1636 Ray Optics
Chapter
29
Ray Optics
Real and Virtual Images (3) There is a phase change of if reflection takes place from denser
medium.
If light rays, after reflection or refraction, actually meets at a point
then real image is formed and if they appears to meet virtual image is Reflection From a Plane Surface (Plane Mirror)
formed.
The image formed by a plane mirror is virtual, erect, laterally inverted,
equal in size that of the object and at a distance equal to the distance of the
object in front of the mirror.
I O O I
(Real image) (Virtual (Real object) (Virtual image)
object) x x
Fig. 29.2
(1) Deviation () : Deviation produced by a plane mirror and by two
Real image inclined plane mirrors.
(Virtual
image)
i r
(Real image)
O (Real object)
I = (180 – 2i) = (360 – 2)
(Virtual
(A) Single Reflection (B) Double Reflection
object) (Virtual
image) Fig. 29.3
(2) Images by two inclined plane mirrors : When two plane mirrors
Reflection of Light are inclined to each other at an angle , then number of images (n) formed
of an object which is kept between them.
When a ray of light after incidenting on a boundary separating two
media comes back into the same media, then this phenomenon, is called 360 o 360 o
reflection of light. (i) n 1 ; If even integer
Normal
360 o
Reflected ray (ii) If odd integer then there are two possibilities
Incident ray
i r
Boundary
Fig. 29.1 Object Object
(1) i = r
/2
(2) After reflection, velocity, wave length and frequency of light /2
remains same but intensity decreases.
(A) Object is placed (B) Object is placed
symmetrically asymmetrically
Fig. 29.4
, Ray Optics 1637
(v) Focus (F) : An image point on principle axis for an object at .
360 360 (vi) Focal length (f) : Distance between P and F.
n 1 n
(vii) Relation between f and R : f
R
2
(f = –ve , f = + ve , f = )
(3) Other important informations concave convex plane
(viii) Power : The converging or diverging ability of mirror
(i) When the object moves with speed u towards (or away) from the
(ix) Aperture : Effective diameter of light reflecting area. Intensity of
plane mirror then image also moves towards (or away) with speed u. But
image Area (Aperture) 2
relative speed of image w.r.t. object is 2u.
(x) Focal plane : A plane passing from focus and perpendicular to
(ii) When mirror moves towards the stationary object with speed u, principle axis.
the image will move with speed 2u in same direction as that of mirror.
(2) Sign conventions :
Incident ray +
O I O I
u u Rest 2u
– +
u
Mirror at rest Mirror is moving Principle axis
(A) (B)
Mirror or Lens –
Fig. 29.5
(iii) A man of height h requires a mirror of length at least equal to Fig. 29.8
(i) All distances are measured from the pole.
h/2, to see his own complete image.
(ii) Distances measured in the direction of incident rays are taken as
(iv) To see complete wall behind himself a person requires a plane positive while in the direction opposite of incident rays are taken negative.
mirror of at least one third the height of wall. It should be noted that
(iii) Distances above the principle axis are taken positive and below the
person is standing in the middle of the room.
principle axis are taken negative.
H H Table 29.1 : Useful sign
E E
M' Concave mirror
M'
h E h Convex
h h 3
2 Virtual image (u< f) mirror
Real image (u ≥ f)
M' M'
L B Distance of object u – u – u –
d d Distance of image v – v + v +
(A) (B)
Focal length f – f – f +
Fig. 29.6
Curved Mirror Height of object O + O+ O +
It is a part of a transparent hollow sphere whose one surface is Height of image I – I + I +
polished. Radius of curvature R – R – R +
Magnification m – m+ m +
C P P C Image Formation by Curved Mirrors
F F
Principal
axis
Concave mirror Convex mirror
Fig. 29.7
Concave mirror converges the light rays and used as a shaving mirror,
In search light, in cinema projector, in telescope, by E.N.T. specialists etc.
Convex mirror diverges the light rays and used in road lamps, side
mirror in vehicles etc. Concave mirror : Image formed by concave mirror may be real or
virtual, may be inverted or erect, may be smaller, larger or equal in size of
(1) Terminology object.
