01 geometrical optics

OPTICS: BASICS CONCEPTS
Md Anisur Rahman (Anjum)
Professor & Head of the
department (Ophthalmology)
Dhaka Medical College, Dhaka
4/5/2019 1anjumk38dmc@gmail.com

What is optical science.
Optical science. Though most people associate the word
‘optics’ with the engineering of lenses for eyeglasses,
telescopes, and microscopes,
In physics the term more broadly refers to the study of
the behavior of light and its interactions with matter.

Three broad subfields of optics
1) Geometrical optics, the study of light as rays
2) Physical optics, the study of light as waves
3) Quantum optics, the study of light as particles

Which is not the physical property of light?
(SBA)
1) Polarization
2) Interference ANS: Reflection
3) Diffraction
4) Superimposition
5) Reflection
4/5/2019 anjumk38dmc@gmail.com 4

Followings are the geometrical properties of
light? (T/F)
1) Polarization Ans: F T F F T
2) Refraction
3) Diffraction
4) Superimposition
5) Reflection

Geometrical optics
Light is postulated to travel along rays – line
segments which are straight in free space but may
change direction, or even curve, when encountering
matter.

Geometrical optics
Two laws dictate what happens when light encounters
a material surface. The law of reflection, evidently
first stated by Euclid around 300 BC, states that when
light encounters a flat reflecting surface the angle of
incidence of a ray is equal to the angle of reflection.

Geometrical optics
• The law of refraction, experimentally determined by
Willebrord Snell in 1621, explains the manner in
which a light ray changes direction when it passes
across a planar boundary from one material to
another.

Geometrical optics
From the laws of reflection and refraction:
 One can determine the behavior of optical devices
such as telescopes and microscopes.
 One can trace the paths of different rays (known as
‘ray tracing’) through the optical system

Geometrical optics
How images can be formed?
 Their relative orientation, and their magnification.
This is in fact the most important use of geometrical
optics to this day: the behavior of complicated optical
systems can, to a first approximation, be determined
by studying the paths of all rays through the system.

If we keep a running tally of how many squirts
hit at each location, we can slowly build up an
average picture of where light energy is being
deposited in above figure.

Physical optics
Looking again at the ray picture of focusing above, we
run into a problem: at the focal point, the rays all
intersect. The density of rays at this point is therefore
infinite, which according to geometrical optics
implies an infinitely bright focal spot. Obviously, this
cannot be true.

Physical optics
• If we put a black screen in the plane of the focal point
and look closely at the structure of the focal spot
projected on the plane, experimentally we would see
an image as simulated below:

Physical optics
• There is a very small central bright spot, but also
much fainter (augmented in this image) rings
surrounding the central spot. These rings cannot be
explained by the use of geometrical optics alone, and
result from the wave nature of light.

Physical optics
• Physical optics is the study of the wave properties of
light, which may be roughly grouped into following
categories:
1) Interference,
2) Diffraction, and
3) Polarization.
4) Dispersion

Quantum optics
We return to the picture of the focal spot illustrated
above and now imagine that the light source which
produces the focal spot is on a very precise dimmer
switch. What happens as we slowly turn the dimmer
switch down to the off position?

• Physical optics predicts that the shape of the focal
spot will remain unchanged; it will just grow less
bright. When the dimmer switch is turned below
some critical threshold, however, something different
and rather unexpected happens: we detect light in
little localized ‘squirts’ of energy, and do not see our
ring pattern at all.

If we keep a running tally of how many squirts
hit at each location, we can slowly build up an
average picture of where light energy is being
deposited in above figure.

Geometric Optics
Reflection
&
Refraction

Geometric Optics
 Geometric Optics deals with the formation of images by using
such optical devices as mirrors, lenses and prisms and with the
laws governing the characteristics of these images, such as
their size, shape, position and clarity.
 Rays of light
 Pencil of light
 Beam of light
• (M.A MATIN P=19)

Reflection
 The law of reflection, evidently first stated by Euclid
around 300 BC, states that when light encounters a
flat reflecting surface the angle of incidence of a ray
is equal to the angle of reflection

Reflection of light
• When light meets an interface between two media, its
behavior depends on the nature of the two media
involved. Light may be absorbed by the new medium
or transmitted onward through it or it may bounch
back into first medium. This bouncing of light at an
interface is called Reflection.
 (M.A MATIN = 21)

Q. What happened to the light when it
strikes a surface?
Ans) 3 things may happen. It may be:
 Absorbed
 Reflected
 Or Refracted

Defination of Reflection
 Reflection is defined as the change of path of light
without any change in the medium.
 All the reflections end up in producing images of the
object kept in front of the reflecting surface.

