Ray Optics | Physics Optional Notes for UPSC PDF Download

 Page 1


RAY OPTICS 
INTRODUCTION 
Optics is a branch of physics that studies how light behaves. When dealing with things 
like mirrors and lenses that are much bigger than the wavelength of light, we can treat 
light as if it travels in straight lines, like rays. This part of optics, where we use simple 
geometric rules to understand how light moves, is called geometric optics. 
PROPAGATION OF LIGHT 
 
Light usually moves in a straight line through a material or in empty space. It only 
changes direction when something gets in its way or when it moves from one material to 
another. This straight-line movement of light is called rectilinear propagation. If light 
starts from one point and goes to another, it actually travels through all the points in a 
straight line between them. We call this straight line path a ray of light. Light rays start 
from every point of a light source and move straight until they hit something, like an 
object or a surface between two materials. A group of light rays together is called a beam 
of light. 
 ( ? ) Apart from vacuum and gases, light can travel through some liquids and solids. A 
medium in which light can travel freely over large distances is called a transparent 
medium. Water, glycerin, glass and clear plastics are transparent. A medium in which 
light cannot travel is called opaque. Wood, metals, bricks, etc., are opaque. In materials 
like oil, light can travel some distance, but its intensity reduces rapidly. Such materials 
are called translucent. 
 
Ray:   The straight line path along which the light travels in a homogeneous medium is 
called a ray. 
 
Beam: A bundle or bunch of rays is called a beam. It is of following three types: 
(a) Convergent beam: In this case diameter of beam decreases in the direction of ray. 
 
Page 2


RAY OPTICS 
INTRODUCTION 
Optics is a branch of physics that studies how light behaves. When dealing with things 
like mirrors and lenses that are much bigger than the wavelength of light, we can treat 
light as if it travels in straight lines, like rays. This part of optics, where we use simple 
geometric rules to understand how light moves, is called geometric optics. 
PROPAGATION OF LIGHT 
 
Light usually moves in a straight line through a material or in empty space. It only 
changes direction when something gets in its way or when it moves from one material to 
another. This straight-line movement of light is called rectilinear propagation. If light 
starts from one point and goes to another, it actually travels through all the points in a 
straight line between them. We call this straight line path a ray of light. Light rays start 
from every point of a light source and move straight until they hit something, like an 
object or a surface between two materials. A group of light rays together is called a beam 
of light. 
 ( ? ) Apart from vacuum and gases, light can travel through some liquids and solids. A 
medium in which light can travel freely over large distances is called a transparent 
medium. Water, glycerin, glass and clear plastics are transparent. A medium in which 
light cannot travel is called opaque. Wood, metals, bricks, etc., are opaque. In materials 
like oil, light can travel some distance, but its intensity reduces rapidly. Such materials 
are called translucent. 
 
Ray:   The straight line path along which the light travels in a homogeneous medium is 
called a ray. 
 
Beam: A bundle or bunch of rays is called a beam. It is of following three types: 
(a) Convergent beam: In this case diameter of beam decreases in the direction of ray. 
 
(b) Divergent beam: It is a beam in which all the rays meet at a point when produced 
backward and the diameter of beam goes on increasing as the rays proceed forward. 
 
 
(c) Parallel beam: It is a beam in which all the rays constituting the beam move parallel 
to each other and diameter of beam remains same. 
 
Naming convention: 
 
REFLECTION OF LIGHT 
When light rays strike the boundary of two media such as air and glass, a part of light is 
bounced back into the same medium. This is called Reflection of light. 
(i) Regular/Specular reflection: 
When the reflection takes place from a perfect plane surface then after reflection rays 
remain parallel. 
It is called Regular reflection. 
 
(ii) Diffused reflection 
When the surface is rough, light is reflected from the surface from bits of its plane 
surfaces in irregular directions. This is called diffused reflection. This process enables us 
to see an object from any position. 
 