(i) Pole (P) : Mid point of the mirror (1) When object is placed at infinite (i.e. u = )
(ii) Centre of curvature (C) : Centre of the sphere of which the mirror
is a part. Image
At F
(iii) Radius of curvature (R): Distance between pole and centre of
Real F P
curvature. (R = –ve , R = +ve , R = )
concave convex plane
Inverted
(iv) Principle axis : A line passing through P and C. Very small in size
Fig. 29.9
, 1638 Ray Optics
Magnification m << – 1 Small in size
Magnification m < + 1
(2) When object is placed between infinite and centre of curvature (i.e.
u > 2f)
Mirror Formula and Magnification
Image For a spherical mirror if u = Distance of object from pole, v = distance
Between F and C
Real of image from pole, f = Focal length, R = Radius of curvature, O = Size of
Inverted C F P object, I = size of image
Small in size
m<–1 1 1 1
(1) Mirror formula :
f v u
Fig. 29.10(i.e. u = 2f)
(3) When object is placed at centre of curvature
(2) Lateral magnification : When an object is placed perpendicular to
Image the principle axis, then linear magnification is called lateral or transverse
At C magnification.
Real
Inverted F P I v f f v
Equal in size C m
O u f u f
m=–1
(* Always use sign convention while solving the problems)
(4) When object is placed between centreFig. curvature and focus (i.e. f
of 29.11
< u < 2f) Axial magnification : When object lies along the principle axis then its
I (v 2 v 1 )
Image axial magnification m
O (u 2 u 1 )
Between 2f and
Real F P 2 2 2
dv v f f v
Inverted C If object is small; m
Large in size du u f u f
m>–1 Areal magnification : If a 2D-object is placed with it's plane
Fig. 29.12 perpendicular to principle axis. It's Areal magnification
(5) When object is placed at focus (i.e. u = f)
Area of image ( Ai ) A
ms ms m 2 i
Image Area of object ( Ao ) Ao
At
Real P
Inverted C F
Very large in size
m >> – 1
(6) When object is placed between focus Fig.
and29.13
pole (i.e. u < f)
Image
Behind the mirror
Virtual
Erect P
Large in size C F
m>+1
Convex mirror : Image formed by convex mirror Fig. 29.14
is always virtual, erect
and smaller in size.
(1) When object is placed at infinite (i.e. u = )
Image
At F
Virtual
Erect P F
Very small in size
Magnification m << + 1
Fig. 29.15 axis
(2) When object is placed any where on the principal
Image
Between P and F
Virtual
Erect
P F C
Fig. 29.16
, Ray Optics 1639
(3) Absolute refractive index : When light travels from vacuum to any
Refraction of Light transparent medium then refractive index of medium w.r.t. vacuum is called
The bending of the ray of light passing from one medium to the other c
it’s absolute refractive index i.e. vacuum medium
medium is called refraction. v
Absolute refractive indices for glass, water and diamond are
3 4 12
respectively g 1.5, w 1.33 and D 2.4
2 3 5
(4) Relative refractive index : When light travels from medium (1) to
medium (2) then refractive index of medium (2) w.r.t. medium (1) is called
v
it’s relative refractive index i.e. 1 2 2 1 (where v and v are the
1 v 2 1 2
Princ (B) (C)
ipal speed of light in medium 1 and 2 respectively).
Axis Fig. 29.17 (5) When we say refractive index we mean absolute refractive index.
2
(1) The refraction of light takes place on going from one medium to
(A) (6) The minimum value of absolute refractive index is 1. For air it is
another because the speed of light is different in the two media. very near to 1. ( ~ 1.003 )
(2) Greater the difference in the speeds of light in the two media, B C
greater will be the amount of refraction. (7) Cauchy’s equation : A ......
2 4
(3) A medium in which the speed of light is more is known as
(Red violet so Red violet )
optically rarer medium and a medium is which the speed of light is less, is
known as optically denser medium. (8) If a light ray travels from medium (1) to medium (2), then
(4) When a ray of light goes from a rarer medium to a denser 2 1 v 1
1 2
medium, it bends towards the normal. 1 2 v 2
(9) Dependence of Refractive index
Incident ray
i Rarer medium (i) Nature of the media of incidence and refraction.