Laws of Reflection
1) The incidence ray and
the reflected ray lie in
the same plane which
is perpendicular to the
mirror surface at the
point of incidence.
2) When light is reflected
off any surface, the
angle of incidence is
always equal to the
angle of reflection,

Laws of Reflection
The law of reflection tells us that light reflects from
objects in a very predictable manner. So the question
is, why do we see objects like a table or a chair?
These objects do not produce their own light, so in
order for us to see any object, light must strike the
object and reflect from the object into our eyes.

Laws of Reflection
So how does the light get from the object to our eyes? It
does so through one of the two types of reflection:
specular and diffuse reflection

specular reflection & diffuse reflection
Reflection of smooth surfaces such as mirrors or a
calm body of water leads to a type of reflection
known as specular reflection.
Reflection of rough surfaces such as clothing, paper,
and the asphalt roadway leads to a type of reflection
known as diffuse reflection.

• Whether the surface is microscopically rough or
smooth has a tremendous impact upon the subsequent
reflection of a beam of light.

specular reflection & diffuse reflection
The diagram depicts two beams of light incident upon
a rough and a smooth surface.4/5/2019 33anjumk38dmc@gmail.com

Applications of Specular and Diffuse
Reflection
There are several interesting applications of this
distinction between specular and diffuse reflection.
One application pertains to the relative difficulty of
night driving on a wet asphalt roadway compared to a
dry asphalt roadway. Most drivers are aware of the
fact that driving at night on a wet roadway results in
an annoying glare from oncoming headlights.

Reflection
The glare is the result of the specular reflection of the
beam of light from an oncoming car. Normally a
roadway would cause diffuse reflection due to its
rough surface. But if the surface is wet, water can fill
in the crevices and smooth out the surface.

Reflection
• Rays of light from the beam of an oncoming car hit
this smooth surface, undergo specular reflection and
remain concentrated in a beam. The driver perceives
an annoying glare caused by this concentrated beam
of reflected light.

Reflection
A second application of the distinction between
diffuse and specular reflection pertains to the field of
photography. Many people have witnessed in person
or have seen a photograph of a beautiful nature scene
captured by a photographer who set up the shot with a
calm body of water in the foreground.

Reflection
The water (if calm) provides for the specular
reflection of light from the subject of the photograph.

Reflection
Light from the subject can reach the camera lens
directly or it can take a longer path in which it reflects
off the water before traveling to the lens.
• Since the light reflecting off the water undergoes
specular reflection, the incident rays remain
concentrated (instead of diffusing).

Reflection
The light is thus able
to travel together to the
lens of the camera and
produce an image (an
exact replica) of the
subject which is strong
enough to perceive in
the photograph. An
example of such a
photograph is shown.

Question
If a bundle of parallel incident rays undergoing
diffuse reflection follow the law of reflection, then
why do they scatter in many different directions after
reflecting off a surface?

Answer
Each individual ray strikes a surface which has a
different orientation. Since the normal is different for
each ray of light, the direction of the reflected ray will
also be different.

Question
Perhaps you have observed magazines which have
glossy pages. The usual microscopically rough
surface of paper has been filled in with a glossy
substance to give the pages of the magazine a smooth
surface. Do you suppose that it would be easier to
read from rough pages or glossy pages? Explain your
answer.

Answer
It is much easier to read from rough pages which provide
for diffuse reflection. Glossy pages result in specular
reflection and cause a glare. The reader typically sees an
image of the light bulb which illuminates the page. If you
think about, most magazines which use glossy pages are
usually the type which people spend more time viewing
pictures than they do reading articles.

Nomenclature
1) Light rays falling on the surface are called incident
rays.
2) Light rays travelling back are called reflected rays.
3) A line at right angle to the reflecting surface is called
normal
4) Light travelling along the normal is reflected back
along the normal

angleofincident.
angleofreflection.

Nomenclature
5) The angle formed by the incident ray and the normal
is called angle of incident.
6) The angle formed by the reflected ray and the normal
is called angle of reflection.
7) The angle of incident and the angle of reflection are
equal.

Nomenclature
8) The incident ray, the reflected ray and the normal are
in the same plane.
9) The line joining the centre of curvature to any point
on the curved mirror is the normal of that mirror.
10) The focal length of the plane mirror is infinity.

Mirror
• A mirror is optical media which reflects light
backwards when fall on it. It may be:
1) Plane mirrors or
2) Spherical mirrors.

Mirror: Rules for rays tracing through a mirror
1) The ray which pass through the pole shall pass
undeviated.
2) The ray which is parallel with the axis shall pass
through the focal point after convergence or
divergence.
3) The ray passing through the focal point & falling on
the mirror surface shall pass parallel to the optical
axis.
4) The ray passing through the centre of curvature of a
mirror shall also pass undeviated.
5) Path of light rays are also reversible.4/5/2019 50anjumk38dmc@gmail.com

Image formation by plain mirror

Types of images
 There are two types of images formed mirrors. They
are:
• 1) Virtual image.
• 2) Real image.

