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MCAT Prep: Tutoring Solution88 chapters | 905 lessons

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Lesson Transcript

Instructor:
*Nichole Miller*

Nichole is a research scientist with a PhD in Materials Science & Engineering.

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.

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 at two different distances because they have two different **focal lengths**. Let's take a closer look!

This schematic shows an example of a convex lens on the top and a concave lens on the bottom. 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.

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 in 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.

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__.

Another important concept is **optical power**, sometimes called the lens power. *Optical power (P) describes the strength of a lens and is defined as the reciprocal of the focal length (1/f).* A lens with a low optical power has a long focal length. The units of optical power are 1/m, also known a diopter. Diopters are the same unit used to measure the strength of prescription eyeglasses, so the optical strength of +3 reading glasses is 3 diopters.

Let's take a look at an example problem for calculating optical power.

*What is the optical power of a lens with a focal length of 1 cm (0.01 m)?*

Focal length (f) is 0.01 m, so the optical power equals 1/(0.01 m), or __100 diopters__.

One of the most important properties of a lens is its **focal length**. Focal length is the distance between a lens and its focal point, while the **focal point** is the point at which parallel light rays converge or diverge. Convex lenses have positive focal lengths, whereas the focal lengths of concave lenses are negative. Focal length is calculated with the equation:

The inverse of the focal length (1/f) is known as the **optical power**, which describes the strength of a lens and is defined as the reciprocal of the focal length and is measured in diopters and is simply calculated with the equation: 1/f

A lens with a short focal length has a high optical power. Although only lenses were discussed in this lesson, all of the concepts and equations discussed here also apply to mirrors.

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MCAT Prep: Tutoring Solution88 chapters | 905 lessons

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