1. LECTURE ON NUMERICAL
PROBLEMS IN OPTICS
BY
KAVITA MONGA(LECTURER-PHYSICS)
GOVT POLYTECHNIC COLLEGE
KHUNIMAJRA,
MOHALI
DATE- 18/4/2013
2. Light :-
i) Light is a form of energy which helps us to see objects.
ii) When light falls on objects, it reflects the light and when the
reflected light reaches our eyes then we see the objects.
iii) Light travels in straight line.
iv) The common phenomena of light are formation of shadows,
formation of images by mirrors and lenses, bending of light by a
medium, twinkling of stars, formation of rainbow etc.
3.
4. • The overall study of how light behaves is called
optics.
• The branch of optics that focuses on the creation
of images is called geometric optics, because it
is based on relationships between angles and
lines that describe light rays.
5. Some Definitions
• Absorption
– When light passes through an object the intensity is reduced
depending upon the color absorbed. Thus the selective
absorption of white light produces colored light.
• Refraction
– Direction change of a ray of light passing from one
transparent medium to another with different optical density.
A ray from less to more dense medium is bent perpendicular
to the surface, with greater deviation for shorter wavelengths
• Diffraction
– Light rays bend around edges - new wavefronts are
generated at sharp edges - the smaller the aperture the
lower the definition
• Dispersion
– Separation of light into its constituent wavelengths when
entering a transparent medium - the change of refractive
index with wavelength, such as the spectrum produced by a
prism or a rainbow
7. • A lens is an optical
device that is used to
bend light in a specific
way.
• A converging lens
bends light so that the
light rays come
together to a point.
• A diverging lens bends
light so it spreads light
apart instead of
coming together.
8. • Mirrors reflect light and allow us to see ourselves.
• A prism is another optical device that can cause
light to change directions.
• A prism is a solid piece of glass with flat polished
surfaces.
9. • An optical system is a collection of mirrors, lenses,
prisms, or other optical elements that performs a
useful function with light.
• Characteristics of optical systems are:
– The location, type, and magnification of the
image.
– The amount of light that is collected.
– The accuracy of the image in terms of
sharpness, color, and distortion.
– The ability to change the image, like a telephoto
lens on a camera.
– The ability to record the image on film or
electronically.
Optical Systems
10. Reflection
• Images appear in mirrors
because of how light is
reflected by mirrors.
• The incident ray follows
the light falling onto the
mirror.
• The reflected ray follows
the light bouncing off the
mirror.
11. Reflection
• In specular reflection each incident ray bounces
off in a single direction.
• A surface that is not shiny creates diffuse
reflection.
• In diffuse reflection, a single ray of light scatters
into many directions.
12. Law of Reflection
The angle of
incidence equals
the angle of
reflection.
The incident ray
strikes the mirror.
The reflected ray
bounces off.
13. Law of reflection
• A light ray is incident on a plane mirror with a 30
degree angle of incidence.
• Sketch the incident and reflected rays and
determine the angle of reflection.
30o 30o
14. Mirror
A dentist uses a mirror to
look at the back of a second
molar (A). Next, she wishes
to look at the back of a
lateral incisor (B), which is
90° away. By what angle
should she rotate her mirror?
A. 90°
B. 45°
C. 180°
A
B
15. Specular vs. Diffuse Reflection
Specular Reflection
•The surface is flat at distance scales near
or above the wavelength of light
•It looks “shiny”, like a mirror.
16. Specular vs. Diffuse Reflection
Diffuse Reflection
•The surface is rough at distance scales
near or above the wavelength of light
•Almost all surfaces reflect in this way!
17. Two plane mirrors form a right angle.
How many images of the ball can you
see in the mirrors?
A. 1
B. 2
C. 3
D. 4
18. Refraction
• Light rays may bend as
they cross a boundary
from one material to
another, like from air to
water.
• This bending of light rays
is known as refraction.
