Mathematical routines (MR)

Images formed by a converging lens

Unit 13
10 points
About 22 minutes

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

A multipart problem where you use math to analyze a physical situation. You draw or sketch a representation such as a circuit diagram, a ray diagram or a graph, derive an equation using letters, calculate a numerical answer with units, and then make a claim or prediction and justify it with physics reasoning. On the exam: Question 1 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 20–25 minutes. This question type started in May 2025, so Physics 2 free-response questions from 2024 and earlier are built differently.

The question

A thin converging glass lens (index of refraction 1.50) has a focal length of 10.0 cm in air. A 4.0 cm tall object is placed upright on the principal axis, 30.0 cm to the left of the lens.

Suggested time: 22 minutes

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Part (a)

2 points

Describe a ray diagram that locates the image. Describe the paths of at least two principal rays from the top of the object, and where the image forms. State whether the image is real or virtual, upright or inverted, and larger or smaller than the object.

Your answer to part (a)

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

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Part (b)

2 points

Derive an expression for the height $h_i$ of the image in terms of the object height $h_o$ , the object distance $s_o$ and the focal length f.

Your answer to part (b)

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

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Part (c)

3 points

Calculate (i) the image distance and (ii) the image height for the object at 30.0 cm. (iii) The object is then moved to 6.0 cm from the lens. Calculate the new image distance and image height, and describe the new image.

Your answer to part (c)

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

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Part (d)

3 points

The lens and object are now placed under water (index of refraction 1.33). (i) A ray inside the glass strikes the glass surface at 20.0° from the normal. Calculate the angle of refraction when the glass is surrounded by air and when it is surrounded by water. (ii) Does the focal length of the lens increase, decrease or stay the same under water? Justify your claim using your results from (i).

Your answer to part (d)

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

0 / 2,500 characters

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