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10. Light - Reflection and Refraction | Class 10 CBSE | Web Notes | Part 9: Lens Formula & Magnification, Power of Lenses
10. LIGHT – REFLECTION AND REFRACTION
Lens Formula and Magnification
10. Light - Reflection and Refraction | Class 10/ CBSE | Web Notes | Part 8: Image Formation by Lenses
10. LIGHT – REFLECTION AND REFRACTION
Image Formation by Lenses
Lenses form images by refracting light.
10. Light - Reflection and Refraction | Class 10 CBSE | Web Notes | Part 7: Refractive Index, Refraction by Spherical Lenses
10. LIGHT – REFLECTION AND REFRACTION
The Refractive Index (n)
It is the ratio of the speeds of light in a pair of media.
10. Light - Reflection and Refraction | Class 10 CBSE | Web Notes | Part 6: Refraction through a Rectangular Glass Slab
10. LIGHT – REFLECTION AND REFRACTION
Refraction through a Rectangular Glass Slab
Fix a white paper on a drawing board and place a rectangular glass slab on its middle.
10. Light - Reflection and Refraction | Class 10 CBSE | Web Notes | Part 5: Refraction of Light
10. LIGHT – REFLECTION AND REFRACTION
REFRACTION
OF LIGHT
Light seems to travel along straight-line paths in a transparent medium.
10. Light - Reflection and Refraction | Class 10 CBSE | Web Notes | Part 4: Sign Convention, Mirror Formula & Magnification
10. LIGHT – REFLECTION AND REFRACTION
Sign Convention for Reflection by Spherical Mirrors
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 New Cartesian Sign
Convention for spherical mirrors
The
conventions are as follows:
a) The object is
always placed to the left of the mirror. i.e., light from the object
falls on the mirror from the left-hand side.
b) All distances parallel to
the principal axis are measured from the pole of the mirror.
c) 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.
d) Distances measured
perpendicular to and above the principal axis (along + y-axis) are taken
as positive.
e) Distances measured
perpendicular to and below the principal axis (along – y-axis) are taken
as negative.
Sign conventions
are applied to obtain the mirror formula and solve related numerical
problems.
Mirror Formula and Magnification
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).
The distance of the principal focus from the pole is called the focal length (f).
This formula is valid in all situations for all spherical mirrors for all positions of the object.
Magnification (m)
It is the enlargement of the image formed
by a spherical mirror, relative to the size of the object.
It is the ratio of the height of the image (h′) to
the height of the object (h).
Magnification is also related to the object distance (u)
and image distance (v). It can be expressed as:
The height of the
object is taken to be positive as the object is placed above the
principal axis.
The height of the image
is taken as positive for virtual images and negative for real
images.
A negative sign in
the value of the magnification indicates that the image is real. A positive
sign indicates that the image is virtual.
Problem: A convex mirror used for
rear-view on an automobile has a radius of curvature of 3.00 m. If a bus is
located at 5.00 m from this mirror, find the position, nature and size of the
image.
Solution
Radius
of curvature, R = + 3.00 m
Object-distance, u =
– 5.00 m
Image-distance, v= ?
Height of the image, h′=
?
Focal length, f = R/2 = + 300 m/2
The
image is 1.15 m at the back of the mirror.
The
image is virtual, erect & smaller by a factor of 0.23.
Problem: 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
Object-size,
h = + 4.0 cm
Object-distance,
u = – 25.0 cm
Focal
length, f = –15.0 cm
Image-distance, v= ?
Image-size,
h′= ?
v = – 37.5 cm
The
screen should be placed at 37.5 cm in front of the mirror. The image is real.
Height
of the image, h′ = – 6.0 cm
The image is inverted and enlarged.
