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147
UNIT 6: UNIT 6: UNIT 6: UNIT 6: OPTICS OPTICS OPTICS OPTICS
RAY OPTICS AND OPTICAL INSTRUMENTS RAY OPTICS AND OPTICAL INSTRUMENTS RAY OPTICS AND OPTICAL INSTRUMENTS RAY OPTICS AND OPTICAL INSTRUMENTS
REFLECTION OF LIGHT
Reflection When light travelling in a medium strikes a reflecting surface, it goes back into the same
medium obeying certain laws. This phenomenon is known as reflection of light.
Laws of reflection of light
(i) The angle of incidence (i.e. i ? ) is equal to the angle of
reflection (i.e. ? r).
(ii) The incident ray, the normal to the mirror at the point of
incidence and the reflected ray lie in the same plane.
Spherical mirror: The portion of a reflecting surface, which forms part of a sphere is called a
spherical mirror.
Concave Spherical mirror. A spherical mirror, whose reflecting surface is towards the centre of
the sphere, of which the mirror forms a part is called concave spherical mirror.
Convex Spherical mirror: A spherical mirror, whose reflecting surface is away from the centre
of the sphere, of which the mirror forms a part is called convex spherical mirror.
Centre of curvature. The centre of the sphere, of which the mirror forms a part, is called the
centre of curvature of the mirror.
Radius of curvature. The radius of the sphere, of which the mirror forms a part, is called the
radius of curvature of the mirror.
Pole. The centre of the spherical mirror is called its pole.
Principal axis: The line joining the pole and the centre of curvature of the mirror is called the
principal axis of the mirror.
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147
UNIT 6: UNIT 6: UNIT 6: UNIT 6: OPTICS OPTICS OPTICS OPTICS
RAY OPTICS AND OPTICAL INSTRUMENTS RAY OPTICS AND OPTICAL INSTRUMENTS RAY OPTICS AND OPTICAL INSTRUMENTS RAY OPTICS AND OPTICAL INSTRUMENTS
REFLECTION OF LIGHT
Reflection When light travelling in a medium strikes a reflecting surface, it goes back into the same
medium obeying certain laws. This phenomenon is known as reflection of light.
Laws of reflection of light
(i) The angle of incidence (i.e. i ? ) is equal to the angle of
reflection (i.e. ? r).
(ii) The incident ray, the normal to the mirror at the point of
incidence and the reflected ray lie in the same plane.
Spherical mirror: The portion of a reflecting surface, which forms part of a sphere is called a
spherical mirror.
Concave Spherical mirror. A spherical mirror, whose reflecting surface is towards the centre of
the sphere, of which the mirror forms a part is called concave spherical mirror.
Convex Spherical mirror: A spherical mirror, whose reflecting surface is away from the centre
of the sphere, of which the mirror forms a part is called convex spherical mirror.
Centre of curvature. The centre of the sphere, of which the mirror forms a part, is called the
centre of curvature of the mirror.
Radius of curvature. The radius of the sphere, of which the mirror forms a part, is called the
radius of curvature of the mirror.
Pole. The centre of the spherical mirror is called its pole.
Principal axis: The line joining the pole and the centre of curvature of the mirror is called the
principal axis of the mirror.
148
Aperture: The diameter of the mirror is called the aperture of the mirror.
Principal focus: The point at which a narrow beam of light which is incident on the mirror parallel
to its principal axis, after reflection from the mirror, meets or appears to come from, is called the
principal focus of the mirror.
Focal length: The distance between the pole and the principal focus of the mirror is called the focal
length of the mirror.
Sign convention
Relation between f and R
Consider a ray parallel to the principal axis striking the mirror at M.
Then CM will be perpendicular to the mirror at M. Let ? be the angle
of incidence, and MD be the perpendicular from M on the
principal axis. Then, ? MCP = ? and ? MFP = 2?
FD
MD
and
CD
MD
= = ? ? 2 tan tan ---------------------------------------- (1)
For small ?, which is true for paraxial rays, tan? ˜ ?, tan 2? ˜ 2?. Therefore, Eq. (1) gives
2
2
CD
FD Or
CD
MD
FD
MD
= = --------------------------------------------- (2)
Now, for small ?, the point D is very close to the point P. Therefore, FD = f and CD = R. Equation (2)
then gives f = R/2
Mirror Formula.
similar are C B A and ABC s
' ' '
?