Page 3


RAY OPTICS 
INTRODUCTION 
Optics is a branch of physics that studies how light behaves. When dealing with things 
like mirrors and lenses that are much bigger than the wavelength of light, we can treat 
light as if it travels in straight lines, like rays. This part of optics, where we use simple 
geometric rules to understand how light moves, is called geometric optics. 
PROPAGATION OF LIGHT 
 
Light usually moves in a straight line through a material or in empty space. It only 
changes direction when something gets in its way or when it moves from one material to 
another. This straight-line movement of light is called rectilinear propagation. If light 
starts from one point and goes to another, it actually travels through all the points in a 
straight line between them. We call this straight line path a ray of light. Light rays start 
from every point of a light source and move straight until they hit something, like an 
object or a surface between two materials. A group of light rays together is called a beam 
of light. 
 ( ? ) Apart from vacuum and gases, light can travel through some liquids and solids. A 
medium in which light can travel freely over large distances is called a transparent 
medium. Water, glycerin, glass and clear plastics are transparent. A medium in which 
light cannot travel is called opaque. Wood, metals, bricks, etc., are opaque. In materials 
like oil, light can travel some distance, but its intensity reduces rapidly. Such materials 
are called translucent. 
 
Ray:   The straight line path along which the light travels in a homogeneous medium is 
called a ray. 
 
Beam: A bundle or bunch of rays is called a beam. It is of following three types: 
(a) Convergent beam: In this case diameter of beam decreases in the direction of ray. 
 
(b) Divergent beam: It is a beam in which all the rays meet at a point when produced 
backward and the diameter of beam goes on increasing as the rays proceed forward. 
 
 
(c) Parallel beam: It is a beam in which all the rays constituting the beam move parallel 
to each other and diameter of beam remains same. 
 
Naming convention: 
 
REFLECTION OF LIGHT 
When light rays strike the boundary of two media such as air and glass, a part of light is 
bounced back into the same medium. This is called Reflection of light. 
(i) Regular/Specular reflection: 
When the reflection takes place from a perfect plane surface then after reflection rays 
remain parallel. 
It is called Regular reflection. 
 
(ii) Diffused reflection 
When the surface is rough, light is reflected from the surface from bits of its plane 
surfaces in irregular directions. This is called diffused reflection. This process enables us 
to see an object from any position. 
 
LAWS OF REFLECTION 
(2) Incident ray, reflected ray and normal lies in the same plane. 
(2) The angle of reflection is equal to the angle of incident i.e. ?i=?r. 
 
 
In vector form 
??ˆ=??ˆ-?? (??ˆ.??ˆ)??ˆ 
Vector form of Law of Reflection: 
AB
????? 
+BD
????? 
=AD
????? 
CB
????? 
+BD
????? 
=CD
????? 
AD
????? 
=-CD
????? 
 
AB
????? 
+BD
????? 
=BC
????? 
+BD
????? 
?? ??ˆ+2(acos ????ˆ)=??ˆ?? ??ˆ=??ˆ+2cos ????ˆ
??ˆ·??ˆ=cos (?? -??)
??ˆ·??ˆ=-cos ?? 
 
From (1) & (2) 
??ˆ=??ˆ-2(??ˆ·??ˆ)??ˆ 
( ? ) Component of ê along the surface (i.e. ? to ??ˆ ) remain same. 
(C) Component of e ˆ ? to the surface (i.e. parallel to r ˆ ) gets inverted. 
( ? ) These laws are valid for any type of surface. 
Example. A light ray travelling along 3??ˆ-4??ˆ is reflected by a plane mirror placed in ?? -
?? plane. Find unit vector along reflected ray. 
Solution: 
Page 4


RAY OPTICS 
INTRODUCTION 
Optics is a branch of physics that studies how light behaves. When dealing with things 
like mirrors and lenses that are much bigger than the wavelength of light, we can treat 
light as if it travels in straight lines, like rays. This part of optics, where we use simple 
geometric rules to understand how light moves, is called geometric optics. 
PROPAGATION OF LIGHT 
 
Light usually moves in a straight line through a material or in empty space. It only 
changes direction when something gets in its way or when it moves from one material to 
another. This straight-line movement of light is called rectilinear propagation. If light 
starts from one point and goes to another, it actually travels through all the points in a 
straight line between them. We call this straight line path a ray of light. Light rays start 
from every point of a light source and move straight until they hit something, like an 
object or a surface between two materials. A group of light rays together is called a beam 
of light. 
 ( ? ) Apart from vacuum and gases, light can travel through some liquids and solids. A 
medium in which light can travel freely over large distances is called a transparent 
medium. Water, glycerin, glass and clear plastics are transparent. A medium in which 
light cannot travel is called opaque. Wood, metals, bricks, etc., are opaque. In materials 
like oil, light can travel some distance, but its intensity reduces rapidly. Such materials 
are called translucent. 
 
