Mirror Equation

Introduction

Light is electromagnetic radiation and is the only part of the electromagnetic spectrum that can be visible to the human eye. If the light illuminates any surface the quantity of light that is received by the surface depends on the light source’s distance from the surface. When a light ray falls on the rough surface it will be seen in all directions. But for a polished surface, the proper illumination is seen at a particular angle because of the reflection of the light. To understand image formation by the mirrors and why they do not create the same type of images, the concept of the mirror equation is used.

What is a Mirror?

A surface that gives back the image of a body that is placed forth is called a mirror.

• The phenomenon of image creation by a mirror depends on the laws of reflection. When light rays from the object fall on the mirror get reflected at an angle and create an image.

• Mirror has a smooth surface so they do regular reflection and reflecting light in one direction helps them in the formation of images but any other white flat surface has a rough surface that makes them do diffused reflection in which light is reflected in all directions and formation of image is not possible.

• Mirrors have flat or curved surfaces. There are three types of mirrors: plane mirrors, and concave and convex mirrors.

Concave Mirror

It is a part of a spherical mirror that is painted from the outer surface and reflects light from the inner surface to one of the inner focal points.

• It is a converging mirror as it gathers light rays falling on it and again focuses all the parallel rays approaching it towards the focus of a mirror.

• This kind of mirror is different from the convex mirror as it can form a real or virtual image of varying size both relying on the distance between the mirror and the object.

Fig:1 Diagram of a concave mirror I, Cronholm144, Concave mirror, CC BY-SA 3.0

Convex Mirror

It is also a part of a hollow spherical mirror which has a reflecting plane at the bulging side of the mirror and is painted from its curved side and reflects light from the outer surface in the outward direction hence cannot be used to focus light rays.

• It is a diverging mirror and forms virtual images only that can never be projected on a screen because the focus and center of curvature of this mirror are inside the mirror and are unapproachable as shown in the diagram below.

• These mirrors always form virtual images only of small size (diminished images) but images can get larger (magnified) if the object is kept near the mirror.

Fig:2 Convex mirror I, Cronholm144, Convex mirror1, CC BY-SA 3.0

Mirror Equation

The correlation between the image distance, object distance, and focal length of the mirror is specified by a mathematical statement known as the mirror equation. This equation is also known as the mirror formula.

$$\mathit{\frac{1}{v}+\frac{1}{u}=\frac{1}{f}}$$

The above equation is justified for concave and convex lenses and every object distance. It is important to use sign convention while using mirror equations.

While using this equation the focal length is taken positively for a convex mirror while it is taken negatively for a concave mirror.

Terms Used in Mirror Equation

In the mirror equation the terms used are −

• u is the distance of an object from a mirror.

• v is the space between the image and the mirror

• f is the distance between the focus and pole of the mirror.

Uses of Mirror

Mirror is a great invention that makes our life easy. They are used in numerous ways in our daily life which are as follows −

• Plane mirrors are used in solar cookers for reflecting sunlight falling on it.

• Plane mirrors are used to see ourselves while getting ready.

• Concave mirrors are used in torches, headlights, and flashlights.

• Dentists use spherical concave mirrors for an enlarged image of the mouth.

• In vehicles convex mirrors are utilized as rear-view side mirrors for the wider view of the road behind the vehicle.

• Concave mirrors are used in microscopes for the magnified image of the specimen and also in telescopes for the reflection of distant celestial bodies.

• Two convex mirrors are used in a magnifying glass.

• Convex mirrors are placed at sharp turns of a road and parking lots for better visibility.

Conclusion

In this tutorial a very important concept of optics physics is explained in which we can understand the use of mirrors and their importance in our life. Mirrors of different shapes are used for different purposes and the desired image formation, the mirror equation or mirror formula is used with sign convention.

FAQs

1. Can mirror equation be written as =v+u ?

$$\mathrm{ We\: know \:that\: the \:mirror\: equation \:is\: \mathit{\frac{1}{f}=\frac{1}{v}+\frac{1}{u}}}$$

$$\mathrm{Now\: resolve\: the\: above\: equation,\: \mathit{\frac{1}{f}=\frac{vu}{v+u}}}$$

To get the value of f, the above equation can be written as

$$\mathit{f=\frac{v+u}{vu}}$$

This is the only way the mirror equation can be written. Hence mirror equation cannot be written as f=v+u.

2. Discuss the applications of the mirror equation.

The applications of the mirror equation are

• It is used to find image distance if the focal length and object distance is given.

• It can also find the distance of an object when image distance and focal length are known.

• If image and object distance is given by using this equation the focal length of the mirror can be obtained.

3. Define the principal focus of the mirror.

When light rays equidistant from the optical axis fall on the part of the hollow spherical mirror get reflected after which it converges to a spot or diverges from a spot on the same axis. This spot is called the principal focus.

4. What is the difference between concave and concave lenses?

An object kept in front and close to a mirror forms an enlarged image and when placed at some gap from the mirror an inverted image is formed whereas a convex mirror at all positions of an object produces only a small and erect image.

5. How is a lens different from a mirror?

The difference between a mirror and a lens is as follows −

S.No	Mirror	Lens
1.	A part of the glass in which one surface is painted silver and the other surface is used for reflecting light.	It is a piece of transparent glass, which is surrounded by two surfaces out of which one surface is curved.
2	It is curved or plane.	It is curved from one or both sides.
3	It is made of glass or metal.	It is made of glass or plastic.
4	It is based on the principle of laws of reflection.	It is based on the principle of laws of refraction.
5	Mirror equation is given by −$$\mathit{\frac{1}{f}=\frac{1}{v}+\frac{1}{u}}$$	Lens formula is given by − $$\mathit{\frac{1}{f}=\frac{1}{v}-\frac{1}{u}}$$