Light – Reflection and Refraction.........(Atul)
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<h1>Science------- Balaji ____________ baba </h1>
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Atul
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<h1>Light – Reflection and
Refraction</h1></div>
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<p>We see a variety of objects in the world around us. However, we are
unable to see anything in a dark room. On lighting up the room,
things become visible. What makes things visible? During the day, the
sunlight helps us to see objects. An object reflects light that falls on it.
This reflected light, when received by our eyes, enables us to see things.
We are able to see through a transparent medium as light is transmitted
through it. There are a number of common wonderful phenomena
associated with light such as image formation by mirrors, the twinkling
of stars, the beautiful colours of a rainbow, bending of light by a medium
and so on. A study of the properties of light helps us to explore them.
By observing the common optical phenomena around us, we may
conclude that light seems to travel in straight lines. The fact that a small
source of light casts a sharp shadow of an opaque object points to this
straight-line path of light, usually indicated as a ray of light.</p>
<p>In this Chapter, we shall study the phenomena of reflection and
refraction of light using the straight-line propagation of light. These basic
concepts will help us in the study of some of the optical phenomena in
nature. We shall try to understand in this Chapter the reflection of light
by spherical mirrors and refraction of light and their application in real
life situations.</p></div>
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<h3>10.1 REFLECTION OF LIGHT</h3></div>
<p>A highly polished surface, such as a mirror, reflects most of the light
falling on it. You are already familiar with the laws of reflection of light.Let us recall these laws –
(i) The angle of incidence is equal to the angle of reflection, and
(ii) The incident ray, the normal to the mirror at the point of incidence
and the reflected ray, all lie in the same plane.
These laws of reflection are applicable to all types of reflecting surfaces
including spherical surfaces. You are familiar with the formation of image
by a plane mirror. What are the properties of the image? Image formed
by a plane mirror is always virtual and erect. The size of the image is
equal to that of the object. The image formed is as far behind the mirror
as the object is in front of it. Further, the image is laterally inverted.
How would the images be when the reflecting surfaces are curved? Let
us explore.The curved surface of a shining spoon could be considered as a curved
mirror. The most commonly used type of curved mirror is the spherical
mirror. The reflecting surface of such mirrors can be considered to form
a part of the surface of a sphere. Such mirrors, whose reflecting surfaces
are spherical, are called spherical mirrors. We shall now study about
spherical mirrors in some detail.</p>
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<h3>10.2 SPHERICAL MIRRORS</h3></div>
<p>The reflecting surface of a spherical mirror may be curved inwards or
outwards. A spherical mirror, whose reflecting surface is curved inwards,
that is, faces towards the centre of the sphere, is called a concave mirror.
A spherical mirror whose reflecting surface is curved outwards, is called
a convex mirror. The schematic representation of these mirrors is shown
in Fig. 10.1. You may note in these diagrams that the back
of the mirror is shaded.
You may now understand that the surface of the spoon
curved inwards can be approximated to a concave mirror
and the surface of the spoon bulged outwards can be
approximated to a convex mirror.
Before we move further on spherical mirrors, we need to
recognise and understand the meaning of a few terms. These
terms are commonly used in discussions about spherical
mirrors. The centre of the reflecting surface of a spherical
mirror is a point called the pole. It lies on the surface of the
mirror. The pole is usually represented by the letter P.The reflecting surface of a spherical mirror forms a part of a sphere.
This sphere has a centre. This point is called the centre of curvature of
the spherical mirror. It is represented by the letter C. Please note that the
centre of curvature is not a part of the mirror. It lies outside its reflecting
surface. The centre of curvature of a concave mirror lies in front of it.
