Quick answer: Geometric optics treats light as rays. Reflection obeys θᵣ = θᵢ, refraction obeys Snell's law n₁ sin θ₁ = n₂ sin θ₂, and mirrors and thin lenses obey 1/dₒ + 1/dᵢ = 1/f with magnification m = −dᵢ/dₒ. This AP Physics 2 lab on thin lens equation gives the aim, the equipment, the safety points, a step-by-step method, sample results and 7 analysis questions; the answers are on a separate page and the lab sheet is a free printable PDF.
How can you measure the focal length of a lens without any knowledge of its curvature? By recording where a sharp image forms for several object distances, you can test the thin lens equation and find f from the straight-line graph or from the mean of the data.
Level: AP Physics 2 (algebra-based) · Curriculum: AP P2 Unit 13
Aim
Find the focal length of a converging lens by measuring pairs of object and image distances, and test the thin lens equation.
Equipment
- converging lens (focal length about 15 cm) in a holder
- bright lamp or phone torch with an arrow-shaped cut-out as the object
- white card as a screen
- metre rule or optical bench
Safety
Never look at the sun or a bright lamp through the lens. Do not leave a lens in sunlight near paper or cloth, because it can start a fire.
Method
- Fix the lamp and the arrow object at one end of the bench. Place the lens 25.0 cm from the object.
- Move the screen until the image of the arrow is as sharp as possible. Read the lens-screen distance dᵢ.
- Repeat for dₒ = 30.0, 35.0, 40.0 and 50.0 cm.
- For each row calculate 1/dₒ and 1/dᵢ in m⁻¹, and their sum.
Results
Sample data for a lens whose focal length is to be found:
| dₒ (cm) | dᵢ (cm) | 1/dₒ (m⁻¹) | 1/dᵢ (m⁻¹) | 1/dₒ + 1/dᵢ (m⁻¹) |
|---|---|---|---|---|
| 25.0 | 37.4 | 4.00 | 2.67 | 6.67 |
| 30.0 | 30.2 | 3.33 | 3.31 | 6.64 |
| 35.0 | 26.0 | 2.86 | 3.85 | 6.70 |
| 40.0 | 24.1 | 2.50 | 4.15 | 6.65 |
| 50.0 | 21.5 | 2.00 | 4.65 | 6.65 |
Analysis questions
Question 1 One value of f
Use the row dₒ = 25.0 cm to calculate the focal length, then give the mean sum 1/dₒ + 1/dᵢ.
Question 2 Mean focal length
The column 1/dₒ + 1/dᵢ should be constant. Calculate its mean and use it to find f in centimetres.
Question 3 Graph
Plot 1/dᵢ (y-axis) against 1/dₒ (x-axis). State the gradient expected and the meaning of the y-intercept.
Question 4 Magnification
Calculate the magnification for dₒ = 25.0 cm and describe the image.
Question 5 Uncertainty
The position of the sharpest image is uncertain by about ±1.0 cm. Calculate the percentage uncertainty in dᵢ for dₒ = 25.0 cm. Explain why this uncertainty exists.
Question 6 Minimum object distance
Explain why no image can be projected when dₒ is less than f.
Question 7 Improvements
Suggest two improvements to reduce the uncertainty in f.
