Qualitative/quantitative translation (QQT)

An object moving toward a concave mirror

Unit 13
8 points
About 18 minutes

You can use a calculator on this question, just like on exam day.

A shorter multipart problem that connects reasoning in words with an equation. You make and justify a claim without equations, derive an equation from a physics principle, and then explain whether the two agree or use them to predict what happens in a changed situation. On the exam: Question 4 of 4. New for May 2027: the free-response section is 95 minutes, down from 100, for all 4 questions (50% of your score), one of each type in this order. Calculator and equation sheet allowed. The CED suggests 15–20 minutes. This question type started in May 2025, so Physics 2 free-response questions from 2024 and earlier are built differently.

The question

A small upright object stands on the principal axis of a concave spherical mirror with focal length f. The object starts at a distance 3f from the mirror and is slowly moved toward the mirror until it is a distance 1.5f from the mirror.

Suggested time: 18 minutes

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Part (a)

3 points

As the object moves from 3f to 1.5f, (i) does the image move toward the mirror, away from the mirror, or stay in the same place, and (ii) does the image get larger, get smaller, or stay the same size? Justify your answers using principal rays. Do not use equations in this part; reason in words.

Your answer to part (a)

Type math plainly, like x^2, sqrt(x) or (x+1)/(x−1).

0 / 2,500 characters

Part (b)

3 points

Derive expressions for the image distance $s_i$ and the magnification M in terms of the object distance $s_o$ and f. Then use them to find $s_i$ and M, in terms of f where needed, for $s_o = 3f$ and for $s_o = 1.5f$ .

Your answer to part (b)

Type math plainly, like x^2, sqrt(x) or (x+1)/(x−1).

0 / 2,500 characters

Part (c)

2 points

(i) Explain how your results from part (b) agree with your claims in part (a). (ii) Using your expressions from part (b), predict what happens to the image as the object is moved from 1.5f to a point between the focal point and the mirror.

Your answer to part (c)

Type math plainly, like x^2, sqrt(x) or (x+1)/(x−1).

0 / 2,500 characters

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