## What is Mirror Equation?

It is an equation relating object distance and image distance with focal length is known as a mirror equation. It is also known as a mirror formula.

**In a spherical mirror:**

- The distance between the object and the pole of the mirror is called the object distance(u).
- The distance between the image and the pole of the mirror is called Image distance(v).
- The distance between the Principal focus and pole of the mirror is called Focal Length(f).

In ray optics, The object distance, image distance, and Focal length are related as,

\(\frac{1}{v}+\frac{1}{u}=\frac{1}{f}\) |

Where,

- u is the Object distance
- v is the Image distance
- f is the Focal Length given by \(f=\frac{R}{2}\)
- R is the radius of curvature of the spherical mirror

The above formula is valid under all situations for all types of spherical mirrors (Concave and Convex) and for all object positions.

**You may also want to check out these topics given below!**

## Sign Conventions

New Cartesian Sign Convention is used to avoid confusion in understanding the ray directions. Refer to the diagram for clear visualization.

- For the measurement of all the distances, the optical center of the lens is considered.
- When the distances are measured opposite to the direction of the incident light, they are considered to be negative.
- When the distances are measured in the same direction of the incident light, they are considered to be positive.
- When the heights are measured upwards and perpendicular to the principal axis, they are considered to be positive.
- When the heights are measured downwards and perpendicular to the principal axis, they are considered to be negative.

### Mirror Equation for concave mirror and Mirror Equation for a convex mirror

The mirror equation \(\frac{1}{v}+\frac{1}{u}=\frac{1}{f}\) holds good for concave mirrors as well as convex mirrors.

## Example of Mirror Equation

**The radius of curvature of a convex mirror used for rearview on a car is 4.00 m. If the location of the bus is 6 meters from this mirror, find the position of the image formed.**

**Solution:**

*Given:*

The radius of curvature (R)= +4.00 m

Object distance(u) = -6.00 m

Image distance(v) = ?

**Formula used: **

**Calculation: **

To calculate the Focal length of the given mirror, substitute the value of Radius of Curvature (R) in the \(f=\frac{R}{2}\). We get-

\(f=\frac{+4.00m}{2}=+2m\)Since, \(\frac{1}{v}+\frac{1}{u}=\frac{1}{f}\) we can re- arrange it as –

\(\frac{1}{v}=\frac{1}{f}-\frac{1}{u}\)On substituting the values in the above equation we get-

\(\Rightarrow\frac{1}{v} =\frac{1}{+2.00}-\frac{1}{\left ( -6.00 \right )}\) \(=\frac{1}{2.00}+\frac{1}{6.00}\) \(\frac{6+2}{2\times 6}=\frac{8}{12}\) \(v=\frac{12}{8}\)= 1.5 meter.

The image is 1.5 meters behind the mirror.

The mirror is a polished surface which reflects the incident light to form the image. Here reflected light will have a wavelength and many other physical properties almost the same as that of the incident light.