Medical Physics

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Physics of the Eyes and Vision
Physics of the Eyes and Vision
Unit Coordinator Prof. Dr. Gehan El-Tabie
Medical Physics
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• Physics of the Eyes and Vision
• Prof. Dr. Gehan El-Tabie
• Objectives
• - Light in medicine
• - Properties of light
• -Types of lenses
• - Eye as an optical system
• - Size of image on the retina
• General law of lenses
• How to describe an image formed using a lens?
• - Normal eye , refractive errors and possible
  correction
• References
• 1- Medical Physics
  textbook by Cameron
• 2- Physics in Biology
  and Medicine, Third Edition by Paul Davidovits
• 3- Physics of the Human
  Body, by Irving P. Herman

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Light in medicine Light therapy or phototherapy
Consists of exposure to daylight or to specific
wavelengths of light using lasers (Light
Amplification by Stimulated Emission of
Radiation), light-emitting diodes (LED) is a
semiconductor light source, fluorescent lamps
or very bright, full-spectrum light, usually
controlled with various devices. Common use of
phototherapy is associated with the treatment of
skin disorders, sleep disorder and some
psychiatric disorders. Light therapy directed at
the skin is also used to treat eczema and
neonatal jaundice ???????. Light therapy which
strikes the retina of the eyes is used to treat
delayed sleep phase syndrome. Other medical
applications of light therapy also include pain
management, accelerated wound healing, hair
growth, improvement in blood properties and blood
circulation. Note In medicine lasers are used
primarily to deliver energy to tissue. Laser is
routinely used in clinical medicine only in
ophthalmology. Laser energy directed at human
tissue causes a rapid rise in temperature and can
destroy the tissue. The amount of damage to
living tissue depends on how long the tissue is
at the increased temperature.
A newborn infant undergoing light phototherapy to
treat neonatal ?????? jaundice
Bright light therapy is a common treatment for
other diseases.
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Properties of light Light is an electromagnetic
radiation (EM) that is visible to the human eye,
and is responsible for the sense of sight.
Primary properties of light are intensity,
propagation direction, frequency or wavelength
spectrum and its speed in vacuum is 3 x 108
(m/s). Light, which is emitted and absorbed in
tiny "packets" called photons, exhibits
properties of both as waves and particles. Light
can be represented as a transverse (EM) made up
of perpendicular, fluctuating electric and
magnetic fields. Absorption of light photon
transfer energy which is equivalent to (E) hf
hc/?, h Plancks constant 6.626 x10-34
(J/sec), f frequency of light, c velocity of
light in vacuum and ? wavelength (i.e., shorter
wavelength higher energy).

