Reflection of Light
Reflection of Light
Light
Light is a form of energy which excites our sense of sight.
Sources of light
During the day, the primary source of light is the Sun and
the secondary source is the brightness of the sky. Other
common sources are flames, electric bulbs, tube lights
(fluorescent tubes), compact fluorescent lamps (CFLs) and
light emitting diodes (LEDs).
☞ Light travels in a straight line in vacuum or in a
homogeneous transparent medium.
2. Some basic terms
Ray of light
Ray of light : A ray of light is the direction in which light travels.
Beam of light : A bundle of light rays is called beam of light (or light beam).
Convergent beam : A beam of light in which all the rays move towards a single point is
called convergent beam (see figure).
[1]
A convergent beam
Divergent beam : A beam of light in which all the rays emerge out from a single point is
called divergent beam (see figure).
A divergent beam
Parallel beam : A beam of light in which all the rays are parallel to each other is called
parallel beam (see figure).
A parallel beam
3. Reflection of light
Reflection of light is the process in which light rays meeting the boundary between two
media ‘bounce back’, to stay in the first medium.
[2]
Reflection of light
Plane of travel
Incident ray
Normal
Reflected ray
Surface
P
Q
R
S
☞ The process of sending back of light rays which fall on the
[3]
Normal : A line perpendicular to the surface of mirror passing through the point of
incidence is called normal.
Angle of incidence : The angle made by incident ray with the normal at the point of
incidence is called angle of incidence.
Angle of reflection : The angle made by reflected ray with the normal at the point of
incidence is called angle of reflection.
🟋 The plane which is discussed in first law of reflection is not the surface of mirror. It is
the plane PQRS (see above figure).
🟋 We are able to see the objects because the light gets reflected from the object and reach
our eyes.
You may have observed the image of the sun in the windows of distant buildings near
the time that the sun is rising or setting. However, the image of the sun is not seen in
the windows of distant building during midday. Explain it, by drawing appropriate
light rays on the given diagram.
Observer
Sun
12.30 pm
Sun
6.30 pm
Windows
House
Explanation
A ray of light (Ray 1), drawn from the sun's position at 6.30 pm to the distant window,
reflects from the window and travels to the observer's eye (see figure). While a ray of light
(Ray 2), drawn from the 12.30 pm sun position to the window, will reflect and travel to the
ground, does not reach to the distant observer's eye.
[4]
Observer
Ray 1
Sun
12.30 pm
Sun
6.30 pm
Windows
House
Ray 2
Building concepts 1
☞ When a light ray falls perpendicular on the surface of a mirror, it reverses its path on
reflection. That is, it exactly retraces its path because angle of incidence and angle of
reflection both are equal to zero (see figure).
🟋 When light incident normally over a reflecting surface angle between incident ray and
reflecting surface is 90° but angle of incidence and angle of reflection is equal to zero.
5. Reflection from plane mirrors
A mirror is a highly polished surface used to reflect the light falling on it. Mirrors are
usually made by depositing a thin layer of silver metal on one side of a plane glass sheet.
Some basic terms
Object : Anything which gives out light rays either of its own or due to reflection is called
an object.
Point object : An object whose dimensions are negligibly small is called point object.
Extended object : An object whose dimensions are quite large is called extended object.
[5]
Image : An image of an object is formed when light rays coming from the object meet or
appear to meet at a point after reflection from a mirror or refraction from a lens.
Real image : A real image is formed when the light rays actually meet at a point and which
can be obtained on a screen. It is always inverted.
Virtual image : A virtual image is formed when the rays do not actually meet at a point but
they appear to meet at a point. Such images cannot be obtained on the screen. It is always
erect or upright.
Image formed by a plane mirror
The properties of image formed by a plane mirrors are (see figure a and b):
(1) The image is virtual and erect.
(2) The distance of image from mirror is equal to distance of object from mirror.
(3) The size of image is exactly equal to the size of object.
(4) The image is laterally inverted.