CB
CB
AB
B A
' ' '
= ------------------------------ (1)
similar are P B A and ABP s
' '
?
PB
PB
AB
B A
' ' '
= ------------------------------- (2)
From equation (1) and (2)
PC PB
PB PC
CB
CB
PB
PB
-
-
= =
' ' '
----------------- (3)
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UNIT 6: UNIT 6: UNIT 6: UNIT 6: OPTICS OPTICS OPTICS OPTICS
RAY OPTICS AND OPTICAL INSTRUMENTS RAY OPTICS AND OPTICAL INSTRUMENTS RAY OPTICS AND OPTICAL INSTRUMENTS RAY OPTICS AND OPTICAL INSTRUMENTS
REFLECTION OF LIGHT
Reflection When light travelling in a medium strikes a reflecting surface, it goes back into the same
medium obeying certain laws. This phenomenon is known as reflection of light.
Laws of reflection of light
(i) The angle of incidence (i.e. i ? ) is equal to the angle of
reflection (i.e. ? r).
(ii) The incident ray, the normal to the mirror at the point of
incidence and the reflected ray lie in the same plane.
Spherical mirror: The portion of a reflecting surface, which forms part of a sphere is called a
spherical mirror.
Concave Spherical mirror. A spherical mirror, whose reflecting surface is towards the centre of
the sphere, of which the mirror forms a part is called concave spherical mirror.
Convex Spherical mirror: A spherical mirror, whose reflecting surface is away from the centre
of the sphere, of which the mirror forms a part is called convex spherical mirror.
Centre of curvature. The centre of the sphere, of which the mirror forms a part, is called the
centre of curvature of the mirror.
Radius of curvature. The radius of the sphere, of which the mirror forms a part, is called the
radius of curvature of the mirror.
Pole. The centre of the spherical mirror is called its pole.
Principal axis: The line joining the pole and the centre of curvature of the mirror is called the
principal axis of the mirror.
148
Aperture: The diameter of the mirror is called the aperture of the mirror.
Principal focus: The point at which a narrow beam of light which is incident on the mirror parallel
to its principal axis, after reflection from the mirror, meets or appears to come from, is called the
principal focus of the mirror.
Focal length: The distance between the pole and the principal focus of the mirror is called the focal
length of the mirror.
Sign convention
Relation between f and R
Consider a ray parallel to the principal axis striking the mirror at M.
Then CM will be perpendicular to the mirror at M. Let ? be the angle
of incidence, and MD be the perpendicular from M on the
principal axis. Then, ? MCP = ? and ? MFP = 2?
FD
MD
and
CD
MD
= = ? ? 2 tan tan ---------------------------------------- (1)
For small ?, which is true for paraxial rays, tan? ˜ ?, tan 2? ˜ 2?. Therefore, Eq. (1) gives
2
2
CD
FD Or
CD
MD
FD
MD
= = --------------------------------------------- (2)
Now, for small ?, the point D is very close to the point P. Therefore, FD = f and CD = R. Equation (2)
then gives f = R/2
Mirror Formula.
similar are C B A and ABC s
' ' '
?
CB
CB
AB
B A
' ' '
= ------------------------------ (1)
similar are P B A and ABP s
' '
?
PB
PB
AB
B A
' ' '
= ------------------------------- (2)
From equation (1) and (2)
PC PB
PB PC
CB
CB
PB
PB
-
-
= =
' ' '
----------------- (3)
149
R PC v PB u PB - = - = - = , ,
'
R u
v R
u
v
+ -
+ -
=
-
-
Or
f R But
uv uv uR vR
2 =
+ = +
uv f u f v 2 2 2 = +
v u f u f v = +
Divide both side by f v u
v u f
1 1 1
+ =
where u and v denote the object and image distances from the pole of the mirror.
Linear magnification: The ratio of the size of the image (formed by the mirror) to size of the
object is called linear magnification produced by the mirror.