Light wave show the two oscillating components of
light an electric field and a magnetic field
perpendicular to each other and to the direction
of motion
Medium particles oscillate up and down about
their individual equilibrium positions as light
wave passes
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Optics Is the study of light. It is the branch
of physics which involves the behavior and
properties of light, including its interactions
with matter and the construction of instruments
used to detect light. Frequency (f) is the number
of occurrences of a repeating event per unit
time. The period (T) is the duration of one cycle
in a repeating event, then T a
1/f. Geometrical optics describes the
propagation of light in terms of "rays" which
travel in straight lines, and whose paths are
governed by the laws of reflection and refraction
at interfaces between 2 transparent different
media. These laws can be summarized as follows
When a ray of light hits the boundary between two
transparent materials, it is divided into a
reflected and a refracted ray. 1- Law of
reflection Reflected ray lies in the plane of
incidence, and the angle of reflection equals to
the angle of incidence. If we draw an imaginary
line perpendicular to the incidence surface, this
line is called the normal line of the surface.
?i ?r ? ?2
Incident
(Refractive index)
Incident medium
i
Refractive medium
(Incidence surface)
r
Refracted
Reflected
(a) Regular (b) Diffuse reflection
Geometry of reflection and refraction of light
rays
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2- Law of refraction When light travels through
two transparent media of different index of
refraction. The simplest case of refraction
occurs when there is an interface between two
uniform transparent media with different index of
refraction n1 n2. In such situations, Snell's
Law describes the resulting refraction of light
ray                          where ?1 and ?2
are the angles between the normal line and both
the incident and refracted waves respectively.
This phenomenon is also associated with a
changing speed of light where where v1 and v2
are the wave velocities through the two media.
(c/v1)
(c/v2)
(Incident ray)
(Refracted ray)
Note The index of refraction (n) is defined as
The ratio of the speed of light in vacuum (c)
divided by the speed of light in the medium (v).
Index of refraction (n) c/v
then n a c n a 1/v
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3- Total internal reflection (T.I.R.)
When light is incident upon a medium of different
index of refraction, the ray will split, some of
the ray will reflect off the boundary and some
will refract as it passes through the boundary.
When the exit (refracting) angle approach 90 in
this case the incident angle is called critical
incident angle ?c . For incident angles greater
than the critical angle, the entire incident ray
of light will reflect off the boundary and none
will pass to the other medium, this is called
total internal reflection (T.I.R.) in the
incidence medium of high index of refraction.
Critical angle is defined as The angle of
incidence above which total internal reflection
occurs.
N
Boundary
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When a ray of light passes from one medium to
another, it bends. If the light travels faster in
the second medium, then this medium is called the
rarer medium. On the other hand, the medium in
which the light travels slower, in this case the
first one, is called the denser medium. When a
ray of light enters a denser medium, it is bent
towards the normal imaginary line perpendicular
on the interface. - When a ray of light enters a
rarer medium, it bents away from the normal.
There is an index of refraction (n) between the
two media. To get a value of n, we have to divide
the sine of the angle in vacuum or air by the
sine of the angle in the denser medium. Hence,
the index of refraction would be n sin a / sin
b c/v
Normal (N)
Rarer medium
Refract away from N
n 1
Incident
(Vacuum)
Interface
Incident
Denser medium
Refract toward N
n 1.333
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Lenses are transparent tissue that bends light
passing through the eye. To focus light, lens can
change shape by bending. Lenses are classified by
the curvature of its two optical surfaces.
Convex Lens A convex lens is thicker in the
middle than on its outside edge. As a result of
the middle being the thickest part, light
traveling through the lens converges into a
single point. Parallel rays of light join at a
single point beyond the lens. How an image
appears in a convex lens depends on the distance
and position of the object being viewed. Eye
lens is a double convex whose front and back
faces have radii of curvature about 10-6 mm.
Concave Lens A concave lens is a diverging lens
which works similar to the convex mirror. This
lens is thicker towards the edges and thin in the
middle and are used in helping correction of
nearsightedness (myopia). All images produced by
concave lenses are virtual, erect, and reduced
(minified).
Types of Lenses
Edge
Center
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Positive convex() and negative concave(-)
lenses
Front
Back
- 0.2 (m)
0.2 m
.
P(100/20) cm5 (D)
Parallel light from a great distance
???? ????? ????? ?????? ????
???? ????? ????? ?????? ????
(ve, Converging)
(-ve, Diverging)

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n 1.337
n 1.336
n 1.376
n 1.406