• The light rays from the
straw are refracted (or
bent) when they cross
from water back into air
before reaching your
eyes.
19. Refraction
When a ray of light crosses from one material to
another, the amount it bends depends on the
difference in index of refraction between the two
materials.
20. Refraction
Water
Air
Refraction is the
bending of light as it
passes from one
medium into another.
refraction
N
qw
qA
Note: the angle of
incidence qA in air
and the angle of
refraction qA in water
are each measured
with the normal N.
The incident and refracted
rays lie in the same plane
and are reversible.
21.
22. Calculate the angle of refraction
• A ray of light traveling through air is incident on a
smooth surface of water at an angle of 30° to the
normal.
• Calculate the angle of refraction for the ray as it
enters the water.
23. solution
• 1) You are asked for the angle of refraction.
• 2) You are told the ray goes from air into water at
30 degrees.
• 3) Snell’s law:
ni sin(θi) = nr sin(θr)
ni = 1.00 (air), nr = 1.33 (water)
• 4) Apply Snell’s law to find θr.
1.00sin(30°) = 1.33 sin(θr)
sin(θr) = 0.5 ÷ 1.33 = 0.376
• Use the inverse sine function to find the angle that has
a sine of 0.376.
• θr = sin-1(0.376) = 22°
28. A fish swims below the surface of the water.
An observer sees the fish at:
A. a greater depth than it really is.
B. its true depth.
C. a smaller depth than it really is.
air
water
Virtual
Image
of Fish
29. A fish swims directly below the surface of
the water. An observer sees the fish at:
A. a greater depth than it really is.
B. its true depth.
C. a smaller depth than it really is.
air
water
30. The Index of Refraction
The index of refraction for a material is the ratio
of the velocity of light in a vacuum (3 x 108 m/s)
to the velocity through the material.
c
v
c
n
v
Index of refraction
c
n
v
Examples: Air n= 1; glass n = 1.5; Water n = 1.33
31. Index of Refraction
n
c
vmedium
• vmedium is the speed of light in a
transparent medium.
• c is the speed of light in a vacuum
(c=3.00×108 m/s)
• n is a dimensionless constant: n≥1
• n=1 in a vacuum
32. Index of refraction
The ability of a material to bend rays of light is
described by the index of refraction (n).
33. Example 1. Light travels from air (n = 1) into glass,
where its velocity reduces to only 2 x 108 m/s.
What is the index of refraction for glass?
8
8
3 x 10 m/s
2 x 10 m/s
c
n
v
vair = c
vG = 2 x 108 m/s
Glass
Air
For glass: n = 1.50
If the medium were water: nW = 1.33. Then
you should show that the velocity in water
would be reduced from c to 2.26 x 108 m/s.
34. Analogy for Refraction
Sand
Pavement
Air
Glass
Light bends into glass then returns along
original path much as a rolling axle would
when encountering a strip of mud.
3 x 108 m/s
3 x 108 m/s
2 x 108
m/s
vs < vp
35. Snell's law of refraction
• Snell’s law is the relationship between the angles
of incidence and refraction and the index of
refraction of both materials.
ni sin Qi = nr sin Qr
Index of
refraction of
refractive
material
Angle of incidence
(degrees)
Angle of refraction
(degrees)
Index of
refraction of
incident
material
37. Snell’s Law
q1
q2
Medium 1
Medium 2
The ratio of the sine of the
angle of incidence q1 to the
sine of the angle of refraction
q2 is equal to the ratio of the
incident velocity v1 to the
refracted velocity v2 .
Snell’s
Law:
1 1
2 2
sin
sin
v
v
q
q
v1
v2
38. Example 2: A laser beam in a darkened room
strikes the surface of water at an angle of 300.
The velocity in water is 2.26 x 108 m/s. What is
the angle of refraction?
