The method and the results are on the thin lens equation lab. Do the analysis yourself first, then check the answers below.
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. These answers go with the AP Physics 2 lab on thin lens equation: the graph, the calculations, the uncertainties and the conclusion explained, for all 7 analysis questions.
Here are the thin lens equation lab answers for AP Physics 2: graph, calculations, uncertainties and conclusion. First do the lab yourself, then compare, and go back to the lesson if needed.
The sample readings give 1/dₒ + 1/dᵢ nearly constant at about 6.66 m⁻¹, which means f is close to 15.0 cm. The answers below show the calculation and discuss the main sources of error.
Level: AP Physics 2 (algebra-based) · Curriculum: AP P2 Unit 13
Thin lens equation lab answers: the analysis explained
Question 1 One value of f
1/f = 1/dₒ + 1/dᵢ = 4.00 + 2.67 = 6.67 m⁻¹, so f = 1 / 6.67 = 15.0 cm.
Question 2 Mean focal length
The five sums are 6.67, 6.64, 6.70, 6.65 and 6.65 m⁻¹ (values are constant within the reading error). Their mean is 6.66 m⁻¹, so f = 1 / 6.66 = 15.0 cm.
Question 3 Graph
From 1/dᵢ = −1/dₒ + 1/f, the graph is a straight line with gradient −1. The y-intercept equals 1/f, about 6.7 m⁻¹.
Question 4 Magnification
m = −dᵢ/dₒ = −37.4 / 25.0 = −1.50: the image is real, inverted and 1.5 times larger.
Question 5 Uncertainty
1.0 / 37.4 = 2.7 %. The uncertainty arises because the image stays acceptably sharp over a small range of screen positions (depth of focus).
Question 6 Minimum object distance
If dₒ < f, then 1/dᵢ = 1/f − 1/dₒ is negative, so dᵢ is negative. The rays diverge and the image is virtual, so it cannot appear on a screen.
Question 7 Improvements
Find the sharpest image by moving the screen from both sides and take the mean position. Use a more distant object and repeat for more pairs of distances. A bigger set of data lowers the random error in f.
