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By
Farrukh Asif
Ø Light
travels in straight lines.
Ø Speed
of Light
Ø Waves
of Light
Ø Colours
of Light
Ø How
Light Travels
Ø To
Summarise
LIGHT AND ITS
PROPERTIES:
Light
from the Sun is a natural example of white light.
Mixing colours of light is an example of additive colour mixing. Red appears red to us because right wavelengths of light are sent towards our eyes. The same is true for all of the other colours. White is created by sending out all of the wavelength of light. So what about black? In additive colour mixing, black is the absence of light. In other words, no wavelength of light is sent out. We perceive this lack of light as black!
Sometimes white light from
the Sun is split apart so that we can see the colours that make it up. A good
example of this are rainbows. Small water droplets split the waves of light so
that we can see each.
How Light
Travels
The final important property
of light to remember is that light always travels in a straight line. We get
shadows when light is blocked by an object. Light can pass through some but not
all objects. We call objects and materials that light can pass through transparent.
We can objects and materials that light cannot pass through opaque.
We call objects that let some, but not all light pass through translucent.
To
Summarise
- Light
travels very fast - at the speed of 299 792 458
m / s in fact!
- Light
travels as waves.
- Light
travels in straight lines.
Can you
remember the order of the colours of a rainbow?
We
can also split light using a prism.
Waves
of Light
Light has the properties of
waves. Like ocean waves, light waves have crests and
troughs.
The distance between one
crest and the next, which is the same as the distance between one trough and
the next, is called the wavelength.
The frequency of
a wave is the number of crests (or troughs) that pass a point in one second.
The wavelength multiplied by the frequency equals the speed at which the wave travels.
These different colours of light have different
wavelengths and frequencies. Red light has the longest wavelength, and the
lowest frequency of the visible spectrum. Violet has the shortest wavelength,
and the highest frequency of the visible spectrum.
Speed
of Light:
The speed of light is : 299 792 458 m / s
Colours
of Light:
You
will remember from art class that the primary colours are red, yellow and blue.
You
can mix these to form the secondary colours orange, green and purple.
Black absorbs all of the colours of light and does not reflect any colours. We perceive this lack of light as black!
The
Primary colors of th Light are red, green and blue.
The
Secondary colours of light are cyan, magenta and yellow.
·
Cyan is made by combining blue and green.
·
Magenta is made by combining blue and red.
·
Yellow is made by combining green and red.
Computer
screens and TV screens use these colours of light to make all of the colours
that you see.
Mixing colours of light is an example of additive colour mixing. Red appears
red to us because right wavelengths of light are sent towards our eyes. The
same is true for all of the other colours. White is
created by sending out all of the wavelength of light.
What do these
experiences suggest?
LIGHT TRAVELS ALONG A
STRAIGHT LINE:
When the boy see at a lighted candle
first through a straight pipe and then through a bent pipe (Fig. 15.2).
Why was Boy not able to
see the candle flame through a bent pipe?
This activity showed that light
travels along straight lines.
How can we change the path of light?
Do you know, what happens when light falls on a polished or shiny surface?
REFLECTION OF LIGHT:
One way to change the direction of
light is to let it fall on a shiny surface. For example, a shining stainless
steel plate or a shining steel spoon can change the direction of light. The
surface of the water can also act like a mirror and change the path of light.
Have you ever seen the reflection of trees or buildings in water?
Any polished or shiny surface can
act as a mirror. What happens when light falls on a mirror? You have learnt in
Class VI that a mirror changes the direction of light that falls on it. This
change of direction by a mirror is called reflection
of light. Place a lighted candle in front of a plane
mirror. Try to see the flame of the candle in the mirror. It appears as
if a similar candle is placed behind the mirror. The candle, which appears
behind the mirror, is the image of the candle formed by the mirror (Fig. 15.6).
The candle itself is the object. Now move the candle to different positions in
front of the mirror. Observe the image in each case.
Was the image upright in each case? Did
the flame appear on top of the candle as in the object? Such an image is called
erect. An image formed by a plane
mirror is erect and of the same size as the object. Now place a
vertical screen behind the mirror. Try to obtain the image of the candle on
this screen.
Can you get the image
on the screen?
Now place the screen in front of the
mirror.
Can you get the image
on the screen now?
You will find that the image of the
candle cannot be obtained on the screen in either case. What about the distance
of the image from the mirror?
Let us perform another activity.