The incident angle is:
qA = 900 – 300 = 600
sin
sin
A A
W W
v
v
q
q
8 0
8
sin (2 x 10 m/s)sin60
sin
3 x 10 m/s
W A
W
A
v
v
q
q qW = 35.30
Air
H2O
300
qW
qA
39. Snell’s Law and Refractive
Index
Another form of Snell’s law can be derived from
the definition of the index of refraction:
from which
c c
n v
v n
1 1 2
1
2 2 1
2
;
c
v v n
n
c
v v n
n
1 1 2
2 2 1
sin
sin
v n
v n
q
q
Snell’s law for
velocities and indices:
Medium 1
q1
q2
Medium 2
40. A Simplified Form of the Law
1 1 2
2 2 1
sin
sin
v n
v n
q
q
Since the indices of refraction for many common
substances are usually available, Snell’s law is
often written in the following manner:
1 1 2 2
sin sin
n n
q q
The product of the index of refraction and the
sine of the angle is the same in the refracted
medium as for the incident medium.
41. Example 3. Light travels through a block of glass,
then remerges into air. Find angle of emergence
for given information.
Glass
Air
Air
n=1.5
First find qG inside glass:
sin sin
A A G G
n n
q q
500
qG
q
0
sin (1.0)sin50
sin
1.50
A A
G
G
n
n
q
q
qG = 30.70
From geometry, note
angle qG same for
next interface.
qG sin sin sin
A G G A
A A
n n n
q
q q
Apply to each interface:
qe = 500
Same as entrance angle!
42. Wavelength and Refraction
The energy of light is determined by the frequency
of the EM waves, which remains constant as light
passes into and out of a medium. (Recall v = fl.)
Glass
Air n=1
n=1.5
lA
lG
fA= fG
lG < lA
;
A A A G G G
v f v f
l l
; ;
A A A A
G G G G
v f v
v f v
l l
l l
1 1 1
2 2 2
sin
sin
v
v
q l
q l
43. The Many Forms of Snell’s
Law:
Refraction is affected by the index of refraction,
the velocity, and the wavelength. In general:
1 2 1 1
2 1 2 2
sin
sin
n v
n v
q l
q l
All the ratios are equal. It is helpful to recognize
that only the index n differs in the ratio order.
Snell’s
Law:
44. Example 4: A helium neon laser emits a beam
of wavelength 632 nm in air (nA = 1). What is
the wavelength inside a slab of glass (nG =
1.5)?
nG = 1.5; lA = 632 nm
;
G
A A A
G
G A G
n n
n n
l l
l
l
(1.0)(632 nm)
1.5
421 nm
G
l
Note that the light, if seen inside the glass, would
be blue. Of course it still appears red because it
returns to air before striking the eye.
Glass
Air
Air
n=1.5
q
qG
q
qG
45. Total Internal Reflection
Water
Air
light
The critical angle qc is the
limiting angle of incidence
in a denser medium that
results in an angle of
refraction equal to 900.
When light passes at an angle from a medium of
higher index to one of lower index, the emerging
ray bends away from the normal.
When the angle reaches a
certain maximum, it will be
reflected internally.
i = r
Critical
angle
qc
900
46.
47. Total Internal Reflection
• Occurs when n2<n1
• θc = critical angle.
• When θ1 ≥ θc, no light is transmitted
through the boundary; 100%
reflection
1
2
sin
n
n
c
q
48. Example 5. Find the critical angle of
incidence from water to air.
For critical angle, qA = 900
nA = 1.0; nW = 1.33
sin sin
W C A A
n n
q q
0
sin90 (1)(1)
sin
1.33
A
C
w
n
n
q
Critical angle: qc = 48.80 Water
Air
qc
900
Critical angle
In general, for media where
n1 > n2 we find that:
1
2
sin C
n
n
q
49. Refraction & Dispersion
Light is “bent” and the resultant colors separate (dispersion).
Red is least refracted, violet most refracted.