Lateral inversion
When an asymmetric object is placed in front of a plane mirror, then the right side of the
object appears to be the left side of image and the left side of the object appears to be the
right side of its image. This change of sides of an object seen in the image is called left -
right inversion or lateral inversion. The image is inverted side ways, thus, also called ‘side
ways inversion’ (see figure c)
Image
Object
i
r
(a) Formation of image
of a point object
1. If you wish to take a picture of your image while standing 5 m in front of a plane mirror, for
what distance should you set your camera to provide the sharpest focus?
2. What evidence can prove that frequency of light does not change upon reflection?
6. Reflection from spherical mirrors
A spherical mirror, as the name suggests, has the shape of a section of a hollow sphere. A
spherical mirror is a mirror whose reflecting surface is made by the part of a hollow
sphere. Suppose a hollow sphere has a polished mirror surface on the inside as well
outside. By removing a section of the sphere, a double-sided spherical mirror is obtained
with a concave reflecting surface on one side and a convex reflecting surface on the other
side (see figure).
A hollow
sphere
Convex
mirror
Concave
mirror
[7]
A spherical mirror formed from a hollow sphere.
Concave mirror
A spherical mirror in which the reflection of light takes place at bent-in surface is called
‘concave mirror’.
Concave mirror is also called ‘converging mirror’. This is because the parallel beam of light
after reflection, converge at a single point.
A concave mirror
Real focus
Convex mirror
A spherical mirror in which the reflection of light takes place at bulging-out surface is
called ‘convex mirror’.
Convex mirror is also called ‘diverging mirror’. This is because the parallel beam of light
after reflection appears to diverge from a single point.
A convex mirror
Virtual focus
The concave reflecting surface is curved inwards. The convex reflecting surface is curved
outwards.
[8]
Step-1 : As we know distance of image from mirror is equal to the distance of object from
mirror.
Step-2 : Image is also 5 m away from plane mirror. Distance between object and image is
5m + 5 m = 10 m.
Step-3 : You have a camera, so distance of camera from image = distance of yourself from
image = 10 m.
2. The colour of an image is identical to the colour of the object forming the image. The fact
that the same colour is evidence that the frequency of light doesn't change upon reflection.
1. Take a large shining spoon and look at its inner curved surface. When your face is quite
close to the spoon, you will see your erect and magnified image. Now, slowly move the
spoon away from you. You will see your inverted and magnified image. As the spoon is
moved further away, the inverted image gradually decreases [see figure (a)].
2. Now, look at the outer curved surface of the spoon. You will see your erect and diminished
image. As the spoon is moved further away, the image remains erect and its size gradually
decreases [see figure (b)].
Conclusion : The inner curved surface of the spoon acts as a concave mirror. The outer
curved surface of the spoon acts as a convex mirror.
(c)
P
F
C
(b)
P
C
F
P
F
C
[11]
(a)
Rules for concave mirrors to obtain images
Convex mirrors
(1) The ray parallel to the principal axis, after reflection, appears to diverge from the
principal focus of a convex mirror [see figure (a)].
(2) A ray which is directed towards the principal focus in a convex mirror, is reflected
parallel to the principal axis [see figure (b)].
(3) A ray directed towards the centre of curvature in a convex mirror, is reflected back
along its own path [see figure (c)].
P
C
F
(a)
(b)
P
C
F
(c)
P
F
C
Rules for convex mirrors to obtain images
🟋 A ray passing through the centre of curvature behave like a normal of a spherical mirror.
What happens when a ray is incident obliquely to the principal axis, towards the pole
of the mirror, on a concave mirror or a convex mirror?
Explanation
[12]
When a ray is incident obliquely to the principal axis, towards the pole of the mirror, on a
concave mirror or a convex mirror, it is reflected obliquely such that the incident ray and
the reflected ray make equal angles with the principal axis. This is because the principal
axis acts as normal at the pole. The incident and reflected rays follow the laws of reflection
at the point of incidence (Pole), making equal angles with the principal axis (see figure).
1. Take a concave mirror and allow the sun rays to fall on it. Take paper and move it towards
the concave mirror till you obtain a bright sharp spot of light on it. The spot obtained is the
image of the sun. Now, measure the distance between paper and the concave mirror. This
distance is an approximate focal length of the concave mirror.
[13]
2. If this spot is kept on the paper for few minutes, the paper will start burning. This is
because the light energy converts to heat energy.