Virtual image
1) Virtual image can not be focused on a screen.
2) It is always upright.
3) No light is really passing through the apparent
location of the image.
4) The virtual image formed by plane mirror is laterally
inverted

Real image
1) Real image can be focus on a screen.
2) It is always inverted.
3) The light passes through the location of the image.

Image formation by plain mirror
If the reflecting surface of the mirror is flat then we
call this type of mirror as plane mirrors. Light always
has regular reflection on plane mirrors.
Given picture below shows how we can find the
image of a point in plane mirrors.

Characteristics of image formed by a plane
mirror.
1) Image is virtual and erect.
2) It is of same size as the object.
3) It has the same distance as object to the mirror.
4) It is laterally reversed.
5) The minimum length of the mirror required to form
full size image of the object is half the size of the
object.

Number of images
How many images can you form by two plane
mirror?
It depends upon the inclination of two mirrors with
each other.
• The number of images formed by two plane mirrors
inclined to each other is calculated by the formula:

Number of images
• N=360/ ᴓ - 1 (Here, N = number of images form, ᴓ is
the angle between two mirrors)
• Less the angle between two mirrors, more the number
of images.

Number of images
 N = 360/90 – 1 = 4 – 1 = 3.
 N = 360/60 – 1 = 6 – 1 = 5
 N= 360/45 – 1 = 8 – 1 = 7.
An object placed between two parallel plane mirrors
will form infinite number of images.
This is true only for mirrors kept at right angles or less
than that.

Uses of Plane Mirrors in daily life
A plane mirror is used:
i. as a looking glass to view ourselves
ii. by interior designers to create an illusion of depth
iii. to fold light as in a periscope and other optical
instruments
iv. to make kaleidoscope, an interesting toy

Uses of plane mirror in ophthalmology
1) A plane mirror is used at a distance of 3 m with a
reverse Snellen’s chart kept at little higher position
than patient’s head.
2) Used in plane mirror retinoscope.
3) Used in both direct & indirect ophthalmoscope.
4) Used in slit lamp, synaptophore, stereoscope, to
change the direction of rays & save space.

Spherical mirror

Spherical Mirrors
• Silvering a piece of glass which would form part of
the shell of a hollow sphere. Silvering the glass on
the outside gives a concave or converging mirror,
while silvering on the inside gives a convex or
diverging mirror.

P: Pole. XY: Principal axis. C: center of curvature. F: focal
point. CP: radius of curvature. PF: Focal length

Nomenclature in spherical mirror
image
1) Pole: It is the vertex of the mirror.
2) Center of curvature: It is the center of curvature of the
sphere out of which the mirror is fashioned.
3) Radius of curvature: It is the line joining the center of
curvature to the pole.
4) Principal axis: It is the ling joining center of curvature
and the vertex.

image
5) Normal in a spherical mirror: It is a line that joins
any point of the mirror to the center of curvature.
6) All the measurements are valid from the pole of the
center.
7) By convention, all the incident rays are taken to
travel from the left to right.

image
• 8) Focal length of a concave mirror is taken as
negative and positive in convex lens

Principal axis
The principal axis of a
spherical mirror is the
line joining the pole P
or centre of the mirror
to the centre of
curvature C which is the
centre of the sphere of
which the mirror forms
a part.
P
C

radius of curvature r
• The radius of curvature r is the distance CP. In the
case of a concave mirror the centre of curvature is in
front of the mirror ; in a convex mirror it is behind.

Principal Focus
• Light rays that are parallel to the principal axis of a
concave mirror converge at a specific point on its
principal axis after reflecting from the mirror. This
point is known as the principal focus of the concave
mirror

Principal Focus in concave mirror

Principal Focus in convex mirror

• What happens when a beam of light parallel to the
principal axis falls on a convex mirror?
• In this case the rays are reflected so that they all
appear to be coming from a principal focus midway
between the pole and centre of curvature behind the
mirror.

• A concave mirror, therefore has a real principal focus,
while the convex mirror has a virtual one.
• The focal length of a spherical mirror is half its radius
of curvature.

Construction of ray diagrams
• Since a point on an image can be located by the point of
intersection of two reflected rays, we have to consider which
are the most convenient rays to use for this purpose.
• Remembering that, by geometry, the normal to a curved
surface at any point is the radius of curvature at that point, one
very useful ray to draw will be one which is incident along a
radius of curvature. Since this is incident normally on the
mirror, it will be reflected back along its own path.