(ii) Colour of light or wavelength of light.
(iii) Temperature of the media : Refractive index decreases with the
Deviation = (i – r) increase in temperature.
Table 29.2 : Indices of refraction for various substances, Measured with
Denser medium Refracted ray light of vacuum wavelength = 589 nm 0
(5) When a ray of light goesFig. 29.18a denser medium to a rarer
from Substance Refractive Substance Refractive
medium, it bends away from the normal. index index
Solids at 20°C Liquids at 20°C
Denser medium Diamond (C) 2.419 Benzene 1.501
Fluorite (CaF2) 1.434 Carbon disulfide 1.628
i
Deviation = (r – i ) Flused quartz (SiO2) 1.458 Carbon tetrachloride 1.461
Glass, crown 1.52 Ethyl alcohol 1.361
r
Glass, flint 1.66 Glycerine 1.473
Rarer medium
o
Ice (H2O) (at 0 C) 1.309 Water 1.333
Fig. 29.19 Polystyrene 1.49 Gases at 0°C,
(6) Snell’s law : The ratio of sine of the angle of incidence to the angle
of refraction (r) is a constant called refractive index 1 atm
Sodium chloride 1.544 Air 1.000293
sin i
i.e. (a constant). For two media, Snell's law can be Zircon 1.923 Carbon dioxide 1.00045
sin r
sini (10) Reversibility of light and refraction through several media
written as 1 2 2
1 sinr Incident ray
1
1 sini 2 sinr i.e. sin constant 1
i 2
Also in vector form : ˆi nˆ ( rˆ nˆ )
r
3
Refractive Index 2
(1) Refractive index of a medium is that characteristic which decides 1
speed of light in it. 1 2 2 3 3 1 1
1
(A) 1 2 (B) 1 3
(2) It is a scalar, unit less and dimensionless quantity.
2 1
or 2 3
1 2
Fig. 29.20
Chapter
29
Ray Optics
Real and Virtual Images (3) There is a phase change of if reflection takes place from denser
medium.
If light rays, after reflection or refraction, actually meets at a point
then real image is formed and if they appears to meet virtual image is Reflection From a Plane Surface (Plane Mirror)
formed.
The image formed by a plane mirror is virtual, erect, laterally inverted,
equal in size that of the object and at a distance equal to the distance of the
object in front of the mirror.
I O O I
(Real image) (Virtual (Real object) (Virtual image)
object) x x
Fig. 29.2
(1) Deviation () : Deviation produced by a plane mirror and by two
Real image inclined plane mirrors.
(Virtual
image)
i r
(Real image)
O (Real object)
I = (180 – 2i) = (360 – 2)
(Virtual
(A) Single Reflection (B) Double Reflection
object) (Virtual
image) Fig. 29.3
(2) Images by two inclined plane mirrors : When two plane mirrors
Reflection of Light are inclined to each other at an angle , then number of images (n) formed
of an object which is kept between them.
When a ray of light after incidenting on a boundary separating two
media comes back into the same media, then this phenomenon, is called 360 o 360 o
reflection of light. (i) n 1 ; If even integer
Normal
360 o
Reflected ray (ii) If odd integer then there are two possibilities
Incident ray
i r
Boundary
Fig. 29.1 Object Object
(1) i = r
/2
(2) After reflection, velocity, wave length and frequency of light /2
remains same but intensity decreases.
(A) Object is placed (B) Object is placed
symmetrically asymmetrically
Fig. 29.4
, Ray Optics 1637
(v) Focus (F) : An image point on principle axis for an object at .
360 360 (vi) Focal length (f) : Distance between P and F.
n 1 n
(vii) Relation between f and R : f
R
2
(f = –ve , f = + ve , f = )
(3) Other important informations concave convex plane
(viii) Power : The converging or diverging ability of mirror
(i) When the object moves with speed u towards (or away) from the
(ix) Aperture : Effective diameter of light reflecting area. Intensity of
plane mirror then image also moves towards (or away) with speed u. But
image Area (Aperture) 2
relative speed of image w.r.t. object is 2u.
