---
title: "Focal Length — AP Physics 2 Definition & Exam Guide"
description: "Focal length (f) is the distance from a mirror or lens to its focal point. It anchors the mirror/lens equation and ray diagrams in AP Physics 2 Unit 13."
canonical: "https://fiveable.me/ap-physics-2-revised/key-terms/focal-length"
type: "key-term"
subject: "AP Physics 2"
unit: "Unit 13"
---

# Focal Length — AP Physics 2 Definition & Exam Guide

## Definition

Focal length (f) is the distance from a mirror or lens to its focal point, the spot where rays parallel to the principal axis converge (or appear to come from). For a spherical mirror, f is half the radius of curvature. It's positive for converging optics and negative for diverging ones in the mirror/lens equation.

## What It Is

Focal length is the distance from the surface of a mirror or the center of a [thin lens](/ap-physics-2-revised/unit-13/4-images-formed-by-lenses/study-guide/jCmOQUUyw4iza3To "fv-autolink") to its **[focal point](/ap-physics-2-revised/key-terms/focal-point "fv-autolink")**. Here's the physical picture from the CED: send in light rays parallel to the principal axis. A concave (converging) mirror or convex (converging) lens bends them all toward one common point, the focal point. A convex (diverging) mirror or concave (diverging) lens spreads them out, but if you trace the spread rays backward, they all appear to come from a single point behind the mirror (or on the incident side of the lens). The distance to that point, real or apparent, is the focal length.

Two facts make focal length usable on problems. First, for a spherical mirror, the focal point sits on the principal axis halfway between the mirror surface and the [center of curvature](/ap-physics-2-revised/unit-13/2-images-formed-by-mirrors/study-guide/INg7VTuspNL1m0MQ "fv-autolink"), so **f = R/2**. Second, focal length carries a sign. Converging optics get a positive f, diverging optics get a negative f, and a plane mirror has a focal point infinitely far away (so 1/f goes to zero). That signed f is what you plug into the mirror/lens equation to find where an image forms.

## Why It Matters

Focal length lives in **[Unit 13](/ap-physics-2-revised/unit-13 "fv-autolink"): Geometric Optics**, specifically Topics 13.2 (Images Formed by Mirrors) and 13.4 (Images Formed by Lenses). It directly supports learning objectives **13.2.A** and **13.4.A**, both of which ask you to describe the [image](/ap-physics-2-revised/key-terms/image "fv-autolink") formed by an optical element. You literally cannot do that without f. The focal length sets everything about the image. Whether the object sits inside or outside the focal length determines if the image is real or virtual, upright or inverted, magnified or shrunk. Focal length is also the bridge between geometry and algebra in this unit. In a ray diagram, it tells you where to aim your principal rays. In the mirror/lens equation, it's the one number that characterizes the optic itself, independent of where you put the object.

## Connections

### [Concave mirror (Unit 13)](/ap-physics-2-revised/key-terms/concave-mirror)

A [concave mirror](/ap-physics-2-revised/key-terms/concave-mirror "fv-autolink") is the classic converging optic, and the CED says its focal point can be approximated as halfway between the mirror surface and the center of curvature. That gives you f = R/2, one of the most-used shortcuts in Unit 13.

### [Converging lens (Unit 13)](/ap-physics-2-revised/key-terms/converging-lens)

A [convex lens](/ap-physics-2-revised/key-terms/convex-lens "fv-autolink") does with refraction what a concave mirror does with reflection. Parallel rays converge to a focal point on the far side of the lens. Same positive f, same equation, just light passing through instead of bouncing back.

### [Ray diagram (Unit 13)](/ap-physics-2-revised/key-terms/ray-diagram)

Two of the three [principal rays](/ap-physics-2-revised/key-terms/principal-rays "fv-autolink") are defined by the focal point. A ray parallel to the axis reflects or refracts through the focal point, and a ray through the focal point comes out parallel. Knowing f is what lets you draw the diagram at all.

