Just imagine living a day without mirrors. How will you get dressed to go to school? While driving, how will you be able to see vehicles behind and on the sides? How will you check out the look of new clothes when you go to shop in the market? It is practically impossible to live without mirrors. In this document, we will study mirrors and their types in detail.
A mirror is a smooth and highly polished surface designed to reflect light in a way that preserves the physical characteristics of the original light. This can be attributed to the law of reflection.
Law of Reflection
There are several types of mirrors, each with unique characteristics and uses. Some of the most common types of mirrors are:
Types of mirrors
Each type of mirror has unique properties that make it suitable for different applications, and understanding these properties is important for choosing the right mirror for a particular use.
A plane mirror is a flat and smooth reflecting surface that reflects light in a way that preserves the physical characteristics of the original light. The following are some important properties and terms related to a plane mirror:
Properties:
In the image formed by a plane mirror the right side of the object appears as the left side and viceversa. This phenomenon is called lateral inversion.
Image formed by a plane mirror
Image formed by a plane mirror
Calculations:
Image formed by a Periscope
A highly polished curved surface whose reflecting surface is a cut part of a hollow at glass sphere is called a spherical mirror.
Spherical mirrors are of two types:
(i) Concave Mirror: A spherical mirror whose bent surface is reflecting surface, is called a concave mirror.
Types of Spherical Mirrors(ii) Convex Mirror: A spherical mirror whose bulging out surface is reflecting surface, is called a convex mirror.
Some Terms Related to Spherical Mirrors are Given Below:
Terms related to Spherical Mirrors
Sign Convention for Spherical Mirrors
Sign Convention for Convex Mirror
Let us consider a point object placed beyond C of a concave mirror. To obtain the image, we make the ray diagram; we can take any two rays.
1. The first ray goes straight along the principal axis and after reflection, it retraces the same path.
2. Another ray is taken, which makes an angle of 𝜃 to the normal drawn and reflects back towards the principal axis.
Both the rays, after reflection, meet each other at some point, say I, that is between F and C. The image is formed at point I.
Let us assume the angle subtended by the object, image, and the center of curvature with the principal axis be 𝛼, 𝛽, and 𝛾.
For triangle AOC,
Concave Mirror
By subtracting equation (ii) from equation (i), we get the following:
The perpendicular drawn from A meets the principal axis at M, and M is very close to P. So, we can treat them as the same points, i.e., AM ≈ AP.
From the diagram,
For small angle,
By substituting the above values in equation (iii), we get the following
This is the mirror formula for a concave mirror.
Let us take a convex mirror of a small aperture and let the object be placed somewhere between P and infinity. To obtain the image, we make the ray diagram and we can take any two rays.
1. The first ray goes along the principal axis and is extended towards the back of the mirror.
2. The second ray falls on the mirror at an angle of 𝜃 with the normal at that point and gets reflected. On extending the reflected ray behind the mirror, it meets the principal axis at some point between P and F.
Both the rays after reflection meet each other at some point, say I, which is between P and F. The image is formed at point I.
Let us assume the angle subtended by the object, image, and the center of curvature with the principal axis be 𝛼, 𝛽, and 𝛾.
Convex Mirror
The perpendicular drawn from A meets the principal axis at a point very close to P.
So, from the diagram,
For small angle ,
By substituting the above values in equation (iii), we get the following
This is the mirror formula for a convex mirror which is the same as a concave mirror.
Mirror Formula: 1/f = 1/v + 1/u
where, f = focal length of the mirror, u = distance of the object, and v = distance of the image.
Newton’s formula for a concave mirror:
⇒
where x_{1} and x_{2} are the distances of the object and image from the focus.
Example 1: What is the image distance of a concave mirror if the object distance is 16 cm? It is given that the focal length of the mirror is 8 cm.
Solution:
As we know the mirror formula: 1/v + 1/u = 1/f
where, u = object distance = 16 cm
v = image distance = ?
f = focal length of the mirror = 8 cm
Putting the values we get,
1/v + 1/16 = 1/8
or, 1/v = 1/16
or, v = 16 cm
Therefore, the object is located 16 cm in the front mirror.
Example 2: Find the image distance of convex mirror if the object distance is 10 cm? It is given that the focal length of the mirror is 10 cm.