Short wavelengths are “bent”
more than long wavelengths
rac
50. Dispersion by a Prism
Red
Orange
Yellow
Green
Blue
Indigo
Violet
Dispersion is the separation of white light into
its various spectral components. The colors
are refracted at different angles due to the
different indexes of refraction.
51. Dispersion and prisms
• When white light passes through a glass
prism, blue is bent more than red.
• Colors between blue and red are bent
proportional to their position in the
spectrum.
52. Dispersion and prisms
• The variation in
refractive index with
color is called
dispersion.
• A rainbow is an example
of dispersion in nature.
• Tiny rain droplets act as
prisms separating the
colors in the white light
rays from the sun.
53. a) Lens formula for spherical lenses :-
The lens formula for spherical lenses is the relationship between the
object distance (u), image distance (v) and focal length (f).
The lens formula is expressed as :-
1 1 1
=
v u f
b) Magnification produced by spherical lenses :-
Magnification for spherical lens is the ratio of the height of the
image to the height of the object.
Height of the image hi
Magnification = m =
Height of the object ho
The magnification is also related to the object distance and image
distance. It can be expressed as :-
hi v
Magnification m = =
ho u
54. Power of a lens :-
The power of a lens is the reciprocal of its focal length
(in metres).
I 1
P = or f =
f (m) P
The SI unit of power is dioptre (D).
1 dioptre is the power of a lens whose focal length is 1
metre.
The power of a convex lens is positive ( + ve ) and the
power of a concave lens is negative ( - ve ).
55. Thin Lens Equation
We can mathematically determine
where an image will be formed in
relation to the optical centre using the
thin lens equation.
56. The Thin Lens Equation
1 = 1 + 1
f di do
Where:
f represents the focal length
do represents from the object to the lens
di represents from the image to the lens
F
F’ 2F
2F’
Focal
length
f
do
di
57. The Thin Lens Equation – Example 1
• A converging lens has a focal length of 17
cm. A candle is located 48 cm from the
lens. What type of image will be formed,
and where will it be located?
59. example 1
1 = 1 + 1
f di do
1 = 1 - 1
di f d0
E:
Rearrange equation:
60. example 1…almost there!
S:
1 = 1 - 1
di 17 cm 48 cm
1 = 0.03799cm-1
di
di = 1 / 0.03799cm-1
di = 26.327165 cm = 26 cm
The image of the candle is real and
will be about 26 cm from the lens
(opposite the object).
S:
S:
61. example – last step!
Sketch the ray diagram for this problem.
62. Example 2: Thin Lens Equation and
Diverging Lenses
• A diverging Lens has a focal length of 29
cm. A virtual image of a marble is
located 13 cm in front of the lens. Where
is the marble (the object) located?
• Follow the same steps as before, but be
careful with the signs! Refer to your
RULES for sign conventions.
64. Example 2:
G: f = - 29 cm
di = -13 cm
d0 = ?
1 = 1 + 1
f do di
1 = 1 - 1
d0 f di
1 = 1 - 1
d0 -29cm -13cm
1 = 0.042444 cm-1
d0
d0 = 23.560456 cm = 24 cm
The marble is located 24
cm from the lens on the
same side as the image.
U
:
E:
S:
S:
S:
65. Magnification Equation
M = hi = - di
ho do
Where:
M stands for magnification
hi stands for height of the image
ho stands for height of the object
F
F’ 2F
2F’
h
o
h
i
66. Magnification Signs and Measurements
• Magnification (M) has no units
• M is POSITIVE for an UPRIGHT image
• M is NEGATIVE for an INVERTED image
If M is…. Then the image is…
• GREATER THAN 1 LARGER than the
object
• BETWEEN 0 AND 1 SMALLER than the
object
• EQUAL TO 1 SAME SIZE as the object
67. Example 3: Finding the Magnification of a
CONVERGING lens
• A toy of height 8.4 cm is balanced in front
of a converging lens. An inverted, real
image of height 23 cm is noticed on the
other side of the lens. What is the
magnification of the lens?