Ray:   The straight line path along which the light travels in a homogeneous medium is 
called a ray. 
 
Beam: A bundle or bunch of rays is called a beam. It is of following three types: 
(a) Convergent beam: In this case diameter of beam decreases in the direction of ray. 
 
(b) Divergent beam: It is a beam in which all the rays meet at a point when produced 
backward and the diameter of beam goes on increasing as the rays proceed forward. 
 
 
(c) Parallel beam: It is a beam in which all the rays constituting the beam move parallel 
to each other and diameter of beam remains same. 
 
Naming convention: 
 
REFLECTION OF LIGHT 
When light rays strike the boundary of two media such as air and glass, a part of light is 
bounced back into the same medium. This is called Reflection of light. 
(i) Regular/Specular reflection: 
When the reflection takes place from a perfect plane surface then after reflection rays 
remain parallel. 
It is called Regular reflection. 
 
(ii) Diffused reflection 
When the surface is rough, light is reflected from the surface from bits of its plane 
surfaces in irregular directions. This is called diffused reflection. This process enables us 
to see an object from any position. 
 
LAWS OF REFLECTION 
(2) Incident ray, reflected ray and normal lies in the same plane. 
(2) The angle of reflection is equal to the angle of incident i.e. ?i=?r. 
 
 
In vector form 
??ˆ=??ˆ-?? (??ˆ.??ˆ)??ˆ 
Vector form of Law of Reflection: 
AB
????? 
+BD
????? 
=AD
????? 
CB
????? 
+BD
????? 
=CD
????? 
AD
????? 
=-CD
????? 
 
AB
????? 
+BD
????? 
=BC
????? 
+BD
????? 
?? ??ˆ+2(acos ????ˆ)=??ˆ?? ??ˆ=??ˆ+2cos ????ˆ
??ˆ·??ˆ=cos (?? -??)
??ˆ·??ˆ=-cos ?? 
 
From (1) & (2) 
??ˆ=??ˆ-2(??ˆ·??ˆ)??ˆ 
( ? ) Component of ê along the surface (i.e. ? to ??ˆ ) remain same. 
(C) Component of e ˆ ? to the surface (i.e. parallel to r ˆ ) gets inverted. 
( ? ) These laws are valid for any type of surface. 
Example. A light ray travelling along 3??ˆ-4??ˆ is reflected by a plane mirror placed in ?? -
?? plane. Find unit vector along reflected ray. 
Solution: 
 
 reflected ray =3?? +4?? unit vector =
3?? +4?? 5
 
Deviation by plane mirror: 
A plane mirror deviates the light through an angle 
?? =180
°
-2i 
Where i is the angle of incidence. The deviation is maximum for normal incidence. 
?? max 
=180
°
 
 
Deviation ?? produced by a plane mirror w 
Real Object: Object is decided by incident rays only. 
An object is real if two or more incident rays actually emanate or seem to emanate from a 
point. 
 
Virtual Object: 
Now consider a converging set of rays as shown in (figure) If not intercepted, the rays 
will meet at a point. However, if the rays are intercepted by an optical element placed as 
shown in the figure, then the point of convergence is a virtual point behind the optical 
element. This point is called the virtual object for the optical element. 
Page 5


RAY OPTICS 
INTRODUCTION 
Optics is a branch of physics that studies how light behaves. When dealing with things 
like mirrors and lenses that are much bigger than the wavelength of light, we can treat 
light as if it travels in straight lines, like rays. This part of optics, where we use simple 
geometric rules to understand how light moves, is called geometric optics. 
PROPAGATION OF LIGHT 
 
Light usually moves in a straight line through a material or in empty space. It only 
changes direction when something gets in its way or when it moves from one material to 
another. This straight-line movement of light is called rectilinear propagation. If light 
starts from one point and goes to another, it actually travels through all the points in a 
straight line between them. We call this straight line path a ray of light. Light rays start 
from every point of a light source and move straight until they hit something, like an 
object or a surface between two materials. A group of light rays together is called a beam 
of light. 
 ( ? ) Apart from vacuum and gases, light can travel through some liquids and solids. A 
medium in which light can travel freely over large distances is called a transparent 
medium. Water, glycerin, glass and clear plastics are transparent. A medium in which 
light cannot travel is called opaque. Wood, metals, bricks, etc., are opaque. In materials 
like oil, light can travel some distance, but its intensity reduces rapidly. Such materials 
are called translucent. 
 