However, it lies behind the mirror in case of a convex mirror. You may
note this in Fig.10.2 (a) and (b). The radius of the sphere of which the
reflecting surface of a spherical mirror forms a part, is called the radius
of curvature of the mirror. It is represented by the letter R. You may note
that the distance PC is equal to the radius of curvature. Imagine a straight
line passing through the pole and the centre of curvature of a spherical
mirror. This line is called the principal axis. Remember that principal
axis is normal to the mirror at its pole. Let us understand an important
term related to mirrors, through an Activity.</p>
<p>The paper at first begins to burn producing smoke. Eventually it
may even catch fire. Why does it burn? The light from the Sun is converged
at a point, as a sharp, bright spot by the mirror. In fact, this spot of light
is the image of the Sun on the sheet of paper. This point is
the focus of the concave mirror. The heat produced due to
the concentration of sunlight ignites the paper. The distance
of this image from the position of the mirror gives the
approximate value of focal length of the mirror.
Let us try to understand this observation with the help
of a ray diagram.
Observe Fig.10.2 (a) closely. A number of rays parallel
to the principal axis are falling on a concave mirror. Observe
the reflected rays. They are all meeting/intersecting at a
point on the principal axis of the mirror. This point is called
the principal focus of the concave mirror. Similarly, observe
Fig. 10.2 (b). How are the rays parallel to the principal axis,
reflected by a convex mirror? The reflected rays appear to
come from a point on the principal axis. This point is called
the principal focus of the convex mirror. The principal focus
is represented by the letter F. The distance between the
pole and the principal focus of a spherical mirror is called
the focal length. It is represented by the letter f.
The reflecting surface of a spherical mirror is by-and-large spherical.
The surface, then, has a circular outline. The diameter of the reflecting
surface of spherical mirror is called its aperture. In Fig.10.2, distance
MN represents the aperture. We shall consider in our discussion only
such spherical mirrors whose aperture is much smaller than its radius
of curvature.
Is there a relationship between the radius of curvature R, and focal
length f, of a spherical mirror? For spherical mirrors of small apertures,
the radius of curvature is found to be equal to twice the focal length. We
put this as R = 2f . This implies that the principal focus of a spherical
mirror lies midway between the pole and centre of curvature</p>
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<h2>10.2.1 Image Formation by Spherical Mirrors</h2></div>
<p>You have studied about the image formation by plane mirrors. You also
know the nature, position and relative size of the images formed by them.
How about the images formed by spherical mirrors? How can we locate
the image formed by a concave mirror for different positions of the object?
Are the images real or virtual? Are they enlarged, diminished or have
the same size? We shall explore this with an Activity.You will see in the above Activity that the nature, position and size of
the image formed by a concave mirror depends on the position of the
object in relation to points P, F and C. The image formed is real for some
positions of the object. It is found to be a virtual image for a certain other
position. The image is either magnified, reduced or has the same size,
depending on the position of the object. A summary of these observations
is given for your reference in Table 10.1.</p>
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<h2>10.2.2 Representation of Images Formed by Spherical
Mirrors Using Ray Diagrams</h2></div>
<p>We can also study the formation of images by spherical mirrors by
drawing ray diagrams. Consider an extended object, of finite size, placed
in front of a spherical mirror. Each small portion of the extended object
acts like a point source. An infinite number of rays originate from each
of these points. To construct the ray diagrams, in order to locate the
image of an object, an arbitrarily large number of rays emanating from a
point could be considered. However, it is more convenient to consider
only two rays, for the sake of clarity of the ray diagram. These rays are
so chosen that it is easy to know their directions after reflection from the
mirror.
The intersection of at least two reflected rays give the position of image
of the point object. Any two of the following rays can be considered for
locating the image. (i) A ray parallel to the
principal axis, after
reflection, will pass through
the principal focus in case of
a concave mirror or appear
to diverge from the principal
focus in case of a convex
mirror. This is illustrated in
Fig.10.3 (a) and (b). (a) (b)
FigureFigure Figure 10.310.3 10.3
Light – Reflection and Refraction 165
(ii) A ray passing through the
principal focus of a concave
mirror or a ray which is
directed towards the
principal focus of a convex
mirror, after reflection, will
emerge parallel to the
principal axis. This is
illustrated in Fig.10.4 (a)
and (b).
