Alexander Fufaev
My name is Alexander FufaeV and here I will explain the following topic:

How do You Determine the Focal Length of a Lens?

Formula

Formula: Lens Equation
Thin lens - object width, image width, focal length
What do the formula symbols mean?

Focal length

Unit
Focal length is the distance between the lens and the focal point of the lens. The focal point is the point into which the lens focuses all light rays. The focal length is a property of the lens and can be found out with the help of the object size \(g\) and the image size \( b \).

For example, if the object is 1 meter away from the lens, so \(g = 1 \, \text{m} \) and the sharp image of the object is 2 centimeters away from the lens, so \(b = 0.02 \, \text{m} \). Then the focal length of the lens is: \begin{align} f &~=~ \frac{ 1 \, \text{m} ~\cdot~ 0.02 \, \text{m}}{ 1 \, \text{m} ~+~ 0.02 \, \text{m} } \\\\ &~=~ 0.02 \, \text{m} \end{align}

Thus, the focal point of the lens used is at a distance of 2 centimeters from the lens.

Object distance

Unit
This is the distance between the lens and the object.

Image distance

Unit
This is the distance between the lens and the sharp image of the object through the lens. You can adjust the sharpness of the image by, for example, changing the distance between the lens and the object.
Explanation

Video

To determine the focal length of a lens, you must create a sharp image of an object on a screen - with a lens. Then you measure the distance \( b \) (screen-lens), as well as the distance \( g \) (object-lens) and can then determine the focal length \( f \) with the help of the lens equation:

Formula anchor
fufaev.org Thin Lens - Object and Image Distance, Focal Length
Thin (ideal) Lens - Object and Image Distance, Focal Length.

Or you can focus a far away object (\( g ~\rightarrow~ \infty \): \(1/g ~=~ 0\)), then the image, because of Eq. 1, lies on the screen exactly at the focal length: \( f ~=~ b \).