor during the series makes the slope ambiguous. Sensor zero offset, field nonuniformity, wire heating and angle error are important limitations.
Student controls
| Trial | Source | Mode | B (T) | I (A) | L (m) | θ | Graph x | Measured F (mN) | Expected F (mN) | Difference (%) |
|---|---|---|---|---|---|---|---|---|---|---|
| No magnetic-force measurements recorded. | ||||||||||
Use the graph required by the selected one-variable design. For angle mode, plot force against sinθ, not θ itself.
No analysis yet.
Uncertainty & limitations
Current, magnetic-field and force measurements all contribute to slope uncertainty. Field nonuniformity, wire alignment and uncertain active wire length are important systematic effects.
Write-up rule: distinguish random scatter from a systematic effect and explain how each one changes the strength or value of the final claim.
Discussion
Interpret proportionality, slope agreement, intercept, sensor zero, field uniformity and wire alignment.
Conclusion
Use all five measurements to decide whether the selected factor follows F = BIL sinθ.
Lab feedback
- Complete five recorded trials to receive evidence-based feedback.
Faraday–Lenz Flux-Change Experiment
Research question: At fixed coil geometry and field change, does the measured induced-emf magnitude follow |ε| = N A |ΔB| / Δt, and does reversing the flux-change direction reverse the measured polarity?
Physical procedure
- Keep the coil face perpendicular to the field so ΔΦ = AΔB.
- Keep N, A and |ΔB| fixed while changing only the sweep time.
- Record both the signed emf and its magnitude.
- Do not average away polarity: the sign is separate directional evidence.
- Compare the magnitude slope with the ideal value 1.
Uncertainty and limitations
Sensor response time, nonuniform field, coil-angle error, uncertainty in sweep duration, lead orientation and incomplete field change affect the result. Very fast sweeps can challenge the voltmeter response.
Student controls
| # | Source | Δt (s) | N A |ΔB|/Δt (V) | Measured ε (V) | Polarity |
|---|---|---|---|---|---|
| No induction trials recorded. | |||||
Magnitude is fitted with absolute values; polarity is evaluated separately with Lenz’s law.
Collect five trials first.
No analysis yet.
Uncertainty & limitations
Flux-change timing, coil geometry and voltage resolution affect the measured emf. Coil resistance, magnet-path alignment and nonuniform magnetic field can change the observed relationship without invalidating Faraday–Lenz reasoning.
Write-up rule: distinguish random scatter from a systematic effect and explain how each one changes the strength or value of the final claim.
Discussion
Complete five trials.
Conclusion
Complete five trials.
Lab feedback
Determine Refractive Index from Snell’s Law
Research question: For one transparent sample, does the ratio of measured sine values obey n₁ sinθ₁ = n₂ sinθ₂, and can the sample refractive index be recovered from the slope of sinθ₁ versus sinθ₂?
Physical procedure
- Measure both angles from the interface normal, not from the surface.
- Keep the same material and interface through all five trials.
- Use a wide incident-angle range without approaching grazing incidence.
- Transform each angle using sine before fitting.
- For air, the slope of sinθ₁ vs sinθ₂ estimates n₂.
Uncertainty and limitations
Normal-line zero error, finite beam width, protractor resolution, sample alignment and identifying the center of the refracted ray dominate uncertainty.
Student controls
| # | Source | Sample | θ₁ | θ₂ | sinθ₁ | sinθ₂ |
|---|---|---|---|---|---|---|
| No ray measurements recorded. | ||||||
Fit sinθ₁ on the vertical axis against sinθ₂ on the horizontal axis.
Collect five trials first.
No analysis yet.
Uncertainty & limitations
Angle-reading resolution dominates the random uncertainty. Beam width, surface alignment and locating the refracted ray centerline can bias the inferred refractive index.
Write-up rule: distinguish random scatter from a systematic effect and explain how each one changes the strength or value of the final claim.
Discussion
Complete five trials.
Conclusion
Complete five trials.
Lab feedback
Thin-Lens Focal Length from Screen Focusing
Research question: Can the focal length of one converging lens be recovered by manually focusing five real images and testing 1/dᵢ = −1/dₒ + 1/f?