(x) Focal plane : A plane passing from focus and perpendicular to
(ii) When mirror moves towards the stationary object with speed u, principle axis.
the image will move with speed 2u in same direction as that of mirror.
(2) Sign conventions :
Incident ray +
O I O I
u u Rest 2u
– +
u
Mirror at rest Mirror is moving Principle axis
(A) (B)
Mirror or Lens –
Fig. 29.5
(iii) A man of height h requires a mirror of length at least equal to Fig. 29.8
(i) All distances are measured from the pole.
h/2, to see his own complete image.
(ii) Distances measured in the direction of incident rays are taken as
(iv) To see complete wall behind himself a person requires a plane positive while in the direction opposite of incident rays are taken negative.
mirror of at least one third the height of wall. It should be noted that
(iii) Distances above the principle axis are taken positive and below the
person is standing in the middle of the room.
principle axis are taken negative.
H H Table 29.1 : Useful sign
E E
M' Concave mirror
M'
h E h Convex
h h 3
2 Virtual image (u< f) mirror
Real image (u ≥ f)
M' M'
L B Distance of object u – u – u –
d d Distance of image v – v + v +
(A) (B)
Focal length f – f – f +
Fig. 29.6
Curved Mirror Height of object O + O+ O +
It is a part of a transparent hollow sphere whose one surface is Height of image I – I + I +
polished. Radius of curvature R – R – R +
Magnification m – m+ m +
C P P C Image Formation by Curved Mirrors
F F
Principal
axis
Concave mirror Convex mirror
Fig. 29.7
Concave mirror converges the light rays and used as a shaving mirror,
In search light, in cinema projector, in telescope, by E.N.T. specialists etc.
Convex mirror diverges the light rays and used in road lamps, side
mirror in vehicles etc. Concave mirror : Image formed by concave mirror may be real or
virtual, may be inverted or erect, may be smaller, larger or equal in size of
(1) Terminology object.
(i) Pole (P) : Mid point of the mirror (1) When object is placed at infinite (i.e. u = )
(ii) Centre of curvature (C) : Centre of the sphere of which the mirror
is a part. Image
At F
(iii) Radius of curvature (R): Distance between pole and centre of
Real F P
curvature. (R = –ve , R = +ve , R = )
concave convex plane
Inverted
(iv) Principle axis : A line passing through P and C. Very small in size
Fig. 29.9
, 1638 Ray Optics
Magnification m << – 1 Small in size
Magnification m < + 1
(2) When object is placed between infinite and centre of curvature (i.e.
u > 2f)
Mirror Formula and Magnification
Image For a spherical mirror if u = Distance of object from pole, v = distance
Between F and C
Real of image from pole, f = Focal length, R = Radius of curvature, O = Size of
Inverted C F P object, I = size of image
Small in size
m<–1 1 1 1
(1) Mirror formula :
f v u
Fig. 29.10(i.e. u = 2f)
(3) When object is placed at centre of curvature
(2) Lateral magnification : When an object is placed perpendicular to
Image the principle axis, then linear magnification is called lateral or transverse
At C magnification.
Real
Inverted F P I v f f v
Equal in size C m
O u f u f
m=–1
(* Always use sign convention while solving the problems)
(4) When object is placed between centreFig. curvature and focus (i.e. f
of 29.11
< u < 2f) Axial magnification : When object lies along the principle axis then its
I (v 2 v 1 )
Image axial magnification m
O (u 2 u 1 )
Between 2f and
Real F P 2 2 2
dv v f f v
Inverted C If object is small; m
Large in size du u f u f
m>–1 Areal magnification : If a 2D-object is placed with it's plane
Fig. 29.12 perpendicular to principle axis. It's Areal magnification
(5) When object is placed at focus (i.e. u = f)
Area of image ( Ai ) A
ms ms m 2 i
Image Area of object ( Ao ) Ao
At
Real P
Inverted C F
Very large in size
m >> – 1
(6) When object is placed between focus Fig.
and29.13
pole (i.e. u < f)
Image
Behind the mirror
Virtual
Erect P
Large in size C F
m>+1
Convex mirror : Image formed by convex mirror Fig. 29.14
is always virtual, erect
and smaller in size.