Take a chessboard. If a chessboard
is not available, draw on a chart paper 64 (8×8)
squares of equal size. Draw a thick line in the middle of the paper. Fix
a plane mirror vertically on this line. Place any small object, such as a
pencil sharpener, at the boundary of the third square counting from the mirror
(Fig. 15.7). Note the position of the image. Now shift the object to the
boundary of the fourth square. Again note the position of the image. Did you
find any relation between the distance of the image from the mirror and that of
the object in front of it?
You will find that the image is at
the same distance behind the mirror as the object is in front of it. Now verify
this by placing the object anywhere on the chart paper.
SPHERICAL MIRRORS:
The curved shining surface of a spoon
acts as a mirror. The most common example of a curved mirror is a spherical
mirror. If the reflecting surface of a spherical mirror is concave, it is
called a concave mirror. If the reflecting surface is convex, then it is a
convex mirror/
Take a concave mirror. Hold it facing the Sun. Try to get the light reflected by the mirror on a sheet of paper. Adjust the distance of the paper until you get a sharp bright spot on it
(Fig. 15.14). Hold the mirror and the
sheet of paper steady for a few minutes.
Does the paper start burning?
This bright spot is, in fact, the
image of the Sun. Notice that this image is formed on a screen. An image formed
on a screen is called a real image.
Recollect that in Activity 15.2 the image formed by a plane mirror could not be
obtained on a screen. Such an image is called a virtual
image. Now let us try to obtain on the screen the image of a candle
flame formed by a concave mirror.
IMAGES FORMED BY LENSES:
You might have seen a magnifying
glass. It is used to read very small print (Fig. 15.21). You might have also
used it to observe the body parts of a cockroach or an earthworm. The
magnifying glass is actually a type of a lens. Lenses are widely used in
spectacles, telescopes and microscopes. Try to add a few more uses of lenses to
this list. Get some lenses. Touch and feel them. Can you find some difference
just by touching? Those lenses which feel thicker in the middle than at the
edges are convex. Those which feel thinner in the middle than at the edges are
concave lenses. Notice that the lenses are transparent and light can pass
through them.
A convex lens converges (bends
inward) the light generally falling on it [Fig. 15.24 (a)]. Therefore, it is
called a converging lens. On the other hand, a concave lens diverges (bends
outward) the light and is called a diverging lens [Fig. 15.24 (b)].
Important Terms
for Image Formation
- Ray Diagrams of Concave Mirror
- Image Formation on Concave Mirror
- Image Formation Tabular Data
- Sign Conventions for Concave Mirror
- Relation between Focal Length and Radius of Curvature
- What is Mirror Equation?
- Linear Magnification (m) Explanation
- Solved Questions of Concave Mirror
- Uses of Concave Mirrors
Important Terms for Image Formation:
1.
Pole: It is the centre of the reflecting
surface of a spherical mirror. It lies on the surface of the mirror, and it is
usually denoted by P.
2.
Centre of curvature: The centre of the sphere formed by the
reflecting part of a spherical mirror is called the centre of curvature. It is
generally denoted by C. This is not a part of the mirror, and it lies outside
the reflecting surface of the mirror. In a concave mirror, it lies in front of
the mirror.
3.
The radius of curvature: It is the radius of the sphere formed
by the reflecting part of the sphere. It is represented by R.
4.
Principal axis: It is the straight line passing through
the pole and centre of curvature of the spherical mirror. This is normal to the
mirror at its pole.
5.
Principal focus: The incident rays coming parallel to
the principal axis after reflection appear to converge to a common point on the
principal axis, and this point is called the principal focus of a concave mirror.
It is usually denoted by F.
6.
Focal length: It is the distance between the pole and
the principal focus of the concave mirror. It is denoted by f.
Ray Diagrams of Concave Mirror:
Ray diagrams are necessary for
understanding the formation of an image by a concave mirror. For constructing
ray diagrams and for a better understanding of image formation, we should
consider at least two incident rays coming from the object. The intersection of
these two rays after reflection gives the position of the image of the object.
For a concave mirror, any of the following four ray diagrams can be used for
locating the image formed:
a) A ray parallel to the principal
axis, after reflection, will pass through the principal focus of a concave
mirror.
b) A ray which is passing through the
principal focus of a concave mirror, after reflection, will emerge parallel to
the principal axis.
c) A ray passing through the
centre of curvature of a concave mirror, after reflection, is reflected along
the same path. The light rays come back along the same path because the
incident rays fall on the mirror along the normal to the reflecting surface.
d) A ray incident obliquely to
the principal axis, towards the point P (pole of the mirror), on the concave
mirror, is reflected obliquely. The incident and reflected rays follow the laws
of reflection at point P, making equal angles with the principal axis.
