# Focal Length: Definition, Equation & Examples

Instructor: Chris Malec

Chris has a PhD in Physics

This lesson explains the meaning of focal length and optical power, presents the equations to calculate these values, and gives an example for each equation.

## Bifocals: Glasses with Two Focal Lengths

Take a look at this picture of bifocal eyeglasses. Each eyepiece can focus at two different distances, allowing someone wearing bifocals to focus nearby when looking down and far away when looking straight ahead. Without bifocals, some people would have to change their glasses when switching between activities like reading a book and driving, which require focusing near and far, respectively. Bifocals are able to focus as two different distances because they have two different focal lengths.

## Focal Length

This schematic shows an example of a convex lens on the top and a concave lens on the bottom. In both cases, the focal point (F) is the point at which parallel light rays cross. The focal length (f) is the distance between the lens and the focal point. Because the focal length measures a distance, it uses units of length, such as centimeters (cm), meters (m), or inches (in). Convex lenses focus the incoming light onto the opposite side of the lens and therefore have a positive focal length. Concave lenses, on the other hand, cause incoming light to diverge rather than focus and thus have a negative focal length.

## Focal Length of a Camera

Let's take the example of a camera like the one in this diagram. The diagram shows an object that is being photographed, a camera lens, and the image that is produced. The labeled distances are the focal length of the lens (f), the distance between the lens and the image (i), and the distance between the lens and the object (o). For an infinitely thin lens (the ideal case), these three distances are related by the equation shown below the diagram. The equation has also been solved for the focal length for your convenience. Note that this equation applies for any infinitely thin lens, not just a lens in a camera.

#### Example

Let's take a look at an example problem for calculating focal length.

If an object that is 50 cm from a lens creates an image 2 cm on the other side of the lens, what is the focal length of this lens?

We are given that o = 50 cm and i = 2 cm. Using the equation for focal length, we can calculate that the focal length (f) is equal to 1/(1/(50 cm) + 1/(2 cm)) or 1.9 cm.

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