– Follow the same steps as ex 1 & 2 to solve
the problem (just use the magnification
equation)
69. Example 3:
h0 = 8.4 cm
hi = -23 cm
M = ?
M = hi
ho
M = -23 cm
8.4 cm
M = -2.738095238 = -2.7
The lens has a
magnification of -2.7,
which means the image is
inverted.
G:
U:
E:
S:
S:
S
:
70. Example 4: Magnification of a
Diverging Lens
• A coin of height 2.4 cm is placed in front of
a diverging lens. An upright, virtual
image of height 1.7 cm is noticed on the
same side of the lens as the coin. What is
the magnification of the lens?
72. Example 4:
h0 = 2.4 cm
hi = 1.7 cm
M = ?
M = hi
ho
M = 1.7 cm
2.4 cm
M = 0.708333 = 0.71
The lens has a
magnification of 0.71,
which means the image
is upright.
G:
U:
E:
S:
S:
S:
73. Drawing ray diagrams
• A ray diagram is the best way to understand what
type of image is formed by a lens, and whether
the image is magnified or inverted.
• These three rays follow the rules for how light
rays are bent by the lens:
1. A light ray passing through the center of the lens is not
deflected at all (A).
2. A light ray parallel to the axis passes through the far
focal point (B).
3. A light ray passing through the near focal point emerges
parallel to the axis (C).
74.
75.
76. Reflection of light :-
When light falls on a highly polished surface like a mirror most of
the light is sent back into the same medium. This process is called
reflection of light.
Laws of reflection of light :-
i) The angle of incidence is equal to the angle of reflection.
ii) The incident ray, the reflected ray and the normal to the mirror at
the point of incidence all lie in the same plane.
77. Image formed by a plane mirror :-
i) The image is erect.
ii) The image is same size as the object.
iii) The image is at the same distance from the mirror as the object is in
front of it.
iv) The image is virtual (cannot be obtained on a screen).
v) The image is laterally inverted.
78. Spherical mirrors :-
Spherical mirror is a curved mirror which is a part of a hollow
sphere. Spherical mirrors are of two types. They are concave mirror
and convex mirror.
i) Concave mirror :- is a spherical mirror whose reflecting surface is
curved inwards. Rays of light parallel to the principal axis after
reflection from a concave mirror meet at a point (converge) on the
principal axis.
ii) Convex mirror :- is a spherical mirror whose reflecting surface is
curved inwards. Rays of light parallel to the principal axis after
reflection from a convex mirror get diverged and appear to come from a
point behind the mirror.
F
F
79. Terms used in the study of spherical mirrors :-
i) Center of curvature :- is the centre of the sphere of which the mirror
is a part (C).
ii) Radius of curvature :- is the radius of the sphere of which the mirror
is a part (CP).
iii) Pole :- is the centre of the spherical mirror (P).
iv) Principal axis :- is the straight line passing through the centre of
curvature and the pole (X-Y).
v) Principal focus :-
In a concave mirror, rays of light parallel to the principal axis after
reflection meet at a point on the principal axis called principal
focus(F).
In a convex mirror, rays of light parallel to the principal axis after
reflection get diverged and appear to come from a point on the
principal axis behind the mirror called principal focus (F).
vi) Focal length :- is the distance between the pole and principal focus
(f). In a spherical mirror the radius of curvature is twice the focal
length.
R = 2f or f = R
2
80. X C F P Y
C – centre of curvature CP – radius of curvature
P – pole XY – principal axis
F – principal focus PF – focal length
81. Reflection by spherical mirrors :-
i) In a concave mirror a ray of light parallel to the principal
axis after reflection passes through the focus.
In a convex mirror a ray of light parallel to the principal
axis after reflection appears to diverge from the focus.
C F P P F C
82. ii) In a concave mirror a ray of light passing through the
focus after reflection goes parallel to the principal axis.