Mathematically,
f
v f
f u
f
u
v
O
I
m
-
=
-
= - = =
According to new Cartesian sign conventions, when the image formed is real (inverted), the
magnification produced by the mirror is negative and when the image formed is virtual (erect),
the magnification produced by the mirror is positive.
REFRACTION OF LIGHT
Refraction: The phenomenon of change in the path of light as it goes from one transparent
medium to another transparent medium is called refraction.
Laws of refraction:
1. The incident ray, the normal to the refracting surface
at the point of incidence and the refracted ray all lie in
the same plane.
2. The ratio of the sine of the angle of incidence to the
sine of the angle of refraction is constant for any two
given media. It is called Snell’s law.
Mathematically,
21
sin
sin
n
r
i
=
Here, n
21
is called the relative refractive index of medium 2 (in which the refracted ray travels)
w.r.t. medium 1 (in which the incident ray travels).
Absolute refractive index: The absolute refractive index of a medium is defined as the ratio of
the velocity of light in the vacuum (c) to the velocity of light in that medium (v).
Mathematically: Absolute refractive index,
v
c
n=
Principle of reversibility of light: It states that if light after suffering any number of reflections
and refractions has its final path reversed, it travels back along the same path in the opposite direction.
It leads to result that the refractive index of the medium 2 w.r.t. medium 1 is equal
to the reciprocal of the refractive index of the medium 1 w. r. t. the medium 2.
Mathematically:
12
21
1
n
n =
REFRACTION THROUGH A PARALLEL SLAB
When a ray of light passes through a parallel-sided transparent slab, the emergent ray is parallel to the
incident ray, although there is a lateral displacement.
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UNIT 6: UNIT 6: UNIT 6: UNIT 6: OPTICS OPTICS OPTICS OPTICS
RAY OPTICS AND OPTICAL INSTRUMENTS RAY OPTICS AND OPTICAL INSTRUMENTS RAY OPTICS AND OPTICAL INSTRUMENTS RAY OPTICS AND OPTICAL INSTRUMENTS
REFLECTION OF LIGHT
Reflection When light travelling in a medium strikes a reflecting surface, it goes back into the same
medium obeying certain laws. This phenomenon is known as reflection of light.
Laws of reflection of light
(i) The angle of incidence (i.e. i ? ) is equal to the angle of
reflection (i.e. ? r).
(ii) The incident ray, the normal to the mirror at the point of
incidence and the reflected ray lie in the same plane.
Spherical mirror: The portion of a reflecting surface, which forms part of a sphere is called a
spherical mirror.
Concave Spherical mirror. A spherical mirror, whose reflecting surface is towards the centre of
the sphere, of which the mirror forms a part is called concave spherical mirror.
Convex Spherical mirror: A spherical mirror, whose reflecting surface is away from the centre
of the sphere, of which the mirror forms a part is called convex spherical mirror.
Centre of curvature. The centre of the sphere, of which the mirror forms a part, is called the
centre of curvature of the mirror.
Radius of curvature. The radius of the sphere, of which the mirror forms a part, is called the
radius of curvature of the mirror.
Pole. The centre of the spherical mirror is called its pole.
Principal axis: The line joining the pole and the centre of curvature of the mirror is called the
principal axis of the mirror.
148
Aperture: The diameter of the mirror is called the aperture of the mirror.
Principal focus: The point at which a narrow beam of light which is incident on the mirror parallel
to its principal axis, after reflection from the mirror, meets or appears to come from, is called the
principal focus of the mirror.
Focal length: The distance between the pole and the principal focus of the mirror is called the focal
length of the mirror.
Sign convention
Relation between f and R
Consider a ray parallel to the principal axis striking the mirror at M.
Then CM will be perpendicular to the mirror at M. Let ? be the angle
of incidence, and MD be the perpendicular from M on the
principal axis. Then, ? MCP = ? and ? MFP = 2?
FD
MD
and
CD
MD
= = ? ? 2 tan tan ---------------------------------------- (1)
For small ?, which is true for paraxial rays, tan? ˜ ?, tan 2? ˜ 2?. Therefore, Eq. (1) gives
2
2
CD
FD Or
CD
MD
FD
MD
= = --------------------------------------------- (2)
Now, for small ?, the point D is very close to the point P. Therefore, FD = f and CD = R. Equation (2)
then gives f = R/2
Mirror Formula.
similar are C B A and ABC s
' ' '
?