Eye as an optical system Eye is like a camera.
Light enters the eye through a small hole called
the pupil and is focused on the retina, which is
like a camera film. Eye also has a focusing lens,
which focuses images from different distances on
the retina. The colored ring of the eye, the
iris, controls the amount of light entering the
eye. It closes when light is bright and opens
when light is dim. A tough white sheet called
sclera covers the outside of the eye except the
cornea. The front of sclera is transparent to
allow the light to enter the eye. Ciliary muscles
control the focusing of lens automatically. Image
on the retina is formed by two elements, the
cornea contributing about 43Diopter and the lens
the remaining 19D.
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Both eye and camera consist of a lens system that
focuses a real inverted image onto a
photosensitive surface. In the eye, as in the
camera, the diameter of the light entrance is
controlled by a diaphragm that is adjusted in
accord with the available light intensity. In a
camera, the image is focused by moving the lens
with respect to the film. In the eye, the
distance between the retina and the lens is
fixed the image is focused by changing the
thickness of the lens.
The eye and the camera
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Retina is facing the cornea with a mesh of nerve
fibers lining the back half of the eye ball. it
converts light images into electrical impulses,
sent to the brain by optic nerve. Near the center
of the retina is a small depression which is
called fovea centralis. This small part of the
retina is responsible for our highest visual
acuity. It consists entirely of cones packed
closely together. When the eye scans a scene, it
projects the region of greatest interest onto the
fovea. The region around the fovea contains both
cones and rods.
The cavity of the eye is filled with two
types of fluid. (1) The front (anterior)
chamber, between the lens and the cornea, is
filled with a watery fluid called aqueous humor
formed by ciliary body n1.336. It contains all
the blood component except the RBCs. (2)The back
(posterior) chamber in the large space between
the lens and the retina is filled with the clear
gelatinous vitreous humor (body) n1.337. It
helps to keep the shape of eye fixed. Visual axis
is a straight line extending from the viewed
object through the center of the pupil to the
fovea. Optic axis  the imaginary straight line
passing through the centers of curvature of the
front and back surfaces of a simple lens.
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Size of image on the retina
The focusing of the light into a real inverted
image at the retina is produced by refraction at
both the cornea and at the crystalline lens. Most
of that refraction in the eye takes place at the
first surface, since the transition from the air
into the cornea is the largest change in index of
refraction which the light experiences. About 80
of the refraction occurs in the cornea and about
20 in the inner crystalline lens. While the
inner lens is the smaller portion of the
refraction, it is the total source of the ability
to accommodate the focus of the eye for the
viewing of close objects. - Image on the retina
is very small. A convenient equation for
determining the size of image on the retina comes
from the ratios of the lengths of the sides of
similar triangles O/I S/S I is the image
size on the retina, O is the object size, S is
the object distance from the lens and S is the
distance between lens and the image. - The
focusing of the eye is controlled by the ciliary
muscle, which can change the thickness and
curvature of the lens. This process of focusing
is called accommodation. When ciliary muscle is
relaxed, the crystalline lens is fairly flat, and
the focusing power of the eye is at its minimum.
On the retina

Focusing by the cornea and crystalline lens
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Example How big is the image on the retina of a
fly on a wall 3.0 m away? Assume that the size of
the fly is 3 (mm) and S 2 cm. Answer m
1000 mm then mm 1/1000 10-3 m S 3 (m), O
3 (mm) 3 x 10-3 (m) and S 2 (cm) 2 x10-2
(m) O/I
S/S I OS/S Example Calculate the length
of the image formed on the retina of a person
1.75 (m) height and 10 (m) away, knowing that
distance between the lens and the image is 0.03
m Answer S 10 (m) , O 1.75 (m) , S 0.03
(m) 1.75/I 10/0.03 then I (1.75 x 0.03)/10
0.00525 (m) 5.25 (mm) Length of Image formed
on the retina (I) 5.25 (mm)

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Convex Lens Ray Diagram - When an object is
placed in front of a thin lens, light rays coming
from the object fall on the lens and get
refracted. The refracted rays produce an image at
a point where they intersect each other. The
formation of images by lenses is usually shown by
a ray diagram. - The nature of images formed by
a convex lens depends upon the distance of the
object from the Optical Center of the lens (O). -
Center of curvature (C) of a lens is defined as
the center of the sphere of which the lens is
part. - Radius of curvature (R 2F), distance
between pole and centre of curvature. - "Pole" P
(axis) the middle or center point of a lens. -The
straight line joining the center of curvature
(C) to the pole (P) is called the Principle Axis.
- Distance between the pole (P) to the principal
focus (F) is called focal length f R/2.


