Uses of Spherical Mirrors: Spherical mirrors are used by all in day-to-day life. It is important that students have a better understanding of the application of spherical mirrors so that they grasp the concept properly. Students often find problems when dealing with the concept because it can prove to be complicated. However, this concept is important because questions from this concept do come in exams.

This article has a detailed explanation of the application of spherical mirrors. Students can find spherical mirror examples which will help them understand the concept. The article has explained in detail the examples of concave and convex mirrors and their definitions, which are important for students to understand. After reading this article students will be able to write the uses of spherical mirrors and ace their exams. To know more, continue to read the article. 

What is Reflection?

We all know what a mirror is. Mirror is a shiny surface made up of glass, which instead of allowing the light to pass through, bounces it back reflecting the image in front of it. This phenomenon of bouncing back of the light is called reflection of light. A calm surface of the water of a lake, which reflects light like a mirror, is another example of reflection of light.

Laws of Reflection

Before we understand the uses of spherical mirrors, we need to understand the law of reflections.

The laws of reflection apply to all types of surfaces: smooth or rough, plane or curved, dull or shiny. To understand the laws of reflection, first, we have to understand few terms related to it.

Incident Ray: It is the ray of light that falls on the reflecting surface.
Reflected Ray: It is the ray that bounces back from the surface.
Normal: It is the line that is perpendicular to a surface.
Point of Incidence: It is the point where the incident ray touches the surface.

1. First Law:
   It states that the incident ray, the reflected ray, and the normal to the surface at the point of incidence all lie in the same plane.
2. Second Law:
   The angle of incidence is equal to the angle of reflection.

Learn Uses Of Convex Mirror & Its Applications

Types of Mirrors

There are two types of mirrors:

1. Plane Mirror
2. Curved Mirror
   Curved mirror further has two types:
   (i) Concave Mirror
   (ii) Convex Mirror

Spherical Mirror Example

The curved mirrors, we are discussing here, are spherical mirrors. We call them so because their surfaces are a part of hollow spheres. There are two types of spherical mirrors: Concave and convex mirrors.

The definition of concave mirror and convex mirrors is given below:

Concave Mirror: Definition

It has the reflecting surface on the sphere’s inner surface; that is, the surface curves inwards or “caves” in.

Convex Mirror: Definition

The reflecting surface is on the sphere’s outer surface; that is, the surface bulges outwards.

Examples of Convex and Concave Mirrors

Some examples of Convex Mirrors are:

• Magnifying glasses
• Telescopes

Some examples of Concave Mirrors are:

• Shaving mirrors
• Headlights
• Solar furnaces

Terms Related to Spherical Mirrors

Some of the essential terms related to spherical mirrors are:

Pole \((O)\) It is the centre of the reflecting surface.

Centre of Curvature \((C)\)

It is the centre of the sphere.
i. For a convex mirror, the centre is behind the mirror.
ii. For a concave mirror, the centre is in front.

Radius of Curvature \((OC)\)

It is the radius of the sphere that the mirror is a part of.

Principal Axis

It is the line from the centre of curvature and passing through the pole. It is always normal to the surface at the pole.

Principal Focus or Focal Point \((F)\)

It is the point on the principal axis. When a ray of light parallel to the principal axis falls on –
i. a concave mirror, the reflected ray passes through the focal point in front of the mirror on the principal axis,
ii. convex mirror, the reflected ray appears to emerge from the focal point behind the mirror on the principal axis.

Focal Length \((OF)\)

It is the distance between the focal point and the pole.

Aperture

It is the diameter of the reflecting surface, as usually, the reflecting surface is circular.

In a convex mirror:

In a concave mirror:

Images Formation by Spherical Mirrors

When we place an object in front of a mirror, each point of it emits a ray of light. But for convenience, only two rays coming out of the ends of the object are considered. The intersection of at least two rays gives the position of the image formed by the mirror.
We consider the following points for representing images by ray diagrams in both concave and convex mirrors:

Incident Ray	Reflected Ray
Parallel to the principal axis:	i. Passes through the focal point \((F)\) in concave. ii. Appears to diverge out of \(F\) in convex.
Passing through the focal point \((F)\) in concave, or directed towards it in convex.	Parallel to the principal axis.
Passing through the centre of curvature \((C)\) in concave, or directed towards it in convex:	Reflected back in the same direction as the incident ray.
Incident on the pole \((P)\) obliquely:	Reflected with the same angle as that of incidence.

Image Formation in a Concave Mirror

A concave mirror converges light rays onto a single point. The type of image formed depends on the position of the object it is reflecting.

Real Image: It can be focused on a screen and captured on a film or sensor. The object and the image will be on the same side of the mirror. There is no lateral inversion of the image.
Virtual Image: We can only see this but cannot focus it on a screen. It will appear behind the mirror. The image is laterally inverted.

Object: At infinity. Image: on the focal point \((F)\), point size, real and inverted.

Object: Near mirror, but beyond centre \((C)\). Image: Between \(F\) and \(C\), diminished, real and inverted.

Object: At the centre of curvature \((C)\). Image: At \(C,\) the same size as the object, real and inverted.

Object: Between \(C\) and \(F\). Image: Beyond \(C\), enlarged, real and inverted.

Object: At focal point \((F).\) Image: At infinity, highly enlarged, real, and inverted.

Object: Between \(F\) and pole \((P).\) Image: Behind the mirror, enlarged, virtual, and erect.