Image Formation on Concave Mirror:
Rays emerging from a point meet at
another point after reflection, and this point is called the image of the first
point. The image is real if the rays converge to the point, and it is virtual
if the rays do not meet it, but appear to diverge from a point when the rays
are produced backwards. During image formation, we assume that the rays are
paraxial, i.e., they are incident at points close to the pole P of the mirror
and make small angles with the principal axis. For a concave mirror, we
consider six positions of the object before the mirror.
Also Read: Difference between
Convex and Concave Mirror
1. When the object is placed at infinity
2. When the object is placed beyond C (centre of curvature)
3. When the object is placed at C
4. When the object is placed between C and F (principal focus)
5. When the object is placed at F
6. When the object is placed between F and P (pole)
When the Object Is at Infinity:
In this condition, we consider two rays
parallel to the principal axis originating from the object. These rays, after
reflection, converge and form an image at F, the principal focus of the mirror,
in front of the mirror. The image thus formed is highly diminished, point size,
real and inverted.
The Object Is Placed Beyond C:
In this situation, we consider two
different rays emerging from the object. One is parallel to the principal axis,
and the other is directed towards the centre of curvature of the mirror. These
rays, after reflection, form an image between the centre of curvature (C) and
the focus (F). The image thus formed is diminished, real and inverted.
The Object Is Placed at C:
Here, the two rays emerging from the
object are one parallel to the principal axis and the other passing through the
focus of the mirror. These rays, after reflection, form an image at point C.
The image formed has the same size as that of the object, and it is real and
inverted.
The Object Is Placed between C and F:
Here, the two rays considered are one parallel to the principal axis and the other passing through the principal focus of the concave mirror. The image is formed beyond C. The image is larger compared to the size of the object, and it is real and inverted.
The Object Is Placed at F:
The rays considered here are one
parallel to the principal axis and the other passing through the centre of
curvature of the mirror. This results in the formation of a highly enlarged
image which is real and inverted at infinity.
The Object Is Placed between F and P:
The rays considered here are one going
parallel to the principal axis and the other passing through the centre of
curvature of the mirror. The image formed here is virtual and erect, and it is
larger than the object.
Image
Formation Tabular Data
|
Position of the Object |
Position of the Image |
Size of the Image |
Nature of the Image |
|
At infinity |
At focus, F |
Highly diminished and pointed in size |
Inverted and real |
|
Beyond C |
Between F and C |
Diminished |
Inverted and real |
|
At C |
At C |
Same size |
Inverted and real |
|
Between C and F |
Beyond C |
Enlarged |
Inverted and real |
|
At F |
At infinity |
Highly enlarged |
Inverted and real |
|
Between F and P |
Behind the mirror |
Enlarged |
Erect and virtual |
Concave Mirror Sign Conventions:
For deriving the relevant formulas for
reflection by spherical mirrors, there is a standard sign convention for
measuring distances. The normally used convention is the Cartesian sign convention.
According to this convention, all the distances are measured from the pole of
the mirror, i.e., the pole (P) of the mirror is assumed as the origin. The
principal axis of the mirror is taken as the x-axis of the coordinate system.
The conventions are as given below:
- The object is always placed on
the left side of the mirror. This means that the light from the object
falls on the mirror from the left-hand side.
- All the distances which are
parallel to the principal axis are measured from the pole of the mirror.
- All the distances measured
towards the right of the origin (along + x-axis) are taken as positive and
while those measured to the left of the origin (along – x-axis) are taken
as negative, or the distances measured in the same direction as that of
the incident light are taken as positive and those measured in the
direction opposite to the direction of incident light are taken as
negative.
- Distances measured
perpendicular to and above the principal axis of the mirrors are taken as
positive.
Relation between
Radius of Curvature and Focal Length
Consider a ray parallel to the
principal axis striking the concave mirror at a point M on its reflecting
surface. Then CM will be perpendicular to the mirror at point M. Let θ be the
angle of incidence, and MD be the perpendicular from M to the principal axis.
