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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. 
Page 2


  
             
             
             
             
             
  
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) 
Page 3


  
             
             
             
             
             
  
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) 
   
 
                                                         
             
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.  
 
 
 
Page 4


  
             
             
             
             
             
  
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) 
   
 
                                                         
             
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


  
             
             
             
             
             
  
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) 
   
 
                                                         
             
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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FAQs on Unit 6: Optics - Ray Optics & Optical Instruments - Class 11

1. What is ray optics and how does it differ from wave optics?
Ans. Ray optics is a branch of optics that deals with the study of light as a ray, considering it as a straight line that travels in a uniform medium. It focuses on the behavior of light when it interacts with objects and surfaces. On the other hand, wave optics considers light as a wave and studies its phenomena such as interference, diffraction, and polarization. The main difference between the two is that ray optics simplifies the behavior of light by assuming it as a straight line, while wave optics takes into account the wave nature of light.
2. How does refraction work in ray optics?
Ans. Refraction in ray optics occurs when light passes from one medium to another with a different refractive index. When light enters a denser medium, it bends towards the normal, and when it enters a rarer medium, it bends away from the normal. This bending is due to the change in the speed of light as it travels from one medium to another. The phenomenon of refraction follows Snell's Law, which states that the ratio of the sine of the angle of incidence to the sine of the angle of refraction is equal to the ratio of the speeds of light in the two media.
3. What are the different types of lenses used in optical instruments?
Ans. There are two main types of lenses used in optical instruments: convex lenses and concave lenses. - Convex lenses are thicker in the middle and thinner at the edges. They converge parallel rays of light to a focal point and are often used in devices such as cameras, telescopes, and magnifying glasses. - Concave lenses are thinner in the middle and thicker at the edges. They diverge parallel rays of light and are used in devices like eyeglasses to correct nearsightedness. Both types of lenses have specific properties that allow them to manipulate light and form images.
4. How does a microscope work based on ray optics?
Ans. A microscope works based on the principles of ray optics. It uses a combination of lenses to magnify small objects and bring them into focus. The objective lens, which is closer to the object being observed, forms a magnified real image of the object. This image is then further magnified by the eyepiece lens, which allows the viewer to see the enlarged virtual image. The overall magnification of the microscope is the product of the magnifications of the objective and eyepiece lenses. The use of lenses in a microscope helps to increase the resolution and clarity of the observed objects.
5. What is the working principle of a telescope?
Ans. A telescope works on the principle of ray optics to observe distant objects. It uses a combination of lenses or mirrors to collect and focus light. The objective lens or mirror gathers incoming parallel rays of light and forms a real, inverted image at the focal point. This image is then magnified by the eyepiece lens, which allows the viewer to see the enlarged, virtual image. The overall magnification of the telescope is determined by the ratio of the focal lengths of the objective and eyepiece lenses. By manipulating the positions and properties of the lenses or mirrors, telescopes can provide enhanced views of celestial objects, making them appear closer and clearer.
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