Select Your Next Topic 👇
👉 Part 1: Reflection of Light
👉 Part 2: Spherical Mirrors
👉 Part 3: Image Formation by Spherical Mirrors
👉 Part 4: Sign Convention, Mirror Formula & Magnification
👉 Part 5: Refraction of Light
👉 Part 6: Refraction through a Rectangular Glass Slab
👉 Part 7: Refractive Index, Refraction by Spherical Lenses
👉 Part 8: Image Formation by Lenses
👉 Part 9: Lens Formula & Magnification, Power of Lenses
10. Light - Reflection and Refraction | Class 10 CBSE | Web Notes | Part 3: Image Formation by Spherical Mirrors
10. LIGHT – REFLECTION AND REFRACTION
Image Formation by Spherical Mirrors
Find out approximate focal
length of a concave mirror.
Mark
3 parallel lines P, F & C on a table such that the distance
between any two successive lines is equal to the focal length of the mirror.
Place
a stand with concave mirror over the line P such that its pole
lies over the line.
Keep a bright object
(e.g. burning candle) at a position far beyond C. Place a paper screen and move
it in front of the mirror to obtain a sharp bright image of the candle flame.
Repeat the activity by
placing the candle (a) just beyond C, (b) at C, (c) between F & C, (d) at F
and (e) b/w P & F.
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 & C.
Representation of Images Formed by Spherical Mirrors Using Ray Diagrams
In an extended
object, each small portion acts like a point source. An infinite
number of rays originate from each point. But it is easier to consider only two
rays, for the clarity of the ray diagram and to know their directions after
reflection.
The intersection of at
least two reflected rays gives the position of image of the point object. Any
two of the following rays can be considered to locate the image.
a)
A ray parallel to the principal
axis. After reflection, it passes through the principal focus in a concave
mirror or appear to diverge from principal focus in a convex mirror.
b) A ray through the principal focus of a concave mirror
or directed towards the principal focus of a convex mirror.
After reflection, it emerges parallel to the principal axis.
c) A ray through the centre of curvature of a concave mirror
or directed in the direction of the centre of curvature of a convex
mirror. Then it is reflected 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 pole (P),
on the concave mirror or a convex mirror. It is reflected obliquely.
In all these cases, the laws of reflection are followed. i.e.,
angle of reflection equals angle of incidence.
(a) Image formation by a Concave
Mirror
Ray diagrams:
Position
of the object |
Position
of the image |
Size
of the image |
Nature
of the image |
At infinity |
At focus F |
Highly diminished, |
Real & inverted |
Beyond C |
b/w F & C |
Diminished |
Real & inverted |
At C |
At C |
Same size |
Real & inverted |
b/w C & F |
Beyond C |
Enlarged |
Real & inverted |
At F |
At infinity |
Highly enlarged |
Real & inverted |
b/w P & F |
Behind the mirror |
Enlarged |
Virtual & erect |
When the object is
between F & P, image is not obtained on the screen. Here, virtual image
can be seen in mirror.
Uses of concave mirrors
· Used in torches, search-lights and vehicles headlights to get
powerful parallel beams of light.
· Used as shaving mirrors to see a larger image of the face.
· Used by dentists to see large images of teeth of patients.
· Large concave mirrors are used to concentrate sunlight to
produce heat in solar furnaces.
(b) Image formation by a Convex Mirror
Show a pencil in the
upright position in front of a convex mirror. Its image in the mirror is erect
and diminished.
As the pencil is moved away
from the mirror, the image becomes smaller and moves closer to the focus.
Two positions of the
object to study the image formed by a convex mirror are shown below.
(a) Formation of image when
the object is at infinity
(b) Formation of image when
the object is at a finite distance from the mirror
Position
of the object |
Position
of the image |
Size
of the |
Nature
of the image |
At infinity |
At the focus F,
behind the mirror |
Highly
diminished, |
Virtual &
erect |
Between infinity
and the pole P |
b/w P & F,
behind the mirror |
Diminished |
Virtual &
erect |
In plane mirrors and
concave mirrors of any sizes, we cannot see a full-length image of a
distant object. But it is possible in a convex mirror with wider field
of view.
A convex mirror is fitted
in a wall of Agra Fort facing Taj Mahal to observe the full image of Taj Mahal.
Uses of
convex mirrors
Convex mirrors give an erect, diminished, virtual image. Also, they have a wider field of view as they are curved outwards. So, they are used as rear-view (wing) mirrors in vehicles. It enables the driver to see traffic behind him.