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1
4
C
P
A ray of light passing through the optical center
(O) of the lens travels straight without
deviation.
2
Focal length
Ray diagrams for a converging lens, showing the
formation of (a) a real image or (b) a virtual
image.
An incident ray parallel to the principal axis
after refraction passes through the focus (F2).
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Principal axis
P
The straight line joining the center of curvature
to the pole is called Principle Axis
An incident ray passing through the focus of the
lens (F1) refract parallel to the principal axis
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(object at different positions)
(Erect)
- Focal length (f) of an optical system is
defined as a measure of how strongly the system
converges or diverges light. - A
system with a shorter focal length has greater
optical power than one with a long focal length
that is, it bends the rays more strongly,
bringing them to a focus in a shorter distance
(i.e. P a 1/f).
????
????
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Lensmaker's equation
Light source
Focal length of a lens in air can be calculated
using the Lensmaker's equation, which is f
focal length of the lens, n Refractive index
of the lens material, R1 Radius of curvature
of the lens surface closest to the light source,
R2 Radius of curvature of the lens surface
farthest from the light source d Thickness of
the lens (the distance along the lens axis
between its two curved surfaces). Notes 1) Focal
length of lens depends on curvature of the lens
and the difference between the curved surfaces
(R1 R2), as given by the lens makers
equation. 2) Line joining the centers of the
spheres making up the lens surfaces is called
axis of the lens. Typically the lens axis passes
through the physical centre of the lens.
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General law of lenses
Positive (convex), converging lens ????? ? ?????
To measure the lenss power (strength)1/f
1/S11/S2 Diopter When f, S1 and
S2 are measured in m When f, S1 and S2
are measured in cm Power is 100/f 100/S1
100/S2 Diopter
Magnification of the formed image is M -
(S2/S1) (has no measuring unit)
f focal length of the lens is (cm), S1 is
distance between object (source of light rays)
and the pole of the lens (S1 value is always
positive as the object cannot be placed behind
the lens), S2 is the distance between the formed
image and the pole of the lens. Properties of
Image formed is real, smaller than object size
and upside down.
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• How to describe an image formed using a lens?
• 1- If the formed image is real then S2 (distance
  between lens and image)
• is positive and if the image is imaginary then S2
  has negative value.
• 2- Focal length (f) for a convex lens is positive
  (thats why it is called positive lens) while,
  for the concave lens f is negative (thats why it
  is called negative lens).
• 3- If magnification (M) value is positive then
  the image position is upright and if M is
  negative then the image is upside down.
• 4- If M value is greater than one then the image
  is magnified (bigger than the size of the object)
  and if M is smaller than one then the formed
  image is not magnified i.e., minified (smaller
  than the size of the object).

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Example If an object is placed in front of a
convex () lens at a distance 1(m) and if the
focal length of the lens was 3(m). Find the
distance at which the image will be formed and
describe the formed image. Answer f 3 (m),
S1 1(m)
1/f 1/S1 1/S2 1/3 (1/1) (1/S2)
hence, 1/S2 (1/3) (1/1) (1-3)/3 -2/3 As
1/S2 -2/3 then S2 (-3/2) -1.5
(m) negative value M - (S2/S1) -
(-1.5/1) 1.5 positive value greater
than 1 Image is imaginary (as S2 has a negative
value), magnified (as M value is greater than 1)
and upright (as M value is positive). P 1/3
0.33 (diopter).
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Normal Eye
Eye is said to be normal, when in a state of full
relaxation, it can focus on the retina objects at
an infinite (8) distance. Looking to a near
object, the eye accommodates itself by changing
the power of its lens in order to form the image
on the retina. Accommodation is the property of
the eye lens by which its effective focal length
is automatically altered to suit the act of
viewing distant or near objects.
S1 8 S2 f
Image formed on the retina

Incident (parallel) light photons
?????
The distance between the farthest and nearest
points which an eye can see distinctly
and without strain is called range of
accommodation. When adapted for the far point,
the change in power is necessary to accommodate
it to its near point is called amplitude or power
of accommodation.

