Lens Formula

Introduction
Lens formula is a mathematical formula that relates the object distance (u), image distance (v), and focal length (f) of a lens. It helps in determining the position and nature of the image formed by a lens. The lens formula is derived from the combination of two equations, namely, the lens-maker's formula and the mirror formula.

Diagram
A simple diagram can help in understanding the lens formula better. Consider a convex lens with a focal length (f), an object placed at a distance (u) in front of the lens, and an image formed at a distance (v) on the other side of the lens.

[Insert diagram of a convex lens with object distance (u), image distance (v), and focal length (f)]

Lens Formula
The lens formula is given by the equation:

1/f = 1/v - 1/u

Where:
- f is the focal length of the lens
- v is the image distance (positive for real images, negative for virtual images)
- u is the object distance (positive for real objects, negative for virtual objects)

Explanation of Variables
Let's break down the variables in the lens formula:

1. Focal Length (f):
- The focal length of a lens is the distance between the lens and its focal point.
- It is represented by the symbol 'f'.
- Focal length can be positive or negative, depending on the type of lens. For convex lenses, the focal length is positive, while for concave lenses, it is negative.

2. Object Distance (u):
- The object distance is the distance between the object and the lens.
- It is represented by the symbol 'u'.
- Object distance can be positive or negative. For real objects, the object distance is positive, whereas for virtual objects, it is negative.

3. Image Distance (v):
- The image distance is the distance between the image and the lens.
- It is represented by the symbol 'v'.
- Image distance can be positive or negative. For real images, the image distance is positive, while for virtual images, it is negative.

Working of the Lens Formula
The lens formula is derived from the combination of two equations: the lens-maker's formula and the mirror formula. It considers the object distance (u), image distance (v), and focal length (f) of the lens.

The lens formula states that the reciprocal of the focal length of a lens is equal to the algebraic sum of the reciprocals of the object distance and the image distance.

1/f = 1/v - 1/u

Sign Convention
To correctly apply the lens formula, it is essential to follow the sign convention:

- Distances measured along the direction of incident light are considered positive, while distances measured opposite to the incident light are negative.
- For a convex lens:
- Focal length (f) is positive.
- Object distance (u) is positive for real objects and negative for virtual objects.
- Image distance (v) is positive for real images and negative for virtual images.
- For a concave lens:
- Focal length (f) is negative.
- Object distance (u) is positive for real objects and negative for virtual objects.
- Image distance (v) is positive for virtual