### [Magnification (Unit 13)](/ap-physics-2-revised/key-terms/magnification)

Focal length controls magnification indirectly. Once f and the object distance fix the image distance through the mirror/lens equation, magnification follows from m = -di/do. Move the object relative to the focal point and the image size and orientation flip around.

## On the AP Exam

Focal length shows up in two main flavors. The quantitative version hands you two of the three quantities in the mirror/lens equation (f, object distance, image distance) and asks for the third, often with a sign-convention trap. For example, a convex mirror forming a virtual image 12 cm behind the mirror means di = -12 cm, and your computed f should come out negative. Magnification problems add another layer, like finding f for a convex mirror given that the image is 1/3 the object's height. The experimental version is just as common. The 2017 Long FRQ asked how to determine the focal length of a convex lens using a light source, lens, and screen, so be ready to design a procedure (vary object distance, measure image distance, plot 1/di vs 1/do, read f from the intercepts) rather than just crunch one equation. Geometry questions also appear, like using f to find the angle a reflected ray makes after a parallel ray strikes a concave mirror off-axis.

## focal length vs radius of curvature

The radius of curvature (R) is the distance from a spherical mirror to its center of curvature, the center of the sphere the mirror is a slice of. The focal length is only half that, f = R/2, because parallel rays converge at the midpoint between the surface and the center. If a problem gives you R and you plug it straight into the mirror equation as f, every answer comes out wrong by a factor that's hard to spot afterward. Always halve R first.

## Key Takeaways

- Focal length is the distance from a mirror or lens to the focal point, where rays parallel to the principal axis converge or appear to originate.
- For a spherical mirror, the focal length is half the radius of curvature (f = R/2), with the focal point on the principal axis.
- Sign convention is everything: converging optics (concave mirrors, convex lenses) have positive f, while diverging optics (convex mirrors, concave lenses) have negative f.
- A plane mirror's focal point is infinitely far away, which is why the mirror equation gives di = -do and a virtual image the same size as the object.
- Whether the object is inside or outside the focal length determines if the image is real or virtual, inverted or upright, and magnified or reduced.
- On the exam, you should be able to find focal length experimentally by measuring object and image distances and using the mirror/lens equation, like the 2017 FRQ asked.

## FAQs

### What is focal length in AP Physics 2?

Focal length (f) is the distance from a mirror surface or thin lens to its focal point, the location where incident rays parallel to the principal axis converge after reflecting or refracting. It appears in the mirror/lens equation 1/f = 1/do + 1/di and is tested in Unit 13 under learning objectives 13.2.A and 13.4.A.

### Is focal length always positive?

No. Focal length is positive for converging optics (concave mirrors and convex lenses) and negative for diverging optics (convex mirrors and concave lenses). Getting this sign wrong is the single most common error in Unit 13 calculations.

### What's the difference between focal length and radius of curvature?

The radius of curvature R is the distance to the center of the sphere the mirror is cut from, while the focal length is the distance to the focal point, which sits halfway there. So f = R/2 for a spherical mirror. They are related but never interchangeable in the mirror equation.

### Does a plane mirror have a focal length?

Yes, but it's infinite. The CED states the focal point of a plane mirror is an infinite distance from the mirror, which means 1/f = 0 in the mirror equation and the image distance always equals the negative of the object distance.

### How do you find the focal length of a lens experimentally?

Place an object (like an illuminated box) at several measured distances from the lens, move a screen until a sharp real image forms, and record each image distance. Plotting 1/di versus 1/do gives a line whose intercepts equal 1/f, which is exactly the kind of procedure the 2017 Long FRQ Q3 rewarded.

## Related Study Guides

- [13.2 Images Formed by Mirrors](/ap-physics-2-revised/unit-13/2-images-formed-by-mirrors/study-guide/INg7VTuspNL1m0MQ)

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