03 mirror and lens

4/23/2021 anjumk38dmc@gmail.com 1

• Mirror, any polished surface that diverts
a ray of light according to the law
of reflection. It may be:
1) Plane mirrors or
2) Spherical mirrors.

circles with increasing
radius. The inner circle has
least radius.
Now take cut out the same
length of aperture from
each circle. You get

Types of mirror
• Plane mirror
• Spherical/Curved mirror
Concave Convex

Different parts of a mirror
P: Vertex/Pole
F: Focal length

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.
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anjumk38dmc@gmail.com

Mirror: Rules for rays tracing through
a mirror
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.

Reflection at a plane surface: What will be the minimum
size of a plane mirror if you want your full image?
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Where the fish is?
Imagine you are fishing from a pier and you spot a
"big one" in front of you a short distance below the
surface of the water. You don't have a fishing rod,
but instead you are armed with a spear (Fig 1-16).
How should you throw the spear to hit the fish?
(Pier: A structure built on posts extending from land out over
water, used as a landing place for ships, jetty)

Where will you see the fish in a lake
when you are at air?
The fisherman must throw the spear in front
of the virtual fish to hit the actual fish

The fish is at……..
• From your knowledge of Snell's law, you
know that the fish is not where it appears
to be. If you throw the spear at the fish,
you will certainly miss it.
• What you have to do is throw the spear in
front of the virtual fish, the one you see,
to hit the real fish.

Total Internal Reflection
Total internal reflection (TIR) occurs when light
travels from a high-index medium to a low-index
medium and the angle of incidence exceeds a
certain critical angle. Under these circumstances,
the incident ray does not pass through the
interface; all light is reflected back into the high-
index medium. The law of reflection governs the
direction of the reflected ray.

Total Internal Reflection (TIR)/Critical angle.

Total internal reflection (TIR) makes it impossible
to view the eye's anterior chamber angle without
the use of a contact lens. Light from the angle
undergoes TIR at the air-cornea interface
(technically, the air-tear-film interface) (Fig 1-
18A). Light from the angle never escapes the eye.

 Using a contact lens to eliminate the air at the
surface of the cornea (Fig 1-18B) overcomes the
problem. Light travels from the cornea (or
coupling gel) to the higher-index contact lens.
 TIR never occurs when light travels from a
medium of lower index to one of higher index, so
light enters the contact lens and is reflected from
the mirror.

 Can you say a condition where you can see the angle of
anterior chamber without the help of Goniolens?

 When the cornea is ectatic (as in some cases of
keratoconus), the angle of incidence is less than
the reflected angle so angle structures are visible
without a gonioscopy lens.
 (If you want to know the explanation go to AAO:
VOL:3, but you have to recapitulate sin Ø, cos Ø
and tan Ø)

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.

Can a mirror form a real image?
 Plane mirrors and convex mirrors only produce virtual
images.
 Only a concave mirror is capable of producing a real image
 and this only occurs if the object is located a distance greater
than a focal length from the mirror's surface.
 The image of an object is found to be upright and reduced in
size

Minimum Required Mirror

Types of images
 There are two types of images formed by
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.

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 mirror in ophthalmology
1) A plane mirror is used at a distance of 3 m with a
reverse Snellen’s chart
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.

• নরসুন্দর ও গ্রাহকের মকযে মুকিামুখি েথা চলকে না। চুকলর
স্টাইল, রং ইত্োখি খনকে েথা হকে আেনার মাযেকম। অথো
নযেনত্ম িযরত্ব েজাে ররকি েথা েলকত্ হকে।

Fig: 1

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.
4/23/2021 36

Fig: 2

Nomenclature
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.

Nomenclature
4) Principal axis: It is the ling joining
center of curvature and the vertex.
5) All the measurements are valid from the
pole of the center.
6) By convention, all the incident rays are
taken to travel from the left to right.

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
4/23/2021 40
Fig: 3

Radius of curvature
• 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.
4/23/2021 41

radius of curvature
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.
Fig: 4

It is just midway between the pole and the centre
of curvature and is called the principal focus F.
Fig: 5

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

angle
of
incident
.
angle
of
reflection
.
Fig 6

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.

Spherical mirror
Pole Center of curvature

• 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.
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Images formed by a concave mirror
L: Relative location.
O: orientation (either upright or inverted).
S: Size (either magnified, reduced or the same size
as the object).
T: type of image (either real or virtual).
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• The best means of summarizing this
relationship between object location and
image characteristics is to divide the
possible object locations into five general
areas or points:

IMAGE FORM BY CONCAVE MIRROR
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Images formed by a concave mirror
 Case 1: the object is located beyond the center of
curvature (C)
 Case 2: the object is located at the center of curvature (C)
 Case 3: the object is located between the center of curvature
(C) and the focal point (F)
 Case 4: the object is located at the focal point (F)
 Case 5: the object is located in front of the focal point (F)
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Images formed by a concave mirror:
5 points location

Case 1: The object is located beyond C
• L: somewhere in
between the center of
curvature and the
focal point.
• O: inverted image.
• S: reduced in size;
• T: Real image

Case 2: The object is located at C
L: at “C”
O: Inverted
S: Same size
T: Real

Case 3: The object is located between C and F
L: Beyond “C”
O: Inverted
S: Large size
T: Real

Case 4: The object is located at F
No image will be
form

Case:5. The object is located in front of F
L: Behind the mirror
O: Upright
S: Large size
T: Virtual
This type of image is formed
by a shaving or make-up
mirror and also by small
concave mirror used by
dentists for examining teeth.