CB
CB
AB
B A
' ' '
= ------------------------------ (1)
similar are P B A and ABP s
' '
?
PB
PB
AB
B A
' ' '
= ------------------------------- (2)
From equation (1) and (2)
PC PB
PB PC
CB
CB
PB
PB
-
-
= =
' ' '
----------------- (3)
149
R PC v PB u PB - = - = - = , ,
'
R u
v R
u
v
+ -
+ -
=
-
-
Or
f R But
uv uv uR vR
2 =
+ = +
uv f u f v 2 2 2 = +
v u f u f v = +
Divide both side by f v u
v u f
1 1 1
+ =
where u and v denote the object and image distances from the pole of the mirror.
Linear magnification: The ratio of the size of the image (formed by the mirror) to size of the
object is called linear magnification produced by the mirror.
Mathematically,
f
v f
f u
f
u
v
O
I
m
-
=
-
= - = =
According to new Cartesian sign conventions, when the image formed is real (inverted), the
magnification produced by the mirror is negative and when the image formed is virtual (erect),
the magnification produced by the mirror is positive.
REFRACTION OF LIGHT
Refraction: The phenomenon of change in the path of light as it goes from one transparent
medium to another transparent medium is called refraction.
Laws of refraction:
1. The incident ray, the normal to the refracting surface
at the point of incidence and the refracted ray all lie in
the same plane.
2. The ratio of the sine of the angle of incidence to the
sine of the angle of refraction is constant for any two
given media. It is called Snell’s law.
Mathematically,
21
sin
sin
n
r
i
=
Here, n
21
is called the relative refractive index of medium 2 (in which the refracted ray travels)
w.r.t. medium 1 (in which the incident ray travels).
Absolute refractive index: The absolute refractive index of a medium is defined as the ratio of
the velocity of light in the vacuum (c) to the velocity of light in that medium (v).
Mathematically: Absolute refractive index,
v
c
n=
Principle of reversibility of light: It states that if light after suffering any number of reflections
and refractions has its final path reversed, it travels back along the same path in the opposite direction.
It leads to result that the refractive index of the medium 2 w.r.t. medium 1 is equal
to the reciprocal of the refractive index of the medium 1 w. r. t. the medium 2.
Mathematically:
12
21
1
n
n =
REFRACTION THROUGH A PARALLEL SLAB
When a ray of light passes through a parallel-sided transparent slab, the emergent ray is parallel to the
incident ray, although there is a lateral displacement.
150
Consider a parallel-sided slab KLMN having parallel faces KL and NM as shown in Fig. A ray of light
AO in air (medium ‘1’) is incident on the glass surface KL (medium ‘2’) at point O. The ray bends
towards the normal and follows the path OB. At point B, again refraction takes place and the ray
bends away from the normal, emerging out of glass follow path BC and the emergent ray BC becomes
parallel to the incident ray AO.
At point O,
1
1
21
sin
sin
r
i
n = ----------------- (1)
At point B,
2
2
12
sin
sin
r
i
n = ------------------ (2)
Now place a plane mirror at C perpendicular to
the emergent ray CB then refracted ray retrace its
path exactly then,
For reversed ray, apply snell’s law at point B on
surface MN
2
2
21
sin
sin
i
r
n = -------------------------------- (3)
From equation 1 and 3
1
1
sin
sin
r
i
2
2
sin
sin
i
r
= ------------------------------ (4)
NM KL Q
2 1
i r = ?
2 1
sin sin i r =
Equation (4 ) becomes
1
1
sin
sin
r
i
1
2
sin
sin
r
r
= ------------------------------ (5)
2 1
2 1
sin sin
r i
r i
=
=
Thus when a ray of light passes through a parallel-sided transparent slab, the emergent ray is parallel
to the incident ray. However, it is laterally displaced.
Expression for lateral displacement
The perpendicular distance between the incident and the emergent rays, when the light is incident
obliquely on a parallel sided slab of a refracting material is called lateral shift / displacement.
Drop a - BD on AO produced.