Important : Avoid looking at the Sun directly or its image formed by the concave mirror as
the intensity of sunlight may damage the eye.
Sun
rays
Bright
spot
Piece
of paper
f
Active physics 2
8. Image formation by a concave mirror
A'
C
B'
A
B
F
P
(a) Object placed between pole and focus
C
A
F
P
(b) Object placed at focus
B
A'
[14]
C
B'
A
B
F
P
(c) Object placed between
focus and centre of curvature
C
A
P
(d) Object placed at C
F
B'
B
A'
A'
C
B'
B
F
P
(e) Object Placed beyond C
A
C
P
(f) Object at infinity
F
Images formed by a concave mirror
Image formation by concave mirror
Position of the object Position of the Image Size of the image Nature of the image
Between P and F Behind the mirror Enlarged Virtual and erect
At F At infinity Highly enlarged Real and inverted
Between C and F Beyond C Enlarged Real and inverted
At C At C Same size Real and inverted
Beyond C Between F and C Diminished Real and inverted
[15]
At infinity At the focus F Highly diminished, Real and inverted
point-sized
🟋 Variation of size of image for different position of object in front of a concave mirror.
Centre of
curvature
Focus
A
A'
B
B'
C
C'
D
D'= at
infinity
E
F
G
G'
F'
E'
Concave mirror
🟋 If the formed image is erect, of the same size and equidistant as of the object, then the
🟋 If the image is erect, virtual but smaller in size than the object, then it is a convex
mirror.
[16]
🟋 If the formed image is erect, virtual and magnified when the mirror is close to the
(2) Concave mirrors are used as reflectors in car head lights, search lights, hand torches,
table lamps, etc. to get powerful parallel beams of light.
A bulb placed at the focus of a concave mirror produces a strong, almost parallel beam
(3) Concave mirrors are used in solar power plants to produce electricity.
Solar
furnace
A solar furnace placed at the focus of a concave mirror
(4) Concave mirrors are used by doctors to concentrate light on body parts like ears and
eyes.
[17]
Concave mirror used by doctor
(5) Concave mirrors are also used by dentists to see large images of the teeth of patients.
9. Image formation by a convex mirror
The image formed by a convex mirror is always behind the mirror that is, it is always
virtual and erect. Also, the size of image is always diminished, that is, its size is always
smaller than that of the object [see figure (a)].
The rays parallel to principal axis, after reflection, appears to diverge from the principal
focus of the convex mirror [see figure (b)]. The image formed at the focus, behind the
mirror is highly diminished. The image is virtual and erect.
C
F
P
(b) Object at infinity
P
C
F
(a) Object placed at some finite distance
B'
A'
B
A
Images formed by a convex mirror
[18]
Image formation by convex mirror
🟋 Variation of size of image for different position of object in front of a convex mirror.
Convex mirror
A
B
C
D
E
F
G
Focus (F)
G'
F'
E'
D'
C'
B'
A'
Suppose that lower half of concave mirror’s reflecting surface is covered with an
opaque (non-reflecting) material. What effect will this have on the image of an object
placed in front of the mirror ?
Explanation
[19]
If lower half of concave mirror is obstructed, full image will be formed but with reduced
brightness. This is because every part of mirror forms complete image. On obstructing the
lower half, half of the light rays are obstructed, forming less bright image. In this case, the
intensity (brightness) of image will be half of the initial value.
1. Take a plane mirror to observe the image of a distant tree. You may not see a full-length
image of the tree. Try with plane mirrors of different sizes. You will observe that there is a
certain minimum size of the plane mirror to see the full-length image of the tree. The size
of the mirror depends on the distance between the mirror and the distant object. More the
distance of the object from the mirror, smaller will be the size of the mirror required to see
its full-length image.
2. Take a concave mirror to observe the image of a distant tree. You will not see the image of
the tree in the mirror. This is because, to see an image in a concave mirror, the object
should be quite close to the concave mirror (between pole and focus).
3. Now, take a convex mirror to observe the image of a distant tree. You will always see the
full-length image of the distant tree. This is because, in a convex mirror, a virtual, erect and
diminished image of the object is always formed for every location of the object.