• Another useful ray is one which falls on the mirror parallel to
the principal axis. By definition, this will be reflected through
the principal focus. Conversely, any incident ray passing
through the principal focus will be reflected back parallel to
the principal axis. The same observations also apply to the
convex mirrors, so we may briefly sum them up into a set of
rules for constructing images formed by spherical mirrors.

1) Rays passing through the centre of curvature are reflected
back along their own paths.
2) Rays parallel to the principal axis are reflected through the
principal focus.
3) Rays through the principal focus are reflected parallel to the
principal axis.
4) (Useful when using squared paper) Rays incident at the pole
are reflected, making the same angle with the principal axis.

Characteristic of the image
L: Location of the image
O: Orientation (either upright or inverted)
S: Size of the image (Magnified, minified or same)
T: Type of image (either real or virtual).
The best means of summarizing this relationship divide
the possible object locations into five general areas or
points:

Images formed by a concave mirror
Case 1: the object is located beyond (C)
Case 2: the object is located at (C)
Case 3: the object is located between (C) and (F)
Case 4: the object is located at (F)
Case 5: the object is located in front of (F)

Case 1: The object is located beyond C
L: Between C and F. O: Inverted. S:
Diminished. T: Real image

Case 2: The object is located at C
L: at C. O: Inverted. S: equal in size. T: real image.

Case 3: The object is located between C and F
L: beyond C. O: Inverted. S: Larger. T: Real image

Case: 4. Object at focus (F)
No image will be formed

Case 5: The object is located in front of F
L: Behind the mirror. O: upright image, S:
magnified and T: virtual

NEXT SLIDE
• Nine different object locations are drawn and
labeled with a number; the corresponding
image locations are drawn in blue and labeled
with the identical number.

IMAGE FORM BY
CONVEX MIRROR

IMAGE FORM BY CONVEX MIRROR

The diagrams above show that in each case,
the image is
located behind the convex mirror
a virtual image
an upright image
reduced in size (i.e., smaller than the object)

Convex mirrors always produce images that
share these characteristics. The location of the
object does not affect the characteristics of the
image. As such, the characteristics of the
images formed by convex mirrors are easily
predictable.

• Another characteristic of the images of objects
formed by convex mirrors pertains to how a
variation in object distance affects the image
distance and size. The diagram below shows
seven different object locations (drawn and
labeled in red) and their corresponding image
locations (drawn and labeled in blue).

• The diagram shows that as the object distance
is decreased, the image distance is decreased
and the image size is increased. So as an object
approaches the mirror, its virtual image on the
opposite side of the mirror approaches the
mirror as well; and at the same time, the image
is becoming larger.

Image formed by concave mirror
Position of
the object
Position
of the
image
Nature of
the image
Inverted/
Erect
Size
Between
focus & pole
Behind the
mirror
Virtual Erect Magnified
At focus Infinity Real Inverted Highly
Magnified
Between
focus &
curvature
Beyond
center of
curvature
Real Inverted Little
Magnified

Image formed by concave mirror
Position of the
object
Position of
the image
Nature
of the
image
Inverte
d/
Erect
Size
Center of curvature Same place Real Inverte
d
Same
size
Beyond the center of
curvature
Between
focus &
center of
curvature
Real Inverte
d
Dimini
shed
At infinity Real Inverte
d
Very
small

Image formed by convex mirror
 The image of an object kept in front of the mirror is
formed behind the mirror.
 It is smaller than the object , erect and virtual.
 The distance between the image and the mirror is less
than between the object and the mirror.

Behavior of images in relation to position of the
object
The image formed by CONVEX and PLANE mirrors
are virtual
The image formed by CONCAVE mirrors can
be real or virtual
The distance between mirror and the image is least in
CONVEX mirror, most in CONCAVE mirror and
equal in PLANE mirror

Refraction

Luminous versus Illuminated Objects
The objects that we see can be placed into one of two
categories: luminous objects and illuminated objects.
 Luminous objects are objects that generate their own
light
 Illuminated objects are objects that are capable of
reflecting light to our eyes.

The sun is an example of a luminous object, while the
moon is an illuminated object.

Refraction
Q) What happened to the light when it strikes a surface?
Ans) 3 things may happen. It may be:
 Absorbed
 Reflected
 Or Refracted

Refraction
Q) What is refraction?
Ans) Refraction of light is a phenomenon of change in
the path of light when it passes from one medium to
another due to change in velocity.

Terms used in refraction
1) NORMAL: This is a line right angles to the interface
2) INCIDENCE RAY: The ray that strikes the interface
at the base of the normal in an angular fashion.
3) REFRACTED RAY: This is the deviated ray in the
second medium.