Image Formation in a Convex Mirror

A convex mirror diverges light rays from a single point. As a result, the image is always virtual, diminished, erect and laterally inverted.

Object: At infinity. Image: On focal point\((F)\), point sized, virtual and erect.

Object: Any point near the mirror. Image: Between \(P\) and \(F\), diminished, virtual and erect.

Mirror Formula

This formula relates the distances between the object and the image with focal length. The distances mentioned are the distances along the principal axis from the pole.

\(\frac{1}{u} + \frac{1}{v} = \frac{1}{f}\)

\(u\) is the distance of the object from the lens.
\(v\) is the distance of the image from the lens.
\(f\) is the focal length.

Sign Convention

1. The object is always placed left of the mirror.
2. Distance of object or image always measured from pole, \(P\)

Magnification Factor

Magnification of a spherical mirror gives the relative extent to which the image is magnified concerning the object.

We define magnification as the ratio of the height of the image to the height of the object.
Magnification, \(M = \frac{{{h_i}}}{{{h_o}}}\)
It is also the ratio of image distance to object distance. Therefore,
\(\frac{{{h_i}}}{{{h_o}}} = \frac{v}{u} = M\)
In wards
\({\text{Magnification=}}\frac{{{\text{image}}\,{\text{height}}}}{{{\text{object}}\,{\text{height}}}}{\text{=}}\frac{{{\text{image}}\,{\text{distance}}}}{{{\text{object}}\,{\text{distance}}}}\)
The equation for magnification is the same for both real and virtual images.

Uses of Concave Mirrors

i. Dentists use them to see the back of teeth.
ii. Men use them while shaving.
iii. They are used to produce parallel beams of light in torches, vehicle headlights and searchlights.
iv. They are used as concentrators in solar cookers and furnaces.
v. They are used in reflecting telescopes.

Solar Cooker

Solar Furnace

Uses of Convex Mirrors

1. We have seen these mirrors on the sides of vehicles. Convex side view mirrors show a larger area in a small space.
2. They are placed at curves of roads to give a view of the bend of the road.
3. Convex mirrors are also used in reflecting telescopes.

Summary

Mirror	Image Type	Magnification Factor	Image Size
Concave	Real	\(M < 1,M = 1,M > 1\)	Can be enlarged, same, or diminished depending on object position
Concave	Virtual	\(M > 1\)	Always enlarged
Convex	Virtual	\(M < 1\)	Always diminished

Spherical Mirrors – Sample Problems

Q.1. The focal length of a concave mirror is \(10\,{\text{cm.}}\) If we place the object at \(5\,{\text{cm}}\) from the pole, where is the image located, and what type of image is it?
Ans: Given,
focal length, \(f =  – 10\,{\text{cm}}\) (Negative for a concave mirror)
object distance, \(u =  – 5\,{\text{cm}}\) (Object at the left of the mirror, therefore, distance is considered negative)
Mirror formula is,
\(\frac{1}{u} + \frac{1}{v} = \frac{1}{f}\)
Therefore,
\( – \frac{1}{5} + \frac{1}{v} =  – \frac{1}{{10}}\)
Solving for \(v,\)
\(v = 10\,{\text{cm}}\)
The image is at \(10\, {\text{cm}}\) from the pole. A positive value means it is on the right side of the mirror or a virtual image.

Q.2. We place an object at a distance of \(20\, {\text{cm}}\) from the pole of a mirror. The image distance is \(10\, {\text{cm}}\) on the opposite side of the object. Find the focal length and magnification factor. What type of lens is this?
Ans: Given,
object distance, \(u =  – 20\,{\text{cm}}\) (Object always at the left of the mirror, so it is considered negative)
image distance, \(v = 10\, {\text{cm}}\)
Mirror formula is,
\(\frac{1}{u} + \frac{1}{v} = \frac{1}{f}\)
Therefore,
\( – \frac{1}{{20}} + \frac{1}{{10}} = \frac{1}{f}\)
Solving for \(f,\)
\(f = 20\,{\text{cm}}\)
A positive value for focal length means that it is a convex mirror.
Magnification factor, \(M = \frac{v}{u} = \frac{{10}}{{20}} = \frac{1}{2}\)
The image is virtual, erect, and diminished.

FAQs on Uses of Spherical Mirrors

Q.1. Are the pole and centre of curvature of a spherical mirror the same?
Ans: No. Pole is the geometrical centre of the mirror. The centre of curvature is the centre of the sphere whose surface the lens is a part.

Q.2. What mirror does a dentist use to see the back of the teeth?
Ans: Dentists use a concave mirror. The virtual image formed by a concave image is enlarged.

Q.3. What is the difference between a real and a virtual image in mirrors?
Ans: A real image is inverted and can be projected on a screen. A virtual image is erect. We cannot project a virtual image on a screen.

Q.4. Are the laws of reflection applicable to spherical mirrors?
Ans: Yes. They apply to both concave and convex mirrors.

Q.5. A steel utensil reflects the surroundings with small, distorted images. What kind of mirror does it behave as?
Ans: The outer surface of a steel utensil behaves like a cylindrical convex mirror.

Q.6. What are the uses of spherical mirrors?
Ans: Spherical mirrors are used as:

• Rear view mirrors (driver’s side mirrors) in vehicles
• Reflectors in street lamps
• Security mirrors in shops
• Surveillance mirrors at curved roads
• Optical instruments such as telescopes, cameras, etc.

We hope you find this article on the Uses of Spherical Mirrors helpful. In case of any queries, you can reach back to us in the comments section, and we will try to solve them.