(1) When object is placed at infinite (i.e. u = )
Image
At F
Virtual
Erect P F
Very small in size
Magnification m << + 1
Fig. 29.15 axis
(2) When object is placed any where on the principal
Image
Between P and F
Virtual
Erect
P F C
Fig. 29.16
, Ray Optics 1639
(3) Absolute refractive index : When light travels from vacuum to any
Refraction of Light transparent medium then refractive index of medium w.r.t. vacuum is called
The bending of the ray of light passing from one medium to the other c
it’s absolute refractive index i.e. vacuum medium
medium is called refraction. v
Absolute refractive indices for glass, water and diamond are
3 4 12
respectively g 1.5, w 1.33 and D 2.4
2 3 5
(4) Relative refractive index : When light travels from medium (1) to
medium (2) then refractive index of medium (2) w.r.t. medium (1) is called
v
it’s relative refractive index i.e. 1 2 2 1 (where v and v are the
1 v 2 1 2
Princ (B) (C)
ipal speed of light in medium 1 and 2 respectively).
Axis Fig. 29.17 (5) When we say refractive index we mean absolute refractive index.
2
(1) The refraction of light takes place on going from one medium to
(A) (6) The minimum value of absolute refractive index is 1. For air it is
another because the speed of light is different in the two media. very near to 1. ( ~ 1.003 )
(2) Greater the difference in the speeds of light in the two media, B C
greater will be the amount of refraction. (7) Cauchy’s equation : A ......
2 4
(3) A medium in which the speed of light is more is known as
(Red violet so Red violet )
optically rarer medium and a medium is which the speed of light is less, is
known as optically denser medium. (8) If a light ray travels from medium (1) to medium (2), then
(4) When a ray of light goes from a rarer medium to a denser 2 1 v 1
1 2
medium, it bends towards the normal. 1 2 v 2
(9) Dependence of Refractive index
Incident ray
i Rarer medium (i) Nature of the media of incidence and refraction.
(ii) Colour of light or wavelength of light.
(iii) Temperature of the media : Refractive index decreases with the
Deviation = (i – r) increase in temperature.
Table 29.2 : Indices of refraction for various substances, Measured with
Denser medium Refracted ray light of vacuum wavelength = 589 nm 0
(5) When a ray of light goesFig. 29.18a denser medium to a rarer
from Substance Refractive Substance Refractive
medium, it bends away from the normal. index index
Solids at 20°C Liquids at 20°C
Denser medium Diamond (C) 2.419 Benzene 1.501
Fluorite (CaF2) 1.434 Carbon disulfide 1.628
i
Deviation = (r – i ) Flused quartz (SiO2) 1.458 Carbon tetrachloride 1.461
Glass, crown 1.52 Ethyl alcohol 1.361
r
Glass, flint 1.66 Glycerine 1.473
Rarer medium
o
Ice (H2O) (at 0 C) 1.309 Water 1.333
Fig. 29.19 Polystyrene 1.49 Gases at 0°C,
(6) Snell’s law : The ratio of sine of the angle of incidence to the angle
of refraction (r) is a constant called refractive index 1 atm
Sodium chloride 1.544 Air 1.000293
sin i
i.e. (a constant). For two media, Snell's law can be Zircon 1.923 Carbon dioxide 1.00045
sin r
sini (10) Reversibility of light and refraction through several media
written as 1 2 2
1 sinr Incident ray
1
1 sini 2 sinr i.e. sin constant 1
i 2
Also in vector form : ˆi nˆ ( rˆ nˆ )
r
3
Refractive Index 2
(1) Refractive index of a medium is that characteristic which decides 1
speed of light in it. 1 2 2 3 3 1 1
1
(A) 1 2 (B) 1 3
(2) It is a scalar, unit less and dimensionless quantity.
2 1
or 2 3
1 2
Fig. 29.20