In a convex mirror a ray of light directed towards the
focus after reflection goes parallel to the principal axis.
C F P P F C
83. iii) In a concave mirror a ray of light passing through the
centre of curvature after reflection is reflected back along
the same direction.
In a convex mirror a ray of light directed towards the
centre of curvature after reflection is reflected back along
the same direction.
C F P P F C
84. iv) In a concave or a convex mirror a ray of light directed
obliquely at the pole is reflected obliquely making equal
angles with the principal axis.
C F i P i P F C
r r
85. Images formed by concave mirror :-
i) When the object is at infinity the image is formed at the
focus, it is highly diminished, real and inverted.
C F P
86. ii) When the object is beyond C, the image is formed
between C and F, it is diminished, real and inverted.
C F P
87. iii) When the object is at C, the image is formed at C, it is
same size as the object, real and inverted.
C F P
88. iv) When the object is between C and F, the image is
formed beyond C, it is enlarged, real and inverted.
C F P
89. v) When the object is at F, the image is formed at infinity, it
is highly enlarged, real and inverted.
C F P
90. vi) When the object is between F and P, the image is formed
behind the mirror, it is enlarged, virtual and erect.
C F P
91. Images formed by convex mirror :-
i) When the object is at infinity, the image is formed at F
behind the mirror, it is highly diminished, virtual and erect.
P F
92. ii) When the object is between infinity and pole, the image
is formed behind the mirror, it is diminished, virtual and
erect.
P F C
93. Uses of spherical mirrors :-
a) Concave mirrors :-
Concave mirrors are used in torches, search lights and head lights of
vehicles to get parallel beams of light.
They are used as shaving mirrors to see larger image of the face.
They are used by dentists to see larger images of the teeth.
Large concave mirrors are used to concentrate sunlight to produce
heat in solar furnaces.
94. b) Convex mirrors :-
Convex mirrors are used as rear-view mirrors in vehicles. Convex
mirrors give erect diminished images of objects. They also have a
wider field of view than plane mirrors.
95. New Cartesian sign convention for spherical mirrors :-
i) The object is always placed on the left of the mirror and light from the
object falls from the left to the right.
ii) All distances parallel to the principal axis are measured from the pole.
iii) All distances measured to the right of the pole are taken as + ve.
iv) All distances measured to the left of the pole are taken as – ve.
v) The height measured upwards perpendicular to the principal axis is
taken as + ve.
vi) The height measured downwards perpendicular to the principal axis
is taken as – ve.
Direction of incident light
Distance towards the left ( - ve
)
Distance towards the right ( + ve )
Height
downwards ( - ve )
Height
upwards ( + ve )
Concave mirror
Object
Image
96. Mirror formula for spherical mirrors :-
The mirror formula for spherical mirrors is the relationship between
the object distance (u), image distance (v) and focal length (f).
The mirror formula is expressed as :-
1 1 1
+ =
v u f
Magnification for spherical mirrors :-
Magnification for spherical mirrors is the ratio of the height of the
image to the height of the object.
Height of the image hi
Magnification = m =
Height of the object ho
The magnification is also related to the object distance and image
distance. It is expressed as :-
hi v
Magnification m = =
ho u
97. Refraction of light :-
When light travels obliquely from one transparent medium into
another it gets bent. This bending of light is called refraction of light.
When light travels from a rarer medium to a denser medium, it bends
towards the normal.
When light travels from a denser medium to a rarer medium to a
rarer medium, it bends away from the normal.
Denser medium Rarer medium
Rarer medium Denser medium
Normal Normal
98. Refraction of light through a rectangular glass
slab :-
When a ray of light passes through a rectangular glass slab, it gets
bent twice at the air- glass interface and at the glass- air interface.
