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AP · AP 2 · free response

AP Physics 2: Algebra-Based · Question 9

AP Physics 2: Algebra-Based · Original GioPhysics question with a detailed, mark-by-mark answer guide.

Demand
discriminating
Marks
12
Topics
1
Answer
Complete
Optical bench carrying an illuminated object, a converging lens and a screenilluminated objectconverging lensscreenoptical benchobject distance uimage distance v
Figure 5An elevation view of an optical bench, drawn as a hatched horizontal rail labelled as carrying a metre scale. Standing on the rail, from left to right, are an illuminated object shown as an upright arrow, a converging lens drawn as a vertical line with outward-pointing arrowheads at each end, and a flat screen shown as a narrow upright board. Two dimension lines below the bench measure the object distance u, from the object to the centre of the lens, and the image distance v, from the centre of the lens to the screen.
free response12 marks

A student is given a converging lens of unknown focal length, an illuminated object, a screen, an optical bench and a meter stick. The student measures the object distance u and the corresponding image distance v for several positions of the lens.

The student's measurements
u / cm20.025.030.040.050.0
v / cm60.037.530.024.021.4
1/u / cm⁻¹0.05000.04000.03330.02500.0200
1/v / cm⁻¹0.01670.02670.03330.04170.0467
  1. (a)

    Describe Describe how the student should obtain each value of v so that the measurement is as accurate as possible.

    3 marks
  2. (b)

    Describe The thin lens equation is 1/u + 1/v = 1/f. Describe how the student should plot the data to obtain a straight line, and state what the slope and the intercepts of that line represent.

    4 marks
  3. (c)

    Determine Use the data to determine the focal length of the lens.

    3 marks
  4. (d)

    Explain The student notices that the point at u = 20.0 cm lies slightly further from the best-fit line than the others. Explain why the measurement of v is least precise for small object distances, and describe one change that would improve it.

    2 marks
Ready to self-mark?Reveal the detailed answer guide
Answer overviewKey answer: 1 point: move the screen until the image of the object is as sharp as possible, then measure from the centre of the lens to the screen 1 point: approach the sharpest position from both directions and take the midpoint of the range over which the image looks focused 1 point: measure with the meter stick parallel to the bench and the eye directly above the scale, to avoid parallax
01

(a)

3 marks

Describe Describe how the student should obtain each value of v so that the measurement is as accurate as possible.

How to approach it

Answer the command word directly and use precise physical vocabulary. Include only the distinct features or facts that earn marks, without burying them in unrelated background information.

  1. 1

    1 point: move the screen until the image of the object is as sharp as possible, then measure from the centre of the lens to the screen

  2. 2

    1 point: approach the sharpest position from both directions and take the midpoint of the range over which the image looks focused

  3. 3

    1 point: measure with the meter stick parallel to the bench and the eye directly above the scale, to avoid parallax

02

(b)

4 marks

Describe The thin lens equation is 1/u + 1/v = 1/f. Describe how the student should plot the data to obtain a straight line, and state what the slope and the intercepts of that line represent.

How to approach it

List the given quantities with units, identify the required quantity, write the governing relationship before substituting, and keep extra digits until the final line so rounding does not distort the result.

  1. 1

    1 point: plot 1/v on the vertical axis against 1/u on the horizontal axis

  2. 2

    1 point: rearranged, 1/v = −(1/u) + 1/f, which has the form y = mx + c

  3. 3

    1 point: the slope is −1

  4. 4

    1 point: both intercepts equal 1/f

03

(c)

3 marks

Determine Use the data to determine the focal length of the lens.

How to approach it

List the given quantities with units, identify the required quantity, write the governing relationship before substituting, and keep extra digits until the final line so rounding does not distort the result.

  1. 1

    1 point: adds 1/u and 1/v for any row — for example 0.0500 + 0.0167 = 0.0667 cm⁻¹

  2. 2

    1 point: confirms the sum is the same for every row, so 1/f = 0.0667 cm⁻¹

  3. 3

    1 point: f = 15.0 cm

04

(d)

2 marks

Explain The student notices that the point at u = 20.0 cm lies slightly further from the best-fit line than the others. Explain why the measurement of v is least precise for small object distances, and describe one change that would improve it.

How to approach it

State the outcome first, then link cause to effect with the relevant physical principle. Each link in the reasoning should be explicit enough to earn its own marking point.

  1. 1

    1 point: at small u the image distance is large, the image is highly magnified and dim, and the range of screen positions over which it looks sharp is widest — so the uncertainty in v is greatest

  2. 2

    1 point: improvement — use a brighter object, work in a darkened room, or take repeated determinations of the sharpest position and average them

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