4/23/2021 60

IMAGE FORM BY CONVEX
MIRROR
4/23/2021 61

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)
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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.
4/23/2021 65

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

4/23/2021 70

Lens
A lens is defined as a portion of a
refracting medium bordered by two
surfaces where one surface must be curve
which have a common axis.
4/23/2021 71

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.
4/23/2021 72

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.
4/23/2021 73

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.
4/23/2021 74

A convex lens causes convergence of
incident light, whereas a concave lens
causes divergence of incident light
(Fig. 5.2).

Image produced by a converging lens
 The image produced by a converging lens can be
located using just three simple rules:
i. An incident ray which is parallel to the optic
axis is refracted through the image focus (Fi) of
the lens.
ii. An incident ray which passes through the object
focus (Fo) of the lens is refracted parallel to
the optic axis.
iii. An incident ray which passes through the optic
centre (O) of the lens is not refracted at all.

What is STURM'S CONOID?
• STURM'S CONOID: It is an optical
condition in which refractive power of
cornea and lens is not the same in all
meridians , therefore instead of single
focal point there are two focal points
separated by focal interval, this is
called strum's conoid

In a Toric surface one principal meridian is more
curved than the second principle meridian.
The principle meridian with minimum curvature ,
& therefore minimum power is called BASE curve
of a toric lens.
The configuration of rays refracted through a
toric surface/astigmatic surface is called strum's
conoid

At point A, the vertical rays [ V ] , the vertical
rays are converging more than the horizontal
rays [ H ]; so the section here is horizontal oval
or an oblate ellipse.

At point B ( first focus), the vertical rays have
come to a focus while the horizontal rays are
still converging & so they form a horizontal line.
(horizontal line)

At point C , the vertical rays are diverging and &
their divergence is less than the convergence of
the horizontal rays; so a horizontal oval is
formed here. (horizontal oval)

at point D, the divergence of vertical rays is
exactly equal to the convergence of the horizontal
rays from the axis.
So here the section is a circle which is called the
circle of least diffusion. (circle of least diffusion)

At point E ,the divergence of vertical rays is
more than the convergence of horizontal rays;
so the section here is a vertical oval.
(divergence of vertical rays>> convergence of
horizontal rays)

At point F; ( second focus), the horizontal
rays have come to a focus while the vertical
rays are divergent.
So a vertical line is formed here. (vertical
line at second focus)

The distance between the two foci (B & F) is
called the focal interval of strum
Beyond f ( as at point G ) : both horizontal and
vertical rays are diverging and so the section will
always be a vertical oval or prolate ellipse.

the shape of bundle of the light rays at
different levels in a strum's conoid is as
follows:

Etiology:
Corneal causes.
• It occurs due to abnormality of curvature of
cornea. (Most common cause of astigmatism.)
• E.g. eyelid pressure, pterygium, corneal scars,
corneal degeneration, keratoconus, mild corneal
opacities

Etiology:
Lenticular causes:
 It is comparatively rare.
 It may be
 Curvature --- lenticonus
 Positional-----congenital tilting & traumatic
subluxation of lens.
 Index----developing cataract/ nuclear sclerosis/
index astigmatism.

FOCUS OF STURM’S CONOID TO THE TYPES
OF ASTIGMATISM:
REGULAR ASTIGMATISM: when the
refractive power changes uniformly from
one meridian to another( i.e. there are
two principal meridian)
The parallel rays of light are not focused
on a point but form two focal lines.

Types
With the rule astigmatism: in this type the
two principal meridian are placed at right
angles to one another. But the vertical
meridian is more curved than the
horizontal.

This is called “with the rule astigmatism”
as similar condition exists normally( the
vertical meridian is normally rendered
0.25D more convex than the horizontal
meridian by the pressure of eyelids.

Against the rule astigmatism: the horizontal
meridian is more curved than the vertical
meridian.
Oblique astigmatism: type of regular
astigmatism where the two principal meridian
are not the horizontal and vertical though these
are at right angle.
Bi-oblique astigmatism: principal meridian are
not at right angle to one another

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
4/23/2021 95

abandoned and the lenses ground with aplanatic
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.
4/23/2021 96

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.

Summary: Correction of Spherical
Aberration
1) by the use of “stops”
2) plano-convex is better than biconvex.
3) spherical surface must be abandoned and the
lenses ground with aplanatic surface,
4) The weaker lens must be of opposite power
Usually, such doublets are designed to be both
aspheric and achromatic.

Image form by lens
• Unlike the mirrors, lenses have got two principal foci
one on each side of the lens and the nodal point is
situated within the substance of the lens just at the
centre. If the image is situated on the other side of the
object, it is called a Real Image and if it is on the
same side it is called a Virtual Image.
4/23/2021 99

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.
4/23/2021 100

Image form by lens
• For, an object in any position, the image can be constructed
using two rays:
1) A ray from the top of the object which passes through the
principal point/nodal point.
2) A ray parallel to the principal axis, which after refraction
passes through (convex) or away from (concave) the second
principal focus.
4/23/2021 101

4/23/2021 102

• Convex lenses are thicker at the middle. Rays of light that pass
through the lens are brought closer together (they converge). A
convex lens is a converging lens.
• 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.
4/23/2021 103

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.
4/23/2021 104

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.
4/23/2021 105

4/23/2021 106
Magnification :The magnification of a lens can be
calculated using the following formula;

03 mirror and lens

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