Ray:   The straight line path along which the light travels in a homogeneous medium is 
called a ray. 
 
Beam: A bundle or bunch of rays is called a beam. It is of following three types: 
(a) Convergent beam: In this case diameter of beam decreases in the direction of ray. 
 
(b) Divergent beam: It is a beam in which all the rays meet at a point when produced 
backward and the diameter of beam goes on increasing as the rays proceed forward. 
 
 
(c) Parallel beam: It is a beam in which all the rays constituting the beam move parallel 
to each other and diameter of beam remains same. 
 
Naming convention: 
 
REFLECTION OF LIGHT 
When light rays strike the boundary of two media such as air and glass, a part of light is 
bounced back into the same medium. This is called Reflection of light. 
(i) Regular/Specular reflection: 
When the reflection takes place from a perfect plane surface then after reflection rays 
remain parallel. 
It is called Regular reflection. 
 
(ii) Diffused reflection 
When the surface is rough, light is reflected from the surface from bits of its plane 
surfaces in irregular directions. This is called diffused reflection. This process enables us 
to see an object from any position. 
 
LAWS OF REFLECTION 
(2) Incident ray, reflected ray and normal lies in the same plane. 
(2) The angle of reflection is equal to the angle of incident i.e. ?i=?r. 
 
 
In vector form 
??ˆ=??ˆ-?? (??ˆ.??ˆ)??ˆ 
Vector form of Law of Reflection: 
AB
????? 
+BD
????? 
=AD
????? 
CB
????? 
+BD
????? 
=CD
????? 
AD
????? 
=-CD
????? 
 
AB
????? 
+BD
????? 
=BC
????? 
+BD
????? 
?? ??ˆ+2(acos ????ˆ)=??ˆ?? ??ˆ=??ˆ+2cos ????ˆ
??ˆ·??ˆ=cos (?? -??)
??ˆ·??ˆ=-cos ?? 
 
From (1) & (2) 
??ˆ=??ˆ-2(??ˆ·??ˆ)??ˆ 
( ? ) Component of ê along the surface (i.e. ? to ??ˆ ) remain same. 
(C) Component of e ˆ ? to the surface (i.e. parallel to r ˆ ) gets inverted. 
( ? ) These laws are valid for any type of surface. 
Example. A light ray travelling along 3??ˆ-4??ˆ is reflected by a plane mirror placed in ?? -
?? plane. Find unit vector along reflected ray. 
Solution: 
 
 reflected ray =3?? +4?? unit vector =
3?? +4?? 5
 
Deviation by plane mirror: 
A plane mirror deviates the light through an angle 
?? =180
°
-2i 
Where i is the angle of incidence. The deviation is maximum for normal incidence. 
?? max 
=180
°
 
 
Deviation ?? produced by a plane mirror w 
Real Object: Object is decided by incident rays only. 
An object is real if two or more incident rays actually emanate or seem to emanate from a 
point. 
 
Virtual Object: 
Now consider a converging set of rays as shown in (figure) If not intercepted, the rays 
will meet at a point. However, if the rays are intercepted by an optical element placed as 
shown in the figure, then the point of convergence is a virtual point behind the optical 
element. This point is called the virtual object for the optical element. 
 
A virtual object that appears to be behind the optical element. 
Image: Image is decided by reflected or refracted rays only. 
An image is the point of convergence or apparent point of divergence of rays after they 
interact with a given optical element. An object provides rays that will be incident on an 
optical element. The optical element reflects or refracts the incident light rays which then 
meet at a point to form an image. 
Real Image: 
Real images are formed when the reflected or refracted rays actually meet or converge to 
a point. If a screen is placed at that point, a bright spot will be visible on the screen. Thus 
a real image can be captured on a screen. Examples of a real images are shown in figure 
(i) and (ii). 
 
A real image formed by a real object placed in front of the convex lens 
Figure (i) 
 
A Real image formed by a virtual object that appears to be behind the mirror Figure (ii) 
Virtual Image: 
When light rays, after interacting with the optical element, actually meet at a point the 
image formed is a real image. However if the rays do not meet at a point but a appear to 
emanate from a point then a virtual image is formed.