# Newton's thin lens equation

x_1 * x_2 = f^2
Newton's thin lens equation.
Enter 'x' in the field to be calculated.

This calculator is the Newton's version of the thin lens equation. It computes the position of the image of an object through a thin lens with distances measured from focal points.

To calculate the image position with distances measured from the lens, use this version Gaussian thin lens equation. x0 : distance from the object to the first focal point in cm (directional distance AF in the diagram)
x1 : distance from the image to the second focal point in cm (directional distance F'A' in the diagram)
f : focal length in cm (OF' in the diagram)
All these distances obey the sign convention below.

Sign convention :
- Object and image distances are measured from the lens focal points.
- The direction of light (from object to lens) is considered as the 'positive direction' (always from left to right).

The Newton's thin lens formula is then expressed as follows,

x_0 * x_1 = f^2

## Example : Calculate the position of the image in the case of a convergent lens

Let's calculate the position of the image of an object located 5 cm to the left of the first focal point of a converging lens. The focal length of the lens is 4 cm. So we have,
- x0 = AF = 5 cm
- focal length: f = 4 cm
We use the calculator and get (enter "x" in the field F'A'),
x2 = 3.20 cm

The image is a real image located to the right of the second lens focal point at a distance of 3.20 cm, that is 3.20+4 = 7.20 cm to the left of the lens.