Reflection at Spherical Surfaces: The phenomenon of reflection is responsible for us to see things around us. The rays of light coming from the sun or other sources of light like a bulb fall on the objects around us and get reflected from their surfaces. The reflected rays of light enter our eyes, and our brain processes the image formed in our eyes. The surfaces of the objects can be of various shapes, and depending on the shape of the reflecting surface, the nature of the image formed will vary.

While the shape of natural reflecting surfaces can be arbitrary, as the surface of the water, in general, reflecting artificial surfaces are either plane or curved. Curved mirrors can either be parabolic or spherical. Plane mirrors are the usual household mirrors that we use every day, parabolic mirrors used in optical devices like a  telescope. An example of spherical mirrors is: Spoons, which on one side are curved outwards and on the other side are curved inwards. Let us learn in detail how reflection takes place at the surface of spherical mirrors.

Spherical Mirrors

Spherical mirrors are a type of curved mirror that is spherical. The reflecting surface of a spherical mirror is a part of a sphere. Thus, it is either curved inwards or curved outwards. The pools of dark water or water stored in vessels or utensils were the first of its kind of spherical mirrors in the history of human civilization. Polished stones like obsidian are the earliest known examples of manufactured mirrors. But it was in 1835, silver-glass mirrors were invented by a German chemist Justus von Liebig.

The spherical mirrors are of the following two types:

1. Concave 
2. Convex

Terms Related to Spherical Mirrors

Spherical mirrors are a part of an imaginary sphere. A sphere has an inner part and an outer part. Thus, its reflecting surface may be curved inwards or outwards. When we discuss such reflecting surfaces, we need to understand the following few terms:

1. Centre of curvature: The reflecting surface of a mirror is a part of a sphere, and the centre of this sphere is called the centre of curvature. It is represented by the letter C.
2. The radius of curvature: The radius of the sphere that the mirror is a part of, or in simple terms, the distance between the centre of curvature and any point on the spherical mirror is called the radius of curvature. 
3. Pole: The point at the middle of the spherical mirror is called the pole. The letter P represents it.
4. Principal axis: It is an imaginary axis passing from the pole and centre of curvature of the spherical mirror.
5. Aperture: The diameter (length) of the reflecting surface of the spherical mirror is called the aperture.
6. Principal focus: All the rays coming parallel to the principal axis after reflection from the spherical mirror pass or appear to pass through the principal focus. It is represented by the letter F.
7. Focal length: The distance between the pole and the principal focus of the spherical mirror is the focal length.

Image Formation by Spherical Mirrors

The rays of light after reflection from the spherical surface meet a point and form an image at that point. For image formation, we need at least two rays of light. For image formation by spherical mirrors, we use the following rules:

1. The rays of light coming parallel to the principal axis, after reflection, pass through the principal focus.
2. After reflection from the spherical surface, the rays of light passing through the focus move parallel to the principal axis.
3. Rays of light passing through the centre of curvature of a spherical mirror, after reflection, retrace their paths.
4. The rays of light incident at the pole of a spherical mirror get reflected at the same angle.

Concave Mirror

Concave mirrors are spherical mirrors with their reflecting surface curved inwards. The inside of a spoon acts like a concave mirror. These are converging mirrors.

Image Formation by Concave Mirrors

Depending on the object’s position in front of the concave mirror, the nature, size, and orientation of the image formed can vary.

1. Objects kept at infinity: The image is formed at the principal focus. It is real, inverted, highly diminished, and point-sized.
2. Objects kept between infinity and centre of curvature: The image is formed between focus and the centre of curvature. It is real, inverted, diminished, and smaller in size compared to the object.
3. Objects kept at the centre of curvature: The image is formed at the centre of curvature. It is real, inverted, and of the same size as the image.
4. Objects kept between the centre of curvature and focus: The image is formed beyond the centre of curvature. It is real, inverted, and enlarged.
5. Objects kept at focus: The image is formed at infinity. It is real, inverted, and highly enlarged.
6. Objects kept between focus and pole: The image is formed behind the mirror. It is virtual, erect, and enlarged.

Convex Mirror

Convex mirrors are spherical mirrors with their reflecting surface curved outwards. The outside of a spoon acts like a convex mirror. These are diverging mirrors.

Image Formation by Convex Mirrors

Depending on the object’s position in front of the convex mirror, the nature, size, and orientation of the image can be given as:

1. Objects kept at infinity: The image is formed at focus behind the mirror. It is virtual, erect, highly diminished, and point-sized.
2. Objects kept between Pole and infinity: The image is formed between pole and focus behind the mirror. It is virtual, erect, and diminished.

Uses of Concave Mirrors

1. Shaving mirrors: The concave mirrors are used as shaving mirrors. When the object is kept close to the concave mirror, between its pole and focus, as is done while shaving, the image formed is virtual, erect, and enlarged. This helps in providing a better and bigger view of the face and helps in shaving.

2. Car Headlights: Concave mirrors are used in headlights of cars and other motor vehicles to generate powerful parallel beams of light.

3. Dentist’s mirrors: Dentists use concave mirrors to have a better view of patient’s teeth. These mirrors provide an enlarged view to the doctors, helping them detect the problems and cavities.

4. Dishes of satellites: The satellites dishes are in the shape of concave mirrors. These dishes are used to receive and amplify the weak signals sent from communication satellites. The parallel rays of lights strike the concave mirror and get reflected. These rays, after reflection, meet at the focus of the mirror and become amplified. Thus, the purpose of the concave mirrors is to collect signals from a large region and concentrate it at a point.

Uses of Convex Mirrors

1. Rearview mirrors: Convex mirrors are used as rear-view mirrors in cars, bikes, and other vehicles because of their curved surface; they provide a larger field of view. These are installed on the side of vehicles. Thus, allowing the drivers to see the traffic behind them. 

2. ATM mirrors: Convex mirrors are installed in ATMs so that a person using the machine can check if there is a person behind them before entering their information. It helps to keep users safe.

Summary

Spherical mirrors are a type of curved mirror that is spherical. The reflecting surface of a spherical mirror is a part of a sphere. Thus, it is either curved inwards or curved outwards. The rays of light after reflection from the spherical surface meet a point and form an image at that point. For image formation, we need at least two rays of light.

Concave mirrors are spherical mirrors with their reflecting surface curved inwards. The inside of a spoon acts like a concave mirror. These are converging mirrors. Depending upon the object’s position in front of the mirror, the image formed by the concave mirror can be real or virtual. These mirrors are used as shaving mirrors, dentist’s mirrors, and satellite dishes.

Convex mirrors are spherical mirrors with their reflecting surface curved outwards. The outside of a spoon acts like a convex mirror. These are diverging mirrors. The image formed by a convex lens is always virtual and erect, and smaller than the object. These mirrors are used as rear-view mirrors and security mirrors at home.

Frequently Asked Questions (FAQs) on Reflection at Spherical Surfaces

Q.1. What is the aperture of a mirror?
Ans: The diameter of the reflecting surface of a spherical mirror is called the aperture of the mirror.

Q.2. Define centre of curvature.
Ans: The centre of curvature is the centre of the spherical mirror, of which the spherical is a part.

Q.3. Give two uses of concave mirrors.
Ans: These are used as:
1. Shaving mirrors
2. Satellite dishes

Q.4. Give the characteristics of an image formed by a convex mirror.
Ans: The image formed by a convex mirror is virtual, erect, and smaller than the object.

Q.5. Why are convex mirrors called diverging mirrors?
Ans: The convex mirrors are called diverging mirrors because they diverge the rays of light falling on their surface.

Study Image Formation By Concave Mirror

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