Concave Mirrors and Convex Mirrors

Concave mirrors form both real and virtual images of objects, while convex mirrors form a virtual and erect image.

We find mirrors at our home, in our cars, beauty salons, etc. The list is endless! However, mirrors are called mirrors in a common language, while scientifically, each one of these is categorized into concave and convex mirrors.

Concave and convex mirrors are spherical mirrors. Now, if I ask you what a concave mirror is and how you differentiate it from a convex mirror, you say that it is possible by looking at the images of these two drawn below:

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Concave and Convex Mirror Images

In the above introduction, you understood the basic diagram of concave and convex mirrors. A ray diagram for a concave mirror varies with the object placed at varying positions. 

Before starting with the ray diagram of each case, we need to know the following terms:

• Principal Axis 

The line passing through the centre of the sphere is called the principal axis.

• Pole 

The centre of the reflecting surface is called the pole (P).

• Centre of Curvature  

A concave mirror is carved out of a sphere, and its centre is called the centre of curvature (C).

• The Radius of Curvature 

Radius of the sphere (R)

• Focus 

The midpoint between C and P.

Sign Conventions:

• When the object is placed in front of the mirror, the object is taken as negative.

• Signs of the radius of curvature and focal length are also taken negatively.

Ray Diagram of Concave 

Now, to understand it in detail, we will first look at the ray diagram concave mirror:

• The Image Formed by a Concave Mirror

A concave mirror forms different images for the objects lying at different positions; let’s look at various cases one-by-one:

1. An Object Placed at Infinity

When an object is placed at infinity, the images coming from the distant object parallel to the principal axis converge at the focus ‘F’, as shown in the ray diagram below:

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2. An Object is Placed at C 

When an object is placed at C, the real and inverted image is formed at C itself, as you can see in the ray diagram below:

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3. An Object Placed Beyond C

When an object is placed beyond C, the real and inverted image is formed between C and F, as you can see in the image below:

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4. An Object Placed Between C and F     

When the object is placed between C and F,  the real and inverted image is formed beyond C, as you can see in the ray diagram below:

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5. An Object is Placed at F

When an object is placed at F, the image coming from the distant object pass through C, strike the surface of the mirror, and hence, the reflected ray comes out parallel to the incident ray, as shown below:

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In all the above cases, the image is formed in front of the mirror. Now, we will look at the case of virtual images formed by the concave mirror.

6. An Object Placed Between P and F

This is a special case for the ray diagram of the concave mirror. When an object is placed between P and F, an image is formed behind the mirror. The rays appear to meet each other, so we represent these rays by a dotted line, as shown in the ray diagram below:

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So, the ray diagram for the image formed for the objects placed at different positions is:

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• Image Formation by a Convex Mirror

We know that the convex mirrors form a virtual and erect image, and now we will look at the ray diagrams of the convex mirror:

1. An Object Placed at Infinity

When an object is placed at infinity, the incident rays passing parallel to the principal axis converge at F. The image formed is virtual and the zero-sized image is formed as you can see in the ray diagram below:

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2. An Object Placed Between Infinity and P

When an object is placed between infinity and P, the virtual and diminished image is formed between F and P, as you can see in the ray diagram below:

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3. An Object Placed at P

When an object is placed at P, the image will form at the pole itself.

The nature of the image is virtual, upright, and of the same size as that of the object.

Now, let’s look at the convex mirror image formation table: