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Physics of the Eyes and Vision
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
Light and Health



Effects through the eye
Effects through the skin
Positive effects
◦ Light on skin
 Vitamin D production
 Light therapy throught the skin
 Endoscpoy: Endoscopy means looking inside and typically refers to looking inside the
body for medical reasons using an endoscope, an instrument used to examine the
interior of a hollow organ or cavity of the body.

Negative effects
 blue-light hazard
 UV radiation to eye  cell deaths in the eye
 Cataract is a form of eye damage in which a loss of transparency in the lens of
the eye clouds vision.
Light on skin

skin cancer
Light in medicine:
Light therapy or phototherapy: is the exposure to daylight or to specific wavelengths of
light using lasers (Light Amplification by Stimulated Emission of Radiation) .
Medical applications of light therapy also include pain management, accelerated wound
healing, hair growth, improvement in blood circulation.
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.
Electromagnetic radiation:
Electromagnetic radiation (EM radiation or EMR) consists of two electric (horizontal
plane) and magnetic (vertical plane) fields perpendicular to each other and perpendicular
to the propagation direction as shown in figure.
Electromagnetic radiation is characterized by:
1- In space, it travels with the speed of light and undergo refraction, attenuation, diffraction,
and reflection.
2- Wavelength (λ Lambda, measured in Length unit (nm) ) is the distance between any two
points have the same phase.
3- Frequency (f) is the number of cycles or vibrations undergone during one unit of time
(Hertz (Hz) or S-1) ( Speed of light C = λ (Wavelength) x f (frequency))
4- Period (T) is the time for one complete cycle (S).
5- Energy of electromagnetic radiation is calculated by (E=hxf) (h is Planck’s constant, h=
6.5821 × 10-16 eV s)
Law of Reflection (consider geometric optics)
When a wave reaches a boundary it is:
Partially reflected (bounces off surface)
Partially transmitted through surface
The angle of incidence
is formed between the
incident ray and the
normal.
The angle of reflection is
formed between the reflected
ray and the normal.
Angle of incidence = Angle of reflection
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
nαc
&
n α 1/v
The laws of refraction: Snell’s laws
• If light travels from material 1 with index of refraction n1 to material 2 with index of
refraction n2 the following laws determine the direction of the refracted ray:
The incident ray, the normal to the
incidence point and the refracted ray
are all in one plane
1
n1 sin( 1 )  n2 sin( 2 )
n1
2

n2
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
n=1
(Vacuum)
n = 1.333
Interface
Denser medium
Total Internal Refraction
•
•
•
At the border of two materials usually both reflection and
refraction appears
In some peculiar situations however the refracted light is
also reflected! --> reflection is total!
This can happen when light travels from a medium with
higher index of refraction to one with a smaller index of
refraction, and the incident angle is big enough
n2
sin(  c ) 
n1
•
•
the critical angle ( c) is defined as the angle of incidence
that provides an angle of refraction of 90-degrees.
Medical Applications: endoscopy
c
n1
2= 90
n2
Problem-1
Determine the critical angle of the following materials when surrounded by air:
a. teflon (n = 1.38)
b. Pyrex glass (n = 1.47)
c. Polycarbonate glass (n = 1.59)
d. Sapphire gemstone (n = 1.77)
e. Diamond (n = 2.42)
Answer:
a. 46.4°
b. 42.9° c. 39.0°
d. 34.4°
e. 24.4°
Problem-2
Determine the critical angle of the following materials when surrounded by water (n =
1.33):
a. teflon (n = 1.38)
b. Pyrex glass (n = 1.47)
c. Polycarbonate glass (n = 1.59)
d. Sapphire gemstone (n = 1.77)
e. Diamond (n = 2.42)
Answer: a. 74.5°
b. 64.8°
c. 56.8°
d. 48.7°
e. 33.3°
Lenses





