# Concave and Convex Mirrors Spherical Mirrors

## Introduction

Let's understand various concepts related to the spherical mirrors, that is to say, concave and convex mirrors. Before starting the tutorial, you must recall some important points about the light and reflection on a plane surface. This will help you to understand the light reflection on the spherical surfaces.

So, let's understand the two main points about the reflection of light on a plane reflecting surface before starting the tutorial on spherical mirrors.

## Reflection of Light on Plane Mirrors

The laws of reflection state that –

• The angle of incidence ($\angle$i) and the angle of reflection ($\angle$r) are always equal to each other ($\angle$i = $\angle$r)

• The incident beam of light reflected beam of light, and normal, are all present in the same plane. (See fig. below)

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Image 1: Laws of Reflection

Now that we have understood the basics of a plane reflecting surface, we can easily understand the concepts of spherical mirrors because of the similarities between both types of surfaces.

Let's us understand about spherical mirrors in detail.

## Spherical Mirrors

Those mirrors which have curved reflecting surfaces are referred to as spherical mirrors. There are two types of spherical mirrors. They are as follows:

• Concave Mirrors: Those mirrors which have a reflecting surface curved from inside are known as concave mirrors.

• Convex Mirrors: Those mirrors which have a reflecting surface curved from the outside are known as convex mirrors.

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Image 2: Spherical Mirrors: Concave and Convex

### Activity

Take a spoon and look at the curved surface of the spoon. The curved surface of the front part can be referred to as a concave surface. It is similar to a concave mirror.

On the other hand, the curved surface of the back of the spoon can be referred to as a convex surface.

Now, you may have clearly understood the difference between concave and convex mirrors. Any curved reflecting surface can be called a spherical mirror. The inwardly curved reflecting surface represents a concave mirror whereas the outward surface represents a convex mirror.

Let's move to the next section of this tutorial.

## Components of Spherical Mirrors

The terms related to components of mirrors are as follows:

• Pole (P): The pole is the center point of the reflecting surface. Denoted by letter 'P'.

• Centre of Curvature (C): The spherical mirrors form a sphere. The center of this imaginary sphere is called as Centre of Curvature, Denoted by the letter 'C'.

• Radius (R): The distance from the Centre of Curvature to the Pole is called the radius. That is to say, the distance PC is denoted by the letter 'R'.

• Principal Axis: An imaginary straight line passing through the Centre of Curvature and Pole is called the Principal Axis.

All these components of spherical mirrors are shown below in the given figure.

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Image 3: Components of a Spherical Mirror

Important Note: The Centre of Curvature does not lie on the surface of the mirror. In a concave mirror, it lies in front of the surface, i.e., towards the observer. In a convex mirror, it lies away from the observer, i.e., behind the mirror.

Let us understand another important term – 'Focus' by performing an interesting activity.

## Activity to Understand Focus Point

Requirements: Concave mirror, white paper sheet.

Procedure: Take a concave mirror and hold it in the direction of the sun. Now, try to get a reflection of sun rays on a white sheet of paper. Adjust the concave mirror near or away from the paper in such a way that you get a bright point of reflection.

As soon as you get a bright point on the sheet, hold it in the same position for some time. Observe what happens after some time.

Observation: What did you observe? You may have seen that after some time, the paper sheet started to burn or started to produce smoke. Why does this happen?

It happens due to the 'Focus' of sunrays at one point for a longer period. That is to say, focusing the sunrays on one point causes the paper to burn. The bright point of reflected sunrays is called 'Focus'.

• Focus (F): A point on the principal axis where all the reflected beams of light are converged. Denoted by letter 'F'.

Concave Mirror: Real Focus (In front of the mirror)

Convex Mirror: Virtual Focus (Behind the mirror)

• Focal Length (f): The distance between Pole (P) and Focus (F) is referred to as 'Focal Length'. Denoted by letter 'f'.

• Aperture (A): The distance from one end of the spherical reflecting surface to the other end of the spherical reflecting surface is known as the aperture. That is to say, the diameter of the reflecting surface. Denoted by the letter 'A'. (Fig. showing the distance MM')

Important Note: The aperture of the spherical mirror should always be smaller than its radius. The radius and focal length have a relationship that can be explained by a formula.

$$\mathrm{R = 2f}$$

The formula states that the radius of the spherical mirrors is double the focal length. Hence, the Focus (F) always comes between Pole (P) and Centre of Curvature (C).

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Image 4: Components of a Spherical Mirror

## Conclusion

In the conclusion, this tutorial has defined the spherical mirrors and explained their components in the simplest terms.

## FAQs

Q1. What are spherical mirrors give examples?

Ans: Spherical mirrors are curved reflecting surfaces.

Examples: Concave and convex mirrors.

Q2. What is a convex mirror?

Ans: A mirror having a curved reflecting surface bulging outwards is called a convex mirror.

Q3. What is a concave mirror?

Ans: A mirror having the reflecting surface curved inwards is called a concave mirror.

Q4. Where is the concave mirror used?

Ans: Concave mirrors are used in headlights and torchlights.

Q5. Are car mirrors concave or convex?

Ans: Mirrors used in cars are the convex mirror. The convex mirror is used as a rear-view mirror in vehicles.