Then from the figure,
∠MCP = θ and ∠MFP
= 2θ
Now,
Tanθ = MD / CD and tan2θ = MD / FD
For small values of θ, which is true
for paraxial rays, tan θ ≈ θ and tan 2θ ≈ 2θ
Therefore, MD / FD = 2 X MD / CD or FD
= CD / 2
Now, FD = f and CD = R, therefore the
above equations become
f = R / 2
This is from the assumption that for
small values of θ point, D is very close to point P.
Mirror Equation:
The figure shows two rays
emerging from the object. These rays, after reflection, form an image A’B’.
From the geometry of ray diagrams, the two right-angled triangles ABF and MPF
are similar. This is because, for paraxial rays, the line MP can be considered
to be a straight line perpendicular to CP. Therefore,
B’A’ / PM =
B’F / FP or B’A’ / BA = B’F /
FP (Since PM = AB) …… (1)
Since ∠APB = ∠A’PB’,
the right-angled triangles A’B’P and ABP are also similar,
B’A’ / BA =
B’P / BP ……………… (2)
Comparing the equations (1) and (2), we
get,
B’F / FP = B’P –
FP / FP = B’P / BP
This is the relationship involving the
magnitude of distances.
In a spherical mirror, the distance of
the object from its pole is called the object distance (u) and the distance of
the image from the pole is called the image distance (v). As mentioned earlier,
the distance of the principal focus from the pole is called the focal length
(f).
Substituting u, v, and f by following
the sign convention, we get,
-v + f / -f = -v / -u or v – f / f = v / u or 1 / u + 1 / v = 1
/ f
This equation is known as the mirror
equation. This is valid for both convex and
concave mirrors.
Linear Magnification (m)
Linear magnification (m) is the ratio
of the height of the image (h’) to the height of the object (h).
m = h’ / h
h’ and h are given a positive or
negative value as per the Cartesian sign convention.
In triangles A’B’P and ABP, we have
B’A’ / BA =
B’P / BP
By applying sign convention, we get
m = h’ / h = – v / u
A negative sign for the value of
magnification indicates that the image is real, and a positive sign indicates
that the image is virtual.
************************************************
Concave Mirror Solved Questions
1. An object is found to be 5 cm in front of a concave mirror
with a radius of curvature of 15 cm. Determine the position, nature, and
magnification of the image in each case.
Answer:
focal length, f = =15/2 cm = 7.5 cm
u = -5 cm
Applying the mirror formula, we get,
1 / V + I / -5 = 1 / -7.5
1 / V = I / -7.5 + 1 / 5 = 1 / 15
Therefore, v =15 cm
Thus, a virtual and erect image is
formed 15 cm behind the mirror.
Magnification, m = – v / u = 15 / -5 =
3
Thus, the image formed is virtual,
erect and magnified by a factor of 3.
2. An object, 4 cm in size, is placed at 25 cm in front of a
concave mirror of focal length 15 cm. At what distance from the mirror should a
screen be placed to obtain a sharp image? Determine the nature and the size of
the image.
Answer:
Object size, h = + 4 cm
Object distance, u = – 25 cm
Focal length, f = –15 cm
By using the mirror equation,
1 / V = I / -15 – 1 / -25 = – 1 / 15 +
1 / 25
1 / V = -5 + 3 / 75 = 2 / 75
i.e. v = – 38.5 cm
To get the image on the screen, the
screen should be placed at a distance of 38.5 cm from the mirror.
Magnification, m = h’ / h = – v / u
Therefore,
h’ = – vh / u = (-38.5 x 4) / -25 =
6.16
Height of the image, h’ = 6 cm, so the
image formed is real, inverted and enlarged.
Uses of Concave Mirrors:
Concave mirrors are used in many
instances. Some of the common ones are given below.
- Torches, searchlights and vehicle headlights use
concave mirrors to get powerful parallel beams of light.
- Shaving mirrors used are usually concave mirrors to get
a magnified image of the face.
- To see large images of the teeth of patients, dentists
use concave mirrors.
- Concave mirrors are also used in reflecting telescopes.
- Concave mirrors are used to form optical cavities,
which are important in the construction of lasers.
- For concentrating sunlight to produce heat in solar
furnaces, large concave mirrors are used.
- Concave mirrors are used as the mirror landing aid
system of modern aircraft carriers.
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Solutions of Science Chapter 15 Light
1.
Fill in
the blanks.
(a) An image that
cannot be obtained on a screen is called a ____________.
(b) Image
formed by a convex __________ is always virtual and smaller in size.
(c) An image
formed by a __________ mirror is always of the same size as that of the object.
(d) An image
which can be obtained on a screen is called a _________ image.