For materials that have the entrance and exit
surfaces non-parallel: the direction of light
beam changes
The best results obtained by lenses: piece of
glass with spherical surfaces
Two main groups of lenses:
- those that converge light rays (like concave
mirrors)
- those that diverge the light rays (like
convex mirrors)
Converging and Diverging lens
Characteristic points and lines:
- center of lens
- optical axis
- focal point (on both sides)
- focal length (equal on both sides)
Focal length of lens is the distance between
the center of a convex lens or a concave
lens and the focal point of the lens or
cocave lens. — the point where parallel rays
of light meet, or converge.
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.
1
C
4
P
A ray of light passing through the optical center
(O) of the lens travels straight without
deviation.
2
Ray diagrams for a converging lens, showing the
formation of (a) a real image or (b) a virtual image.
Focal length
An incident ray parallel to the principal axis
after refraction passes through the focus (F2).
3
Principal axis
P
An incident ray passing through the focus of
the lens (F1) refract parallel to the principal
The straight line joining the center of curvature to
the pole is called Principle Axis
General law of lenses
Positive (convex), converging lens
Front of the lens
d
1
Back of the lens
Center of lens
.
2
F1
Incident rays of light which
produce image
3
1
F2
(Upside
down)
2
3
Pole of the Refracted rays of light
lens
To measure the lens’s power (strength):1/f =1/S1+1/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.
Three cases for converging (Convex) lens
Past 2f
Image
Object
f
Image
Between
f & 2f
Inverted Reduced Real
An example is the human eye
f is the focal length of the length
Inverted Enlarged Real
Object
f
Inside f
Upright Enlarged Virtual
Image Object
f
14
Positive [convex(+)] and negative [concave(-)] lenses
Front
= 0.2 m
Back
.
= - 0.2 (m)
P=(100/20) cm=5 (D)
Parallel light from a great
distance
(+ve, Converging)
(-ve, Diverging)
The optical power of a lens is a measure of how much the lens bends light. The greater
the optical power, the more the lens bends light. The optical power is the reciprocal of
the focal length of the lens.
P = 1/f(m)
Power of a lens is measured in Diopter
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).
16
[n =
1.336]
n = 1.406
Eye as an optical system
[n = 1.337]
[n =
1.376]
Eye is like a camera. Light enters the eye through a small hole called the pupil and is focused on the
retina,. Eye 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.
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 fluids.
(1) The front (anterior) chamber, between the lens and the cornea, is filled with a
watery fluid called aqueous humor formed by ciliary body [n=1.336]. 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) [n=1.337]. 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.
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.
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= S1/S2
I is the image size on the retina, O is the object size, S1 is the object distance from the lens
and S2 is the distance between lens and the image.
S2
O/I= S1/S2
On the retina
S2
Focusing by the cornea and crystalline lens
19
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 S2 = 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 S2= 2 (cm) = 2 x10-2 (m)
O/I = S1/S2
I = OS1/S2 =
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: S1 = 10 (m) , O = 1.75 (m) , S2 = 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)
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 (that’s why it is called
positive lens) while, for the concave lens f is negative (that’s 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)].
21
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 (∞) 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.
Incident (parallel) light
photons
S2 = f
Image formed 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 = ∞
The distance between the farthest and nearest points which an eye can see distinctly and without strain is called
range of accommodation.
The far point (infinity) is the point furthest from the
eye where an object can be seen
clearly by the eye without straining it.
The point of the least distance from the eye such that
an object can be seen clearly without strain is called the
near point.
Visual defects: When an eye cannot focus an object's image on the retina (Image
formed in front of or behind the retina).
Results in blurred vision
Typical causes:
Abnormal length of the eyeball
Abnormal curvature of the cornea
Abnormal accommodation
Correction: Glasses or Contact lenses
Myopia (Nearsightedness)
1- Inability of the eye to focus on DISTANT objects
2- “Can see near” – no difficulty focusing on nearby objects
3- Images of distant objects are formed in front of the retina
4- Far point is closer than normal
Correction: by using a concave (Negative lens) of Focal length which is equal to the far
point of the patient.
Hypermetropic (Longsightedness)
1- INABILITY of the eye to focus on NEARBY objects
2- “Can see far” – no difficulty focusing on distant objects
3- Images of nearby objects are formed at a location BEHIND the retina
4- Near point is located farther away from the eye
Correction: by using a convex (converging, Positive lens)
Astigmatism

Most common refractive error

In ophthalmology, the vertical and horizontal
planes are identified as tangential and sagittal
meridians, respectively. Ophthalmic astigmatism
is a refraction error of the eye in which there is a
difference in degree of refraction in different
meridians

Blurred or sometimes distorted vision at any
distance
Cause:
◦ Irregularly shaped cornea or lens
 More oblong than spherical
 Refractive power differs between regions of
the cornea


Correction
◦ Glasses
 Cylindrical Lenses with different radii of
curvature in different planes