Let ? BOD = d = Deviation on refraction at surface KL
In ? BOD,
BD = OB sin d ----------------------- (6)
In ? OEB,
1
cos r
OE
OB= ---------------------------- (7)
where OE = t = Thickness of glass slab
From equation (6)
( )
1
1 1
1
cos
sin
sin
cos r
r i t
r
t
BD
-
= = d = lateral shift / displacement
Page 5
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UNIT 6: UNIT 6: UNIT 6: UNIT 6: OPTICS OPTICS OPTICS OPTICS
RAY OPTICS AND OPTICAL INSTRUMENTS RAY OPTICS AND OPTICAL INSTRUMENTS RAY OPTICS AND OPTICAL INSTRUMENTS RAY OPTICS AND OPTICAL INSTRUMENTS
REFLECTION OF LIGHT
Reflection When light travelling in a medium strikes a reflecting surface, it goes back into the same
medium obeying certain laws. This phenomenon is known as reflection of light.
Laws of reflection of light
(i) The angle of incidence (i.e. i ? ) is equal to the angle of
reflection (i.e. ? r).
(ii) The incident ray, the normal to the mirror at the point of
incidence and the reflected ray lie in the same plane.
Spherical mirror: The portion of a reflecting surface, which forms part of a sphere is called a
spherical mirror.
Concave Spherical mirror. A spherical mirror, whose reflecting surface is towards the centre of
the sphere, of which the mirror forms a part is called concave spherical mirror.
Convex Spherical mirror: A spherical mirror, whose reflecting surface is away from the centre
of the sphere, of which the mirror forms a part is called convex spherical mirror.
Centre of curvature. The centre of the sphere, of which the mirror forms a part, is called the
centre of curvature of the mirror.
Radius of curvature. The radius of the sphere, of which the mirror forms a part, is called the
radius of curvature of the mirror.
Pole. The centre of the spherical mirror is called its pole.
Principal axis: The line joining the pole and the centre of curvature of the mirror is called the
principal axis of the mirror.
148
Aperture: The diameter of the mirror is called the aperture of the mirror.
Principal focus: The point at which a narrow beam of light which is incident on the mirror parallel
to its principal axis, after reflection from the mirror, meets or appears to come from, is called the
principal focus of the mirror.
Focal length: The distance between the pole and the principal focus of the mirror is called the focal
length of the mirror.
Sign convention
Relation between f and R
Consider a ray parallel to the principal axis striking the mirror at M.
Then CM will be perpendicular to the mirror at M. Let ? be the angle
of incidence, and MD be the perpendicular from M on the
principal axis. Then, ? MCP = ? and ? MFP = 2?
FD
MD
and
CD
MD
= = ? ? 2 tan tan ---------------------------------------- (1)
For small ?, which is true for paraxial rays, tan? ˜ ?, tan 2? ˜ 2?. Therefore, Eq. (1) gives
2
2
CD
FD Or
CD
MD
FD
MD
= = --------------------------------------------- (2)
Now, for small ?, the point D is very close to the point P. Therefore, FD = f and CD = R. Equation (2)
then gives f = R/2
Mirror Formula.
similar are C B A and ABC s
' ' '
?
CB
CB
AB
B A
' ' '
= ------------------------------ (1)
similar are P B A and ABP s
' '
?
PB
PB
AB
B A
' ' '
= ------------------------------- (2)
From equation (1) and (2)
PC PB
PB PC
CB
CB
PB
PB
-
-
= =
' ' '
----------------- (3)
149
R PC v PB u PB - = - = - = , ,
'
R u
v R
u
v
+ -
+ -
=
-
-
Or
f R But
uv uv uR vR
2 =
+ = +
uv f u f v 2 2 2 = +
v u f u f v = +
Divide both side by f v u
v u f
1 1 1
+ =
where u and v denote the object and image distances from the pole of the mirror.
Linear magnification: The ratio of the size of the image (formed by the mirror) to size of the
object is called linear magnification produced by the mirror.
Mathematically,
f
v f
f u
f
u
v
O
I
m
-
=
-
= - = =
According to new Cartesian sign conventions, when the image formed is real (inverted), the
magnification produced by the mirror is negative and when the image formed is virtual (erect),
the magnification produced by the mirror is positive.
