# Physics Lens Formula

## What is Lens Formula?

Convex lenses can also be known as converging lenses since the rays converge after falling on the convex lens while the concave lens is known as diverging lenses as the rays diverge after falling on the concave lens. Images formed by these convex lenses can be real or virtual depending on their position from the lens and can have a different size too. The image distance can be calculated with the knowledge of object distance and focal length with the help of the lens formula.

In optics, the relationship between the distance of an object (o), the distance of an image (i), and the focal length (f) of the lens are given by the formula which is known as the Lens formula. Lens formula is applicable for concave as well as convex lenses. These lenses have negligible thickness. Lens equation or lens formula is an equation that relates the focal length, image distance, and object distance for a spherical mirror. It is given as,

Lens Formula - 1/u + 1/v = 1/f

where.

v = Distance of the image from the lens.

u = Distance of the object from the lens.

f = Focal length of the lens.

This lens formula is applicable to all situations and with appropriate sign conventions. This lens formula is applicable to both the concave lens and convex lens. If the equation shows a negative (-ve) image distance, then the image is a virtual image on the same side of the lens as the object. If this equation shows a negative (-ve) focal length, then the lens is a diverging lens rather than the converging lens. This equation is used to find image distance for either real images or virtual images.

### What is the Power of Lens?

The power of a lens can be defined as the measure of the degree of convergence or divergence of the light rays falling on it. The degree of divergence or convergence depends upon the focal length of the lens. Thus, the power of the lens can be defined as the reciprocal of the focal length of the lens used. It is given as,

Where f is equal to the focal length of the lens used. SI unit of power is Dioptre (D). The power of the concave lens is said to be negative, while the power of the convex lens can be positive.

### Solved Examples

Example 1: What image is produced by placing an object 6 cm away from a convex lens of focal length equal to 3 cm?

Solution: The question states that u = 6 cm and f = 3 cm. This can be substituted into the lens formula as given below:

1/u + 1/v = 1/f

Therefore, 1/6 + 1/v = 1/3

1/v = 1/3 - 1/6 = 1/6

So v = 6 cm. From the ray diagram we see that this is an inverted, real image.