Uses of convex mirrors
Rear view mirrors : Convex mirrors are commonly used as rear-view (wing) mirrors in
vehicles. These mirrors are fitted on the sides of the vehicle, enabling the driver to see
traffic behind him/her to facilitate safe driving.
i1
r1
r2
i2
F
C
Wide field of view
[20]
Narrow field of view
r2
i2
i1
r1
(a) Plane mirror
A convex mirror has wider field of view as compared to a plane mirror.
(b) Convex mirror
☞ Convex mirrors are preferred as rear view mirrors because they always give an erect,
though diminished image. Also, they have a wider field of view as they are curved
outwards. Thus, convex mirrors enable the driver to view much larger area than would be
possible with a plane mirror [see figure (a) and figure (b)].
Street lamps : Street lamps also use convex mirrors to diverge light over an extended area.
You can see a full-length image of a tall building/tree in a small convex mirror.
1. A real, extended object when placed in front of a mirror, a virtual and erect image is formed.
Predict the type of mirror if (a) the image is diminished, (b) the image is exactly same size
that of the object, (c) the image is magnified.
2. Is it possible to obtain an image between principal focus and the centre of curvature of a
convex mirror ?
3. At what location, the image meets the object in case of a concave mirror ? What is the size
and the nature of the image at this location ?
10. Sign convention for reflection by spherical mirrors
While dealing with the reflection of light by spherical mirrors, we follow a set of sign
conventions called the new cartesian sign convention. In this convention, the pole (P) of the
mirror is taken as the origin. The principal axis of the mirror is taken as the x-axis (X’X) of
the coordinate system.
The conventions are as follows [see figure (a) and (b)] :
(1) The object is always placed to the left of the mirror. This implies that the light from the
object falls on the mirror from the left-hand side.
(2) All distances parallel to the principal axis are measured from the pole of the mirror.
All the distances along XX’ axis are measured from P.
(3) All the distances measured to the right of the origin (along + x-axis) are taken as
positive while those measured to the left of the origin (along – x-axis) are taken as
negative.
(4) Distances measured perpendicular to and above the principal axis (along + y-axis) are
taken as positive. Distances measured perpendicular to and below the principal axis
(along – y-axis) are taken as negative.
[21]
☞ Distances along the direction of incident light are considered ‘positive’. Distances
measured opposite to the direction of incident light are considered ‘negative’.
+y
–y
–x
[22]
+x
☞ If image is virtual and erect i.e., above principal axis, its height is taken ‘positive’. If image is
real and inverted i.e., below principal axis, its height is taken ‘negative’.
Magnification (m)
The ratio of height of image (h2) to the height of object (h1) is called ‘magnification’ or
‘linear magnification’.
Magnification
Magnitude, |m|
Sign (+ or –)
Positive
Negative
Virtual,
Erect
Real,
Inverted
Represents nature of image
has
Represents size of image
Diminished,
image
Same size
image
Magnified
image
|m|<1
|m|>1
[24]
|m|=1
A spherical mirror produces a magnification of +1.5. Explain the nature and size of
the image formed by it. Which type of spherical mirror is this?
Explanation
Since, the sign of magnification is positive, this means the image is virtual and erect. Now,
|m| = 1.5, which is greater than one, this means the image is magnified. The spherical
mirror in this case is a concave mirror (a converging mirror) as it produces a virtual, erect
and magnified image.
B
P
B'
F
C
A'
A
B
P
C
F
[25]
B'
A
Object moves away
from the mirror
Image moves away
from the mirror
Object moves
towards the mirror
Image moves away
from the mirror
Effect on the position of the image formed
when an object is moving away from a convex
mirror
Effect on the position of the image formed
when an object is moving towards a concave
mirror
A'
Height of image
Object Image distance (v) Focal Height of
(h2)
Mirror distance length object
Real & Virtual Real & Virtual
(u) (f) (h1)
inverted & erect inverted & erect
[26]
Images Image
Convex Negative does not Positive Positive Positive does not Positive
form form
Concave Negative Negative Positive Negative Positive Negative Positive
2
24, 15
Step-2 : Write the quotient and the number which is not divisible by the above prime
number in the second row.
