AP Physics 2 · Exam guide
AP Physics 2 Optics Question: The Lens Equation and Image Types
A thin-lens question gives a focal length and an object distance and asks where the image is and what it looks like. The equation is short, and the points are in the signs and the description of the image. This guide works two cases with the same lens.
The equations
The thin-lens equation is \(\dfrac{1}{d_o} + \dfrac{1}{d_i} = \dfrac{1}{f}\), and the magnification is \(M = -\dfrac{d_i}{d_o}\). For a converging lens, \(f\) is positive. A positive \(d_i\) means a real image on the opposite side of the lens, and a negative \(d_i\) means a virtual image on the same side as the object.
Example 1: an object beyond the focal point
A converging lens has \(f = 10\) cm. An object is 15 cm from the lens. Where is the image, and what is it like?
\(\dfrac{1}{d_i} = \dfrac{1}{10} - \dfrac{1}{15} = \dfrac{1}{30}\), so \(d_i = 30\) cm. The magnification is \(M = -\dfrac{30}{15} = -2\). The image is real, inverted, and twice as large as the object, on the far side of the lens.
Example 2: an object inside the focal point
The same lens, with the object 5 cm from the lens.
\(\dfrac{1}{d_i} = \dfrac{1}{10} - \dfrac{1}{5} = -\dfrac{1}{10}\), so \(d_i = -10\) cm. The magnification is \(M = -\dfrac{-10}{5} = +2\). The image is virtual, upright, and twice as large, on the same side as the object. This is how a magnifying glass works.
It does not say whether the image is real or virtual, upright or inverted, which the question asks.
It uses the sign of each result to describe the image fully.
Quick checks
- An object beyond the focal point of a converging lens gives a real, inverted image.
- An object inside the focal point gives a virtual, upright, enlarged image.
- A diverging lens always gives a virtual, upright, smaller image.
Common mistakes
- Forgetting to take the reciprocal at the end.
- Using the wrong sign for a diverging lens or for a virtual image.
- Describing the magnification as a distance and not a ratio.
- Mixing up the object distance and image distance.
Frequently asked questions
What is a real image?
An image formed where light rays actually meet, which can be projected on a screen.
What does a negative magnification mean?
The image is inverted.
Does the exam use mirrors too?
Yes. The same equation works for mirrors, with the sign conventions in your course.
Where can I find the official scoring rules?
Exam formats change a little from year to year, so check the current course and exam description on the College Board site before test day.
Keep practicing
Every lesson in the AP Physics courses ends with practice problems and an Exam focus box that shows how the topic is tested, and every unit has a review with worked answers. These free lessons also build the skills the free-response section tests:
See the AP Physics 2 course Free lessons and lesson list
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Multiple choice
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