The emergent ray is parallel to the incident ray and is displaced
through a distance.
i
e
Normal
Incident ray
Emergent ray
Refracted ray
Glass
Air
Normal
r
Glass
Air
Rectangular glass slab
displacement
Angle of emergence
Angle of incidence
Angle of refraction
99. c) Laws of refraction of light :-
i) The incident ray, the refracted ray and the normal to the interface of
two transparent media at the point of incidence, all lie in the same
plane.
II) The ratio of the sine of angle of incidence to the sine of angle of
refraction is a constant, for the light of a given colour and for the
given pair of media.( This law is also known as Snell`s law of
refraction.) sine i
= constant
sine r
d)Refractive index :-
The absolute refractive index of a medium is the ratio of the speed
light in air or vacuum to the speed of light in medium.
Speed of light in air or vacuum c
Refractive index = n =
Speed of light in the medium v
The relative refractive index of a medium 2 with respect to a
medium 1 is the ratio of the speed of light in medium 1 to the
speed of light in medium 2.
n
21
= Speed of light in medium 1 n 21
= v
1 / v2
Speed of light in medium 2
100. Spherical lenses :-
A spherical lens is a transparent material bounded by two surfaces
one or both of which are spherical.
Spherical lenses are of two main types. They are convex and concave
lenses.
i) Convex lens :- is thicker in the middle and thinner at the edges.
Rays of light parallel to the principal axis after refraction through a
convex lens meet at a point (converge) on the principal axis.
ii) Concave lens :- is thinner in the middle and thicker at the edges.
Rays of light parallel to the principal axis after refraction get diverged
and appear o come from a point on the principal axis on the same side
of the lens.
F F
101. Refraction by spherical lenses :-
i) In a convex lens a ray of light parallel to the principal
axis after refraction passes through the focus on the other
side of the lens. In a concave lens it appears to diverge
from the focus on the same side of the lens.
2F1 F1 O F2 2F2 2F1 F1 O F2 2F2
102. ii) In a convex lens a ray of light passing through the focus
after refraction goes parallel to the principal axis. In a
concave lens a ray of light directed towards the focus after
refraction goes parallel to the principal axis.
2F1 F1 O F2 2F2 2F1 F1 O F2 2F2
103. iii) In a convex lens and concave lens a ray of light passing
through the optical centre goes without any deviation.
2F1 F1 O F2 2F2 2F1 F1 O F2 2F2
104. Images formed by convex lens :-
i) When the object is at infinity the image is formed at the
focus F2, it is highly diminished, real and inverted.
2F1 F1 O F2 2F2
105. ii) When the object is beyond 2F1, the image is formed
between F2 and 2F2, it if diminished, real and inverted.
2F1 F1 O F2 2F2
106. iii) When the object is at 2F1, the image is formed at 2F2, it
is the same size as the object, real and inverted.
2F1 F1 O F2 2F2
107. iv) When the object is between 2F1 and F1, the image is
formed beyond 2F2, it is enlarged, real and inverted.
2F1 F1 O F2 2F2
108. v) When the object is at F1 the image is formed at infinity, it
is highly enlarged, real and inverted.
2F1 F1 O F2 2F2
109. vi) When the object is between F1 and O, the image is
formed on the same side of the lens, it is enlarged, virtual
and erect.
2F1 F1 O F2 2F2
110. Images formed by concave lens :-
i) When the object is at infinity, the image is formed at the
focus F1 on the same side of the lens, it is highly
diminished, virtual and erect.
F1 O
111. ii) When the object is between infinity and F1, the image is
formed between F1 and O on the same side of the lens, it is
diminished, virtual and erect.
FI O
112. Sign convention for spherical lenses :-
The sign convention for spherical lenses is the same as in
spherical mirrors except that the distances are measured from the
optical centre (O).
The focal length of a convex lens is positive ( + ve ) and the focal
length of a concave lens is negative ( - ve ).
O
Direction of incident light
Distance towards the left (- ve )
Height
downwards ( - ve )
Height
upwards ( + ve )
Convex lens
Object
Image
Distance towards the right ( + ve )