4) ANGLE OF INCIDENCE: Angle between the
normal and the incident ray
5) ANGLE OF REFRACTION: The angle between the
refracted ray & the normal is called ANGLE OF
REFRACTION
6) The two angles are never equal.

Snell’s Law

Total Internal Reflection (TIR)

Critical Angle
Critical angle is the angle of incidence above which total internal
reflection occurs.
It is defined as the angle when the incidence ray is of such an
angle that the refracted ray is at right angles to the normal

Critical Angle
• Critical angle of glass is 48.60, diamond is 240 (refractive
index is 2.42) and water is 48.750. An incident ray when
passing through a slab of glass with air on either side will exit
the slab as refracted ray and will be parallel to incident ray.

• The complete reflection of a light ray reaching an
interface with a less dense medium when the angle of
incidence exceeds the critical angle.

Different uses of TIR
1) Gonioscopy employs total internal reflection to view
the anatomical angle formed between the
eye's cornea and iris.
2) Total internal reflection is the operating principle
of optical fibers, which are used in endoscopes and
telecommunications.

Different uses of TIR
3) Total internal reflection is the operating principle of
automotive rain sensors, which control
automatic windscreen/windshield wipers

Lenses

Lenses
A lens is defined as a portion of a refracting medium
bordered by two curved surfaces which have a
common axis.
When each surface forms part of a sphere the lens is
called a spherical lens.

Sometimes, a spherical lens has a one plane surface, it
is acceptable because a plane surface can be thought
of as part of a sphere of infinite radius.

Spherical Lens
Lens may be spherical (when each surface forms part
of sphere, the lens is called a Spherical lens) where
the concavity or convexity two different meridians
are equal.

Cylindrical Lens
It may be cylindrical where there is unequal
concavity in two meridians. The two meridians
usually remains at right angels to each other and the
less curved meridian being designed as axis of the
lens.

Lenses: (A–F), Spherical lenses: (A), biconvex; (B), biconcave;
(C), planoconvex; (D), planoconcave; (E), concavoconvex,
periscopic convex, converging meniscus; (F), convexoconcave,
periscopic concave, diverging meniscus; (G, H), cylindrical lenses,
concave and convex.

Why convex lens is called converging lens?
A convex lens is called converging lens because of its
ability to converge a parallel beam of light on a point
called principal focus

principal focus & focal length.
• When parallel rays of light pass through a convex
lens the refracted rays converge at one point called
the principal focus.
• The distance between the principal focus and the
centre of the lens is called the focal length.

The point at which the principal plane and principal axis intersect is
called the principal point or nodal point. Rays of light passing through
the nodal point are undeviated.
Light parallel to the principal axis is converged or diverged from the
point F, the principal focus.

A ray of light passing through the Optical Center of the
lens travels straight without suffering any deviation.
This holds good only in the case of a thin lens.

An incident ray parallel to the principal axis after
refraction passes through the focus.

An incident ray passing through the focus of a lens
emerge parallel to the principal axis after refraction.

The nature of images formed by a convex lens
depends upon the:
distance of the object from the Optical Center of
the lens. Let us now see how the image is formed
by a convex lens for various positions of the
object

1. When the Object is Placed between F1 and O:
L:Same side of the lens. O: Erect S: Magnified.
T: Virtual

2. When the Object is Placed between the Optical
Center (O) and first Focus (F1)
L: same side. O: Erect. S: Magnified. T: Virtual

3. When the Object is Placed at 2F1
L: Formed at 2F2. O: Inverted. S: Same size.
T: Real.

4.When the Object is Placed between F1 and F2
L: Formed beyond 2F2
. O: Inverted. S: Same size. T: Real.

5. When the Object is Placed at F1
L: Formed at infinity
. O: Inverted. S: Magnified. T: Real.

6.When the Object is Placed beyond 2F1
L: Formed between F2 and 2F2
. O: Inverted. S: Diminished. T: Real.

7. When the Object is Placed at Infinity
L: Formed at F2
. O: Inverted. S: Highly diminished T: Real

Position
of the
object
Position
of the
image
Nature
of the
image
Size
of the
image
Application
Between
O and
F1
on the
same
side of
the lens
Erect
and
virtual
Magni
fied
Magnifying lens
(simple microscope),
eye piece of many
instruments
At 2F1 At 2F2 Inverted
and real
Same
size
Photocopying camera
Between
F and
2F1
Beyond
2F2
Inverted
and real
Magni
fied
Projectors, objectives
of microscope

Position
of the
object
Position
of the
image
Nature
of the
image
Size of
the
image
Application
At F1 At
infinity
Inverted
and real
Magnif
ied
Theatre spot lights
Beyond
2F1
Between
F2 and
2F2
Inverted
and real
Dimini
shed
Photocopying
(reduction camera)
At
infinity
At F2 Inverted
and real
Dimini
shed
Objective of a
telescope

• The following rays are considered while
constructing ray diagrams for locating the
images formed by a concave lens for the
various position of the object.