(iii) A ray passing through the
centre of curvature of a
concave mirror or directed
in the direction of the centre
of curvature of a convex
mirror, after reflection, is
reflected back along the
same path. This is
illustrated in Fig.10.5 (a)
and (b). The light rays come
back along the same path
because the incident rays
fall on the mirror along the
normal to the reflecting
surface.
(iv) A ray incident obliquely to
the principal axis, towards
a point P (pole of the mirror),
on the concave mirror
[Fig. 10.6 (a)] or a convex
mirror [Fig. 10.6 (b)], is
reflected obliquely. The
incident and reflected rays
follow the laws of reflection
at the point of incidence
(point P), making equal
angles with the principal axis.
(a) (b)
Figure 10.4
Remember that in all the above cases the laws of reflection are followed.
At the point of incidence, the incident ray is reflected in such a way that
the angle of reflection equals the angle of incidence.
(a) Image formation by Concave Mirror
Figure 10.7 illustrates the ray diagrams for the formation of image
by a concave mirror for various positions of the object</p>
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<h2>Uses of concave mirrors</h2></div>
<p>Concave mirrors are commonly used in torches, search-lights and
vehicles headlights to get powerful parallel beams of light. They are
often used as shaving mirrors to see a larger image of the face. The
dentists use concave mirrors to see large images of the teeth of patients.
Large concave mirrors are used to concentrate sunlight to produce
heat in solar furnaces.</p>
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<h3>(b) Image formation by a Convex Mirror</h3></div>
<p>We studied the image formation by a concave mirror. Now we shall
study the formation of image by a convex mirror. We consider two positions of the object for studying the image formed
by a convex mirror. First is when the object is at infinity and the second
position is when the object is at a finite distance from the mirror. The ray
diagrams for the formation of image by a convex mirror for these two
positions of the object are shown in Fig.10.8 (a) and (b), respectively.
The results are summarised in Table 10.2You have so far studied the image formation by a plane mirror, a
concave mirror and a convex mirror. Which of these mirrors will give the
full image of a large object? Let us explore through an Activity.You can see a full-length image of a tall building/tree in a small
convex mirror. One such mirror is fitted in a wall of Agra Fort facing Taj
Mahal. If you visit the Agra Fort, try to observe the full image of Taj
Mahal. To view distinctly, you should stand suitably at the terrace
adjoining the wall.</p>
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<h3>Uses of convex mirrors</h3></div>
<p>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. Convex
mirrors are preferred 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.</p>
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<h3>10.2.3 Sign Convention for Reflection by Spherical Mirrors</h3></div>
pWhile dealing with the reflection of light by spherical mirrors, we shall
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 (Fig. 10.9). The principal axis of the mirror is taken as the x-axis
(X’X) of the coordinate system. The conventions are as follows –
(i) 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.
(ii) All distances parallel to the principal axis are measured from the
pole of the mirror.
(iii) 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.
(iv) Distances measured perpendicular to and above the principal axis
(along + y-axis) are taken as positive.
(v) Distances measured perpendicular to and below the principal axis
(along –y-axis) are taken as negative.The New Cartesian Sign Convention described above is illustrated in
Fig.10.9 for your reference. These sign conventions are applied to obtain
the mirror formula and solve related numerical problems.
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<h3>10.2.4 Mirror Formula and Magnification</h3></div>
<p>In a spherical mirror, the distance of the
object from its pole is called the object
distance (u). The distance of the image from
the pole of the mirror is called the image
distance (v). You already know that the
distance of the principal focus from the pole
is called the focal length (f). There is a
relationship between these three quantities
given by the mirror formula which is
expressed as
1/v + 1/u = 1/f
This formula is valid in all situations for all
spherical mirrors for all positions of the
object. You must use the New Cartesian Sign
Convention while substituting numerical
values for u, v, f, and R in the mirror formula
for solving problems</p>
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<h3>Magnification</h3></div>
<p>Magnification produced by a spherical mirror gives the relative extent to
which the image of an object is magnified with respect to the object size.
It is expressed as the ratio of the height of the image to the height of the
object. It is usually represented by the letter m.......
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<h1>End </h1></div>
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<p>Thx</p></div>