Physical procedure
- Measure dₒ and dᵢ from the lens principal-plane approximation used by the bench.
- Use only real images that can be sharply focused on the screen.
- Do not record a trial until the focus indicator is within tolerance.
- Keep the same lens throughout the series.
- Interpret slope, intercept and the focal length inferred from the intercept.
Uncertainty and limitations
Focus judgment, ruler zero, lens thickness, distance reference points and parallax affect the fit. A narrow object-distance range weakens the transformed fit.
Student controls
| # | Source | Lens | dₒ (cm) | dᵢ (cm) | 1/dₒ | 1/dᵢ |
|---|---|---|---|---|---|---|
| No focused trials recorded. | ||||||
For the thin-lens model, slope should be near −1 and intercept should be 1/f.
Collect five focused trials first.
No analysis yet.
Uncertainty & limitations
Object-distance and image-distance readings propagate strongly when the object is near the focal region. Lens thickness, principal-plane location and judging best focus are systematic/subjective limitations to discuss.
Write-up rule: distinguish random scatter from a systematic effect and explain how each one changes the strength or value of the final claim.
Discussion
Complete five trials.
Conclusion
Complete five trials.
Lab feedback
Wave Evidence Laboratory
Research question: Can a manually tuned standing-wave station and a manually measured double-slit station recover the model slopes predicted by wave speed and interference geometry?
Physical procedure
Complete the steps below in order before accepting a trial. Keep the selected station and its control variables unchanged except for the intended independent variable.
Station A — standing wave
At fixed string length L, tension T and linear density μ, the resonance frequencies satisfy fₙ = n v/(2L) with v = √(T/μ). Graph fₙ vs n.
Station B — double slit
At small angles, Δy ≈ λL/d. Keep wavelength and screen distance fixed, vary slit spacing d, and graph Δy vs 1/d.
Student controls
| # | Source | Station | Graph x | Measured y | Control summary |
|---|---|---|---|---|---|
| No wave trials recorded. | |||||
Analyze only one station at a time; each station has its own physically meaningful graph.
Collect five trials first.
No analysis yet.
Uncertainty & limitations
Length/spacing measurements and identifying a resonance or fringe center create scatter. End corrections, finite slit width and imperfect source coherence are model-dependent systematic effects; use only the graph appropriate to the chosen station.
Write-up rule: distinguish random scatter from a systematic effect and explain how each one changes the strength or value of the final claim.
Discussion
Complete five trials.
Conclusion
Complete five trials.
Lab feedback
Modern Physics Evidence Laboratory
Research question: Can a manually operated photoelectric station recover the linear stopping-potential slope, and can a manually counted decay station recover a sample half-life from population data?
Physical procedure
Complete the steps below in order before accepting a trial. Keep the selected station and its control variables unchanged except for the intended independent variable.
Photoelectric station
For above-threshold light, eVstop = hf − φ. The slope of Vstop vs f is h/e. Below-threshold points are valid observations but do not belong in the linear stopping-potential fit.
Decay station
For a large population, N(t)=N₀e−λt. Plot ln N vs t; slope = −λ and t½ = ln2/λ. Counting fluctuations are expected statistical scatter.
Student controls
| # | Source | Station | Target | Measured value | Analysis value |
|---|---|---|---|---|---|
| No modern-physics trials recorded. | |||||
Use above-threshold photoelectric points only; use ln N for the decay fit.
Collect five trials first.
No analysis yet.
Uncertainty & limitations
Photoelectric voltage nulling includes contact-potential/voltage-resolution effects; decay counts include statistical counting fluctuations. Keep those uncertainty models separate and fit only above-threshold photoelectric points or transformed decay data as appropriate.
Write-up rule: distinguish random scatter from a systematic effect and explain how each one changes the strength or value of the final claim.
Discussion
Complete five trials.
Conclusion
Complete five trials.
Lab feedback
After each investigation, use the FRQ Self-Grader and check whether your procedure, graph, uncertainty and evidence would be clear to someone who did not watch you perform the experiment.