An incident ray of light coming from the object parallel to
the principal axis of a concave lens after refraction
appears to come from its focus.

An incident ray of light passing through the Optical
Center comes out of the lens without any deviation.

A concave lens always gives a virtual, erect and
diminished image whatever may be the position of the
object.
Position of the images when the object is placed
 at infinity and
 between O and F1 and
 any position between infinity and O.

L: Formed at F1. O: Erect. S:Diminished. T: Virtual
When the Object is at Infinity

L: between O and F1. . O: Erect S: Diminished. T:
Virtual
When the Object is Placed between O and F:

When the Object is Placed at any Position
between O and Infinity
L: between O and F1. . O: Erect S: Diminished.
T: Virtual

Difference between Convex & Concave lens
Basic
comparison
Convex lens Concave lens
Figure
Curve Outward Inward
Light Convergences Divergences
Centre and edges Thicker at the
center, as
compared to its
edges.
Thinner at the
center as
compared to its
edges.4/5/2019 anjumk38dmc@gmail.com 147

Difference between Convex & Concave lens
Basic
comparison
Convex lens Concave lens
Focal length Real and inverted
image.
Image Real and inverted
image.
Virtual, erect and
magnified image.
Objects Appear closer
and larger.
Appear smaller
and farther.
Used to Correct
hyperopia.
Correct myopia.

Spherical Aberration
The prismatic effect of the peripheral parts of the
spherical lens causes spherical aberration.
It was seen that the prismatic effect of a spherical lens
is least in the paraxial zone and increases towards the
periphery of the lens.

Spherical Aberration
Thus, rays passing through the periphery of the lens
are deviated more than those passing through the
paraxial zone of the lens.

Correction of Spherical Aberration
Spherical aberration may be reduced by occluding the
periphery of the lens by the use of “stops” so that
only the paraxial zone is used.
Lens form may also be adjusted to reduced spherical
aberration, e,g plano-convex is better than biconvex.
To achieve the best results, spherical surface must be

abandoned and the lenses ground with aplantic surface,
that the peripheral curvature is less than the central
curvature.
Another technique of reducing spherical aberration is
to employ a doublet. This consists of a principal lens
and a somewhat weaker lens of different R.I
cemented together.

The weaker lens must be of opposite power, and
because it too has spherical aberration, it will reduce
the power of the periphery of the principal lens more
than the central zone. Usually, such doublets are
designed to be both aspheric and achromatic.

• A convex lens is thicker at the centre than at the
edges.

Use of Convex Lenses
 Use of Convex Lenses – The Camera
 A camera consists of three main parts.
I. The body which is light tight and contains all the mechanical
parts.
II. The lens which is a convex (converging) lens.
III. The film or a charged couple device in the case of a digital
camera.

Use of Convex Lenses – The Camera
• The rays of light from the person are converged by the convex
lens forming an image on the film or charged couple device in
the case of a digital camera.
• The angle at which the light enters the lens depends on the
distance of the object from the lens. If the object is close to the
lens the light rays enter at a sharper angled. This results in the
rays converging away from the lens. As the lens can only bend
the light to a certain degree the image needs to be focussed in
order to form on the film. This is achieved by moving the lens
away from the film.

Use of Convex Lenses – The Camera
• Similarly, if the object is away from the lens the rays
enter at a wider angle. This results in the rays being
refracted at a sharper angle and the image forming
closer to the lens. In this case the lens needs to be
positioned closer to the film to get a focused image.
• Thus the real image of a closer object forms further
away from the lens than the real image of a distant
object and the action of focusing is the moving of the
lens to get the real image to fall on the film.
• The image formed is said to be real because the rays of
lighted from the object pass through the film and
inverted (upside down).

The Magnifying Glass
A magnifying glass is a convex lens which produces a magnified
(larger) image of an object.
• A magnifying glass produces an upright, magnified virtual
image. The virtual image produced is on the same side of the
lens as the object. For a magnified image to be observed the
distance between the object and the lens must be shorter than
the focal length of the lens.

For a magnified image to be observed the distance
between the object and the lens has to be shorter than
the focal length of the lens. The image formed is
upright, magnified and virtual.

Magnification :The magnification of a lens can be
calculated using the following formula;

Aspheric lens
• An aspheric lens or asphere is a Lens whose surface
profiles are not portions of a sphere or cylinder.
• The asphere's more complex surface profile can
reduce or eliminate spherical aberration and also
reduce other optical aberration compared to a simple
lens.

PRISM

What is prism?
A prism is defined as a portion of a refracting
medium bordered by two plane surfaces which are
inclined at a finite angle.