REFRACTION OF LIGHT
Refraction: The phenomenon of change in the path of light as it goes from one transparent
medium to another transparent medium is called refraction.
Laws of refraction:
1. The incident ray, the normal to the refracting surface
at the point of incidence and the refracted ray all lie in
the same plane.
2. The ratio of the sine of the angle of incidence to the
sine of the angle of refraction is constant for any two
given media. It is called Snell’s law.
Mathematically,
21
sin
sin
n
r
i
=
Here, n
21
is called the relative refractive index of medium 2 (in which the refracted ray travels)
w.r.t. medium 1 (in which the incident ray travels).
Absolute refractive index: The absolute refractive index of a medium is defined as the ratio of
the velocity of light in the vacuum (c) to the velocity of light in that medium (v).
Mathematically: Absolute refractive index,
v
c
n=
Principle of reversibility of light: It states that if light after suffering any number of reflections
and refractions has its final path reversed, it travels back along the same path in the opposite direction.
It leads to result that the refractive index of the medium 2 w.r.t. medium 1 is equal
to the reciprocal of the refractive index of the medium 1 w. r. t. the medium 2.
Mathematically:
12
21
1
n
n =
REFRACTION THROUGH A PARALLEL SLAB
When a ray of light passes through a parallel-sided transparent slab, the emergent ray is parallel to the
incident ray, although there is a lateral displacement.
150
Consider a parallel-sided slab KLMN having parallel faces KL and NM as shown in Fig. A ray of light
AO in air (medium ‘1’) is incident on the glass surface KL (medium ‘2’) at point O. The ray bends
towards the normal and follows the path OB. At point B, again refraction takes place and the ray
bends away from the normal, emerging out of glass follow path BC and the emergent ray BC becomes
parallel to the incident ray AO.
At point O,
1
1
21
sin
sin
r
i
n = ----------------- (1)
At point B,
2
2
12
sin
sin
r
i
n = ------------------ (2)
Now place a plane mirror at C perpendicular to
the emergent ray CB then refracted ray retrace its
path exactly then,
For reversed ray, apply snell’s law at point B on
surface MN
2
2
21
sin
sin
i
r
n = -------------------------------- (3)
From equation 1 and 3
1
1
sin
sin
r
i
2
2
sin
sin
i
r
= ------------------------------ (4)
NM KL Q
2 1
i r = ?
2 1
sin sin i r =
Equation (4 ) becomes
1
1
sin
sin
r
i
1
2
sin
sin
r
r
= ------------------------------ (5)
2 1
2 1
sin sin
r i
r i
=
=
Thus when a ray of light passes through a parallel-sided transparent slab, the emergent ray is parallel
to the incident ray. However, it is laterally displaced.
Expression for lateral displacement
The perpendicular distance between the incident and the emergent rays, when the light is incident
obliquely on a parallel sided slab of a refracting material is called lateral shift / displacement.
Drop a - BD on AO produced.
Let ? BOD = d = Deviation on refraction at surface KL
In ? BOD,
BD = OB sin d ----------------------- (6)
In ? OEB,
1
cos r
OE
OB= ---------------------------- (7)
where OE = t = Thickness of glass slab
From equation (6)
( )
1
1 1
1
cos
sin
sin
cos r
r i t
r
t
BD
-
= = d = lateral shift / displacement
151
Real and apparent depth: When an object is placed in an optically denser medium, the apparent
depth of the object is always less than its real depth.
Mathematically: 1.
21
Re
n
depth Apparent
depth al
=
Mathematically: 2. Normal shift,
?
?
?
?
?
?
?
?
- =
21
1
1
n
t d
Advance sunrise and delayed sunset due to atmospheric refraction.
Total internal reflection: The phenomenon of reflection of light that takes place when a ray of
light traveling in a denser medium gets incident at the interface of the two media at an angle greater
than the critical angle for that pair of media.
Mathematically:
c
i
n
sin
1
21
=
Here, n
21
is the refractive index of the denser
medium 2 w.r.t. the rarer medium 1 and
c
i is
the critical
Critical angle: for a given pair of media it
is the angle of incidence for which the angle of refraction is 90
o
when light is traveling from denser
medium to rarer medium.
Mathematically:
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