(e) An image
formed by a concave ___________ cannot be obtained on a screen.
Answer:
(a) An image that cannot be obtained on a
screen is called a virtual image.
(b) Image
formed by a convex mirror is always virtual and smaller in size.
(c) An image
formed by a plane mirror is always of the same size as that of the
object.
(d) An image which can be obtained on
a screen is called a real image.
(e) An image
formed by a concave lens cannot be obtained on a screen.
2.
Mark ‘T’
if the statement is true and ‘F’ if it is false.
(a) We can
obtain an enlarged and erect image by a convex mirror. (T/F)
(b) A concave
lens always form a virtual image. (T/F)
(c) We can
obtain a real, enlarged and inverted image by a concave mirror. (T/F)
(d) A real
image cannot be obtained on a screen. (T/F)
(e) A concave
mirror always forms a real image. (T/F)
Answer:
a) False
b) True
c) True
d) False
e) False
3.
Match the
items given in Column I with one or more items in Column II.
|
Column-I |
Column-II |
|
(a)
A plane mirror |
(i)
Used as a magnifying glass. |
|
(b)
A convex mirror |
(ii)
Can form images of objects spread over a large area. |
|
(c)
A convex lens |
(iii)
Used by dentists to see an enlarged image of teeth. |
|
(d)
A concave mirror |
(iv)
The image is always inverted and magnified. |
|
(e)
A concave lens |
(v)
The image is erect and of the same size as the object. |
|
(vi)
The image is erect and smaller in size than the object. |
Answer:
|
Column-I |
Column-II |
|
(a)
A plane mirror |
(v)
The image is erect and of the same size as the object. |
|
(b)
A convex mirror |
(ii)
Can form an image of objects spread over a large area. |
|
(c)
A convex lens |
(i)
Used as a magnifying glass. |
|
(d)
A concave mirror |
(iii)
Used by dentists to see an enlarged image of teeth. |
|
(e)
A concave lens |
(vi)
The image is erect and smaller in size than the object. |
4.
State the
characteristics of the image formed by a plane mirror.
Answer:
Characteristics
of the image formed by a Plane Mirror are as follows:
·
Image distance and object distance are
equal.
·
The size of the object and image are
equal.
·
The image formed is erect and virtual.
·
Images are laterally inverted.
5.
Find out
the letters of the English alphabet or any other language known to you in which
the image formed in a plane mirror appears exactly like the letter itself.
Discuss your findings.
Answer:
A,
H, I, M, O, T, U, V, W, X, and Y alphabets form images in a plane mirror
exactly like the letter itself because these alphabets are laterally symmetric.
6.
What is a
virtual image? Give one situation where a virtual image is formed.
Answer:
The
image that cannot be obtained on a screen is called a virtual image. The image
formed by a plane mirror is virtual.
7. State two differences between a convex and a concave lens.
Answer:
|
Convex Lens |
Concave Lens |
|
Thick
in the middle and thin at the edge. |
Thin
in the middle and thick at the edge. |
|
The
image formed is real or virtual. |
The
image formed is virtual. |
8.
Give one
use each of a concave and a convex mirror.
Answer:
·
Concave mirrors are used in the
headlights of cars and scooters.
·
Convex mirrors are used as side-view
mirrors in vehicles.
9.
Which type
of mirror can form a real image?
Solution:
·
The concave mirror can form a
real image.
10.
Which type
of lens always forms a virtual image?
Answer:
·
A concave lens forms a
virtual image.
Choose
the correct option in questions 11–13.
11.
A virtual
image larger than the object can be produced by a
(i) concave lens (ii)
concave mirror
(iii) convex mirror
(iv) plane mirror
Answer:
ü The
correct answer is option (ii) concave mirror.
12.
David is
observing his image in a plane mirror. The distance between the mirror and his
image is 4 m. If he moves 1 m towards the mirror, then the distance between
David and his image will be
(i) 3 m (ii) 5 m
(iii) 6 m (iv) 8 m
Answer:
ü The
answer is option (iii) 6 m
13.
The
rearview mirror of a car is a plane mirror. A driver is reversing his car at a
speed of 2 m/s. The driver sees in his rearview mirror the image of a truck
parked behind his car. The speed at which the image of the truck appears to
approach the driver will be
(i) 1 m/s (ii) 2 m/s
(iii) 4 m/s (iv) 8 m/s
Answer:
ü The
correct answer is option (iii) 4 m/s.
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