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Refractive Errors
A refractive error, is an error in the focusing
of light by the eye and a frequent reason for
reduced visual acuity. People with refraction
error frequently have blurry vision.
Far point is the distance between the eye and
the furthest object that can be brought into
focus. The far point is effectively infinity (8)
for normal vision.
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Common eye defects are often called "refractive
errors". Refractive errors usually can be
"corrected" with eyeglasses or contact lenses, or
they can be permanently treated with LASIK and
other vision correction surgery (also called
refractive surgery).
Myopia (short sight)
Myopia is due to a slight increase in the
diameter (length) of the eye-ball or in the
curvature of the cornea. Thus the image of a far
object is formed in front of the retina, light
rays diverge to cause blurred image. But, near
object is clear. Myopia requires correction using
a concave, (-) diverging lens to compensate for
the excess refraction in the eye and to form an
image of far object on the retina.
Image of far object
(Nearsightedness)
Focus point
Retina
Far object
(diverging)
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Hypermetropic (Long sight)
This defect is due to a (1) decrease in the
diameter of the eye ball (i.e., eye is too short)
or (2) in the power of the cornea or lens (i.e.,
cornea is too flat) or combination of both 1 2.
Light from a near object isnt bent sufficiently
so that it focuses at a point behind the retina.
Hyperopic eye can focus light from a far object
but, it has trouble with near object. This defect
is corrected using a convex, () lens, which
adds to the focusing power of the eye and to
converge the light rays so that the image is
formed on the retina. In this case the eye cannot
focus properly on near objects. Hyperopic vision
becomes worse by age due to losing the focusing
power.
) Farsightedness)
Parallel light rays
Focus point of light from a near object
-----
-----
Retina
(convex)
(a) Hyperopia
(b) Its correction
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The irregularity of the corneal curvature in
astigmatism is due to that the horizontal and
vertical lines at the same distance will not be
in focus at the same time. It is compensated by a
cylindrical lens, which focuses light rays along
one axis but not along the other. Cylindrical
lenses are curved in one direction and flat in
the other.
Astigmatic person experience blurred vision. It
occurs when light entering the eye come into
focus at multiple points even in front of or
behind the retina instead of on the retina. It
may differ in degree in the two eyes. It is
caused by inequality of one or more refractive
surfaces usually in the cornea and sometimes in
the lens, so that the light rays dont converge
(come together) to a point on the retina. An
oval-shaped cornea, is more sharply curved along
one plane than another therefore, it cannot form
simultaneously sharp images of two perpendicular
lines. One of the lines is always out of focus,
resulting in astigmatism.
In astigmatism the image on the retina is
distorted
?????
A- Plano-Convex cylindrical lens B -
Plano-Concave cylindrical lens
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Presbyopia As we age, the ability of our eyes to
focus both near and far begins to diminish. This
happens whether you are nearsighted, farsighted,
or haven't used vision correction at all. This
condition is called presbyopia. It is the
dependence on reading glasses that comes to most
people with age. The lens inside the eye becomes
less flexible with time and so cannot focus on
close objects. Presbyopia is a manifestation of
getting older not a disease, but it often causes
great inconvenience. It may occur on its own or
with any of the other focus defects. It means
weakness of power of accommodation as by old age
the total power of the eye decreases and it
become hypermetropic. Besides, the ciliary
muscles will either totally or partially loose
their elasticity's and therefore, the amplitude
of accommodation decrease with the advance in
age. In this case the eye cannot focus properly
on close objects, but it could be corrected using
bifocal lens.
In presbyopia the image of close objects is
focused behind the retina
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Summary of various Focusing Problems and Their
Characteristics
Focusing Common name
Usual cause
Corrected with Myopia
Near-sighted vision Long
eyeball Negative
lens too
curved cornea Hypermetropia
Far-sighted vision Short
eyeball Positive
lens See better at long distance than short
Cornea not curved enough Astigmatism

Unequal curvature lens
of cornea Presbyopia
Old-age vision Lack of
accommodation Bifocals
Concave
Convex
(Curved in one direction, flat in the other).
cylindrical

Bifocals are eyeglasses with two distinct optical
powers. The upper part of the lens is generally
used for distance vision, while the lower part is
used for near vision. Usually, a segment line
separates the two parts.
Astigmatism is caused by a distortion of cornea
shape. Normally the cornea is almost spherical
but in astigmatism its curvature is greater in
one region than another. Vision is blurred at all
distances. Astigmatism usually occurs with either
short or long sight.
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Physics of the Eyes and Vision
Unit Coordinator Prof. Dr. Gehan El-Tabie
Medical Physics