Solution:
As we know the mirror formula: 1/v + 1/u = 1/f
where, u = object distance = 10 cm
v = image distance = ?
f = focal length of the mirror = =10 cm
Putting the values we get,
1/v + 1/10 = 1/10
or, 1/v = 1/10 – (1/10)
or, 1/v = 1/10 + 1/10
or, 1/v = 2/10
or, 1/v = 1/5
or, v = 5 cm
Therefore, the image is located 5 cm behind the mirror.
Magnification is a measure of the extent to which an object's size is visually enlarged or reduced by an optical system, such as a lens or a mirror. It is the ratio of the size of the image produced by the optical system to the size of the object itself.
1. Linear Magnification  The ratio of the height of the image (I) formed by a mirror to the height of the object (O) is called linear magnification (m).
Linear magnification (m) = I/O = v/u
2. Areal and Axial Magnification 
Areal Magnification
Example 1: What is the magnification if the object height is 12 cm and the image height is 48 cm below the principal axis?
Solution:
As we know the magnification can be calculated using the following formulas: m = h’/h
Given, height of the image h’ = 48 cm, height of the object (h) = +12 cm
The signs are given using sign convention.
therefore, m = h’/h
or, m = 48 cm/ 12 cm
0r, m = 4
Thus the magnification is 4.
Example 2: Rohit kept a pencil perpendicular to the principal axis of a concave mirror just ahead of it. The Mirror has a focal length of 30 cm. The image produced is two times the pencil size. If the image is real, what is the object's distance from the mirror?
Solution:
Magnification =h(i)/h(o) =−v/u
For real image
m=−v/u=−2
v=2u
Using the mirror equation,
1/v+1/u=1/f
1/2u+1/u=1/−30
u=45 cms.
When the object lies too close to a concave mirror, it forms a virtual, upright, and magnified image of the object. This property of concave mirrors is used in
As all the above mirrors are required to produce a magnified image of the person in front of it, concave mirrors are used. A concave mirror can also direct the light from a source (spreading in all directions) in one direction by reflecting it. Because of this property, concave mirrors are used in
A convex mirror covers a wide area in the image it forms. Because of this property, it is used as:
1. The incident ray, the normal and the reflected ray all lie in the same plane.
2. The angle of incidence and Angle of reflection are always equal.
3. f=r/2, both f, and r are positive for concave mirror and negative for convex mirror.
4. Mirror formula for any type of mirror:
5. Magnification of a mirror is given by:
where h_{i} is the height of the image, h_{o} is the height of the object, d_{i} is the distance of the image from the pole, and d_{o} is the distance of the object from the pole.
Answer: b
Explanation: If the magnification of the mirror is one, then it is a plane mirror. If magnification is more than one, the mirror is concave. If magnification is less than one, then the mirror is convex. So the X required in this question is a concave mirror.
Q.2. Which of the following causes refraction of light?
a) Change in the density of light from one medium to another
b) Change in viscosity of light from one medium to another
c) Change in the speed of light from one medium to another
d) Change in direction of light from one medium to another
Answer: c
Explanation: Light travels at different speeds in a different medium. The bending or refraction of light occurs due to the change in the speed of light as it passes from one medium to another. Other statements are not true regarding the refraction of light.
Q.3. If a concave mirror of focal length 10cm is immersed in water, its focal length will ________.
a) Be reduced
b) Be increased
c) Remain unchanged
d) More than one of the above
e) None of the above
Answer: The correct answer is to Remain unchanged.
Explanation: In the case of mirrors, for both concave and convex the focal length shall remain unchanged for the mirrors when immersed in water.
Q.4. As the object moves towards the plane mirror the size of the image:
a) Increases
b) Decreases
c) Remain unchanged
d) Can't say
e) None of the above/More than one of the above.
Answer 3 : Remain unchanged
Explanation:
Q.5. The magnification of ‘X’ is more than unity. Identify X.
a) Convex mirror
b) Concave mirror
c) Plane mirror
d) Prism
Answer: b
Explanation: If the magnification of the mirror is one, then it is a plane mirror. If magnification is more than one, the mirror is concave. If magnification is less than one, then the mirror is convex. So the X required in this question is a concave mirror.
105 videos425 docs114 tests

1. What is the mirror formula for a concave mirror? 
2. What is the mirror formula for a convex mirror? 
3. What are the applications of spherical mirrors? 
4. What is magnification in the context of mirrors? 
5. What are some properties related to plane mirrors? 

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