In the second row, write the quotient we get after the division of 24 by 2. Since 15 is not
divisible by 2, write 15 in the second row as it is.
Step-3 : Divide the numbers with another least prime number.
[27]
2
24, 15
12, 15
2
Step-4 : Continue division until the remainder is a prime number or 1.
2
24, 15
12, 15
2
6, 15
3, 15
1, 5
1, 1
2
3
5
Step-5 : Multiply all the divisors and remaining prime number (if any) to obtain the LCM.
LCM of 24 and 15 = 2 × 2 × 2 × 3 × 5 = 120.
or
[28]
or or
or = + 1.15m
= + 0.23
+
virtual
& erect
m=±n
–
Real &
inverted
m = n (size of image is ‘n’ times that of object)
2. An object, 4.0 cm in size, is placed at 25.0 cm in front of a concave mirror of focal
length 15.0 cm. At what distance from the mirror should a screen be placed in order
to obtain a sharp image ? Find the nature and the size of the image.
Solution
Given, object size, h1 = + 4 cm ; object distance, u = – 25 cm ; focal length, f = –15 cm ; image
distance, v = ? ; image size, h2 = ?
Mirror formula,
[29]
or
or
or
or
v = – 37.5 cm
Now, magnification,
or
= – 6 cm
The image is real, inverted and enlarged.
3. An object is placed at 10 cm in front of a converging mirror of radius of curvature 15
cm. Find the magnification of the image.
Solution
Given, object distance, u = –10 cm ;
radius of curvature, R = – 15 cm ;
image distance, v = ? ; magnification, m = ?
Focal length, f = –15/2 cm
Mirror formula,
[30]
or
or
or
or v = – 30 cm
∴m=
∴ m' =
But m'= 3m
or
or f + 15 = 3f + 27
or f = – 6 cm.
[31]
[32]
Some Basic Terms
1. Electromagnetic waves : A changing magnetic field will induce a changing electric field
and vice-versa. These changing fields form electromagnetic waves. Electromagnetic wave
do not required a medium to propagate.
2. Source of light : Any object which emits light is called source of light. To able to see
anything, we need a source of light.
3. Natural source of light : A natural source of light is light that occurs without human
involvement. Natural sources of light can come from objects of living species.
Examples : Sun, star, fireflies etc.
4. Artificial source of light : Artificial sources of light are man made objects that emit light.
Examples : Bulbs, tube lights, candles, lasers etc.
5. Medium : A medium is defined as the substance that transfers the energy or light from one
substance to another substance or from one place to another. The medium act as a carrier
here. The medium can transfer any form of energy, sound wave, light and heat.
6. Homogeneous medium : An optical medium which has a uniform composition throughout
is called a homogeneous medium.
Examples : Glass, diamond, distilled water etc.
7. Transparent: A medium that allows light to pass through it easily is called a transparent
medium.
Examples : Glass, air etc.
8. Waves : A wave is a disturbance that transfers energy from one place to another in a
regular and organized way.
9. Wavelength : Wavelength is the distance from one crest to another, or from one trough to
another of a wave (Which may be an electromagnetic wave, a sound wave or any other
wave). Crest is the highest point of the wave where as the trough is the lowest. SI unit is
metre (m).
10. Amplitude : It is the maximum displacement from its mean position to extreme position of
a particle of the medium in which a waves propagates. SI unit is metre (m).
11. Intensity : It is the amount of light falling on a surface. It is measured in terms of lumens
per square metre (lux).
[33]
12. Frequency : It is the number of complete cycles of waves passing a point in unit time. The
SI unit of frequency is Hertz (Hz).
13. Asymmetric object : Asymmetric objects have two sides that are not mirror images of
each other. If you draw a line down the middle of an asymmetric object an fold it in half, the
two side will not match.
14. Symmetric object : If any object can be divided into two halves such that one half forms
the mirror image of the other half.
15. Obliquely : Obliquely refers that when a light falling on the surface in slanting position
neither perpendicular nor horizontal.
16. Angle : An angle is geometric shape formed by the intersection of two line segments, lines
or rays.
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