Refracting/ Apical
angle of the prism: The
angle between the two
surfaces
Axis of the prism: A line
bisecting the angle.
Apex: The thin edge where
the intersecting surfaces
meet
Base: The opposite surface.

Light is deflected as it
enters a material with
refractive index > 1. A
ray of light is
deflected twice in a
prism.
The sum of these deflections is the deviation angle.
When the entrance and exit angles are equal, the
deviation angle of a ray passing through a prism will be
a minimum

The deviation angle in a prism depends upon:
1) Refractive index of the prism: The refractive index
depends on the material and the wavelength of the
light. The larger the refractive index, the larger the
deviation angle.
2) Angle of the prism: The larger the prism angle, the
larger the deviation angle.

The deviation angle in a prism depends upon:
3) Angle of incidence: The deviation angle depends on
the angle that the beam enters the object, called angle
of incidence. The deviation angle first decreases with
increasing incidence angle, and then it increases.

Refraction of light through prism
Light passing through a prism obey Snell’s law at
each surface.
The ray is deviated towards the base of the prism.
This causes objects to be displaced away from the
base of the prism towards its apex. The net change in
direction of the ray, angle D is called the angle of
deviation.

The net change in direction of the ray, angle D
is called the angle of deviation

• All varieties of spectacle lens have the effect of a
prism when viewed through a point away from the
optical center. The further the away from the optical
center, the greater is the prismatic effect.

For a prism in air, the angle of deviation is
determined by three factors.
i. The refractive index of the material of which the
prism is made.
ii. The refracting angle of the prism.
iii. The angle of incidence of the ray considered.

• Light rays entering and leaving a prism are bent
towards the base of the prism. This cause objects to
be displaced away from the base of the prism towards
its apex.
 Base down prism - upward.
 Base up prism – downward

Characteristic of prism
 A prism does not change the vergence of the rays.
 A prism does not magnify or minify the image.
 A prism also disperses incident pencil rays into its
component colours.

Image formation by a prism
i. The object being viewed through the prism appears
displaced toward the apex of the prism.
ii. Although the light rays themselves bent toward the
base
iii. The image formed by a prism is erect virtual &
displaced towards the apex of the prism.

Positions of prism
There are two primary positions in which the power
of a prism may be specified
i. The position of minimum deviation
ii. The prentice position.

Angle of deviation is least when the angle of incidence
equals the angle of emergence
The angle of deviation equals half the refracting angle of
the prism
The position of
minimum deviation

The prentice position
• The deviation of light in the prentice position is
greater than that in the position of minimum
deviation, because in the prentice position the angle
of incidence does not equal the angle of emergence.
Therefore the Prentice position power of any prism is
greater than its power in the position of minimum
deviation

The power of any prism can be express in various units.
The Prism Diopter (∆) a prism of one diopter power
(1∆) produces a liner apparent displacement of 1 cm, of
an object O, situated at 1 m.
Notation of prism

Notation of prism
• Angle of apparent deviation: The apparent
displacement of the object O can also be measured in
terms of the angle ᴓ, the angle of apparent deviation.
Under condition of ophthalmic usage a prism of 1
prism diopter power produces an angle of apparent
deviation of ½ 0. Thus 1 prism diopter= ½ 0

Notation of prism
• Centrad (): This unit differs from the prism diopter
only in that the image displacement is measured
along an arc 1 m from the prism. The Centrad
produces a very slightly greater angle of deviation
than the prism diopter, but the difference, in practice,
is negligible.
• (Prism diopter in the US and degrees in Europe)

Use of prism
1) Diagnostic
2) Therapeutic
3) Instruments
4) Miscellaneous

Diagnostic use of PRISM
1) Assessment of squint & heterophoria
a) Measurement of angle objectively by prism cover test
b) Measurement of angle subjectively by maddox rod
c) To assess likelihood of diplopia after proposed squint
surgery in adults.
d) Measurement of fusional reserve
e) 4 ∆D base out test

• 2) Assessment of simulated blindness if a prism is
placed in front of a seeing eye, the eye will move to
regain fixation

1.Assessment of squint & heterophoria
a) Measurement of angle objectively by
prism cover test
b) Measurement of angle subjectively by
maddox rod
c) To assess likelihood of diplopia after
proposed squint surgery in adults.

a) Measurement of angle objectively by prism
cover test
 If the reflection of a fixation light is decentered on
the cornea of one eye (i.e., the deviating eye), a
prism is held over the fixating eye. This will induce
a conjugate movement of both eyes (version) in the
direction of the apex of the prism.

a) Measurement of angle objectively by prism
cover test
 The correct prism strength is reached when the
position of the corneal light reflex is symmetric
between both the eyes.
 Centering of the corneal light reflex with a prism over
the fixating eye measures the angle of strabismus.

