# Spherical mirrors, types, uses, rules of image formation, practice problems, FAQs

A child was eating food, and suddenly he started playing with the spoon. He saw his face from one side of the spoon, it looked very abnormal and smaller in size. Now he turns the spoon and looks at the face again, he finds that his image is larger in size. He gets confused and goes to the plane mirror in the house, and looks at his normal size image. But what is the problem with the spoon? Why is it not showing the normal image? The spoon can be considered a spherical mirror and the spherical mirror has different properties and functions than a plane mirror. Let's understand the spherical mirror in detail !

Table of content

• Spherical mirror
• Types of spherical mirror
• Terminology of spherical mirrors
• Rules of image formation through spherical mirrors
• Uses of spherical mirror
• Practice problems
• FAQs

Spherical mirror

Spherical mirrors are the mirrors that are curved in shape and are the part of an imaginary hollow sphere. Spherical mirrors are constructed from the glass. One surface of the spherical part is silvered and the other part is used for reflection. Spherical mirrors can be of different types.

Types of spherical mirror

The spherical mirrors are basically of two types- concave mirror and convex mirror.

1. Concave mirror - If the cut-out part of the sphere is silvered on the outside surface and inner part is used for reflection then it is called a concave mirror. As they converge the light ray to a point after reflection, so Concave mirrors are called converging mirrors also. The concave mirror is shown in figure below.

1. Convex mirror- If the part of the sphere is silvered on the inner surface and the outer surface is used for reflection, then it is known as convex mirror.The convex mirror diverts the light rays after reflection, so they are also called diverging mirrors. The figure of the convex mirror is shown below.

Terminology of spherical mirrors

There are following terms needed to know about the spherical mirror-

1. Center of curvature - The center of the sphere from which the spherical mirror is taken is known as the center of curvature of the spherical mirror. In the figure above, the center of curvature is denoted by C.
2. Radius of curvature - The radius of the sphere of which the spherical mirror is the part is called radius of curvature. We can also say the radius of curvature is equal to the distance between any point on the spherical mirror to the center of curvature. It is denoted by R.
1. Pole - The center of the curved portion on the mirror is termed as Pole of the mirror. It is denoted by P.
1. Principal axis - A line which passes from the center of curvature and the pole of the mirror is known as the principal axis.
1. Focus - When the parallel rays coming from infinity fall on the spherical mirror, after the reflection it passes or appears to pass through a point. This point is known as the focus of the spherical mirror. It is represented by the letter F.
1. Focal length- The distance between focus (F) and pole (P) is known as focal length of spherical mirror.

Rules of image formation through spherical mirrors

The image formed by a spherical mirror can be traced by using following rules -

1. A ray parallel to the principal axis incident from infinity

(a). When it falls on the concave mirror after the reflection it passes through the focus of the concave mirror.

(b). When it falls on the convex mirror after the reflection it appears to pass through the focus of the convex mirror.

1. A ray incident towards focus:

(a). A ray incident from the focus of the concave mirror after the reflection becomes parallel to the principal axis of the concave mirror.

(b). A ray directed towards the focus on a convex mirror after the reflection becomes parallel to the principal axis of the convex mirror.

1. A ray incident towards center of curvature:

(a).A ray incident from the center of curvature falls on the concave mirror after reflection it reflects back along the same path.

(b).A ray directed towards the center of curvature after reflection from a convex mirror reflects back along the same path.

1. A ray incident on pole:

(a). An incident ray that falls obliquely on the pole of a concave mirror is reflected obliquely the same as a plane mirror.

(b). An incident ray that falls obliquely on the pole of a convex mirror is reflected obliquely the same as a plane mirror.

Uses of spherical mirror

• Concave mirror
1. Shaving mirror - Shaving glasses have concave mirrors. When the face is kept close to the mirror, between focus and pole, the virtual, erect and enlarged image of face is formed.
2. Headlight of car - In headlights concave mirror is used to generate a parallel beam of light.
3. Satellite dishes - The dishes of satellites are made concave in shapes. The parallel ray of light strikes on the concave surface and focuses on the device which amplifies the signal.
• Convex mirror
1. Rearview mirror - The side mirror used in cars is a convex mirror. They form small, erect and virtual images and have a wide field of view.
2. Mirror at corner of the roads - Here the convex mirror is used. It shows both the roads simultaneously so we can see the person or vehicle on the other road.

Practice problems

Q. Draw a ray diagram for image formation through a concave mirror if the object is placed between infinity and center of curvature. Discuss the features of the image.

A. Consider the following steps -

1. Draw a ray parallel to the principal axis, after the reflection it will pass through the focus.
2. A ray passed through the center of curvature will return back to the same path.
3. The intersection of both the reflected rays will give the image.

• The image is formed between the center of curvature and focus of the mirror.
• The image is real and inverted and of diminished size.

Q. Draw a ray diagram for image formation through a concave mirror if the object is placed between the center of curvature and focus of the mirror. Discuss the features of the image.

A. If the object is between the center of curvature and focus then

1. A ray of light parallel to the principal axis after the reflection will pass through the focus.
2. A ray directed along the center of curvature after reflection will pass through the center of curvature.
3. The intersection of reflected rays will form the image of the object.

The image is formed away from the center of curvature. The size of the image is enlarged. The image is real and inverted.

Q. Discuss the ray diagram for image formation through a concave mirror if the object is placed between the focus and pole of the mirror. And what are the features of the image?

A. When the object is between focus and pole, then

1. When a ray falls on the mirror at poles it will reflect just as a plane mirror (i=r)
2. A ray directed along the center of curvature after reflection will pass through the center of curvature.
3. Both the reflected rays are not meeting in real, if we project these rays back of the mirror, they will meet at a point.

The image is formed behind the mirror, the image is virtual, erect and enlarged in size.

Q. Draw a ray diagram for image formation through a convex mirror if the object is placed between infinity and the pole. Discuss the features of the image.

A. For the image the following steps can be taken -

1. The ray coming from infinity after the reflection will appear to pass through the focus.
2. The ray directed towards the center of curvature will return along the same path.
3. Intersection of projection of the reflected ray behind the mirror will give you the location and size of image.

From the ray diagram we can say an image is formed behind the mirror between pole and focus. As the image is behind the mirror so it is virtual. The image is erect and diminished in size.

## FAQs

Q. Which mirror is used in cars?
A. A convex mirror is used so that maximum things can be observed.

Q. Why do dentists use concave mirrors?
A Concave mirror is used because it produces a bigger image of the tooth, so it can be examined properly.

Q. Is the image seen in the mirror real or virtual?
A. The image seen in the mirror is virtual in nature.

Q. Will the image formed by half of a spherical mirror be half or complete?
A. As every small part of the spherical mirror forms a complete image of the object, so the image will be complete.

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