Prism bar cover test

b) Measurement of angle subjectively by maddox
rod
• The Maddox rod is a handheld instrument composed
of red parallel Plano convex cylinder lens, which
refracts light rays so that a point source of light is
seen as a line or streak of light. Due to the optical
properties, the streak of light is seen perpendicular to
the axis of the cylinder

rod
• The Maddox rod test can be used to subjectively
detect and measure a latent, manifest, horizontal or
vertical strabismus for near and distance. The test is
based on the principle of diplopic projection.
Dissociation of the deviation is brought about by
presenting a red line image to one eye and a white
light to the other,

rod
• While prisms are used to superimpose these and
effectively measure the angle of deviation (horizontal
and vertical). The strength of the prism is increased
until the streak of the light passes through the centre
of the prism, as the strength of the prism indicates the
amount of deviation present.

b ) Measurement of angle subjectively by maddox rod
A) Esodeviation, B) Exodeviation, C) Hyper-deviation,
D) Hypo-deviation, E) No deviation

c) To assess likelihood of diplopia after proposed
squint surgery in adults.
Squint surgery in adult sometimes may cause intractable
diplopia, but before surgery if we assess the squint
with prism we can be aware of it to the patient.

Increasingly powerful prisms are placed before one eye
until fusion breaks down. This is very useful in
assessing the presence of binocular vision in children
below two years of age.

This is a delicate test for small degrees of esotropia
(microtropia). A four-diopter prism placed base-out
before the deviating eye causes no movement as the
image remains within the suppression scotoma. When
placed before the normal (fixing) eye, movement
occurs.

Forms of diagnostic prisms
i. Single un mounted prisms
ii. Trial lens set prisms
iii. Prism bars: These are bars composed of adjacent
prisms of increasing power.

Therapeutic use of prism
a) To relive Convergence insufficiency
b) To relieve diplopia

To relive Convergence insufficiency
The commonest therapeutic use of prisms in the
orthoptic department is in building up the fusional
reserve of patients with convergence insufficiency.

To relive Convergence insufficiency: Base out
prism exercises
Base out prisms can also be used to stimulate the
converge reflex. The base out prism induces crossed
diplopia and the patient must converge to overcome
the prism strength and obtain BSV.

To relieve diplopia
To relieve diplopia in certain cases of squint, these
include decompanseted heterophoria, small vertical
squints and some paralytic squints with diplopia in
the primary position. Prisms are reserved for those
patients for whom surgery is not indicated.

Forms of therapeutic prism
Temporary wear prisms:
Used in treatment include clip- on spectacle prisms
for trial wear. Eg:-Fresnel prism (pronounced fre-
nell') prisms,)
Permanent wear:
Prism can be mounted in spectacles permanently.

Prisms in optical instruments:
i. Slit lamp bio microscope.
ii. Applanation tonometer
iii. keratometry

Different types of prism used in
ophthalmology
1) Porro prism:
2) Right Angle Prisms
3) Dove prism

Different types of prism used in ophthalmology
Porro-prism:
It is a type
of reflection prism
used in optical
instruments to alter
the orientation of
an image.

Porro-prism
 An image travelling through a Porro prism is rotated
by 180° and exits in the opposite direction offset from
its entrance point. Since the image is reflected twice,
the handedness of the image is unchanged.

Right Angle Prisms
i. Right Angle Prisms are typically used to bend image
paths or for redirecting light at 90°.
ii. Right Angle Prisms are Prisms designed with a 90°
angle.
iii. Right Angle Prisms produce inverted or reverted left
handed images, depending on the orientation of the
prism.

Right Angle Prisms
• Using two Right Angle Prisms together is ideal for
image or beam displacement applications. These
prisms are also known as image reflection or
reflecting prisms.

Different types of prism used in ophthalmology
Right angle - prism:
Function
Deviate the
Ray Path by
90°
Image is
Left-Handed
Used in
Combination
for
Image/Beam
Displacemen
t

Right angle prism: Application
i. Endoscopy
ii. Microscopy
iii. Laser Alignment
iv. Medical Instrumentation

Dove prism

Dove prism
It is a type of reflective prism which is used to invert an
image. It is shaped from a truncated right-angle prism.
A beam of light entering one of the sloped faces of the
prism undergoes total internal reflection from the inside
of the longest (bottom) face and emerges from the
opposite sloped face.

Dove prism
Images passing through the prism are flipped, and
because only one reflection takes place, the image is
inverted but not laterally transposed.

Application of Dove Prism
i. Interferometry
ii. Astronomy
iii. Pattern Recognition
iv. Imaging Behind Detectors or Around Corners

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