Physics of the Eyes and Vision

Physics of the Eyes and Vision

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

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 اليرقان. 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.

Bright light therapy is a common treatment for other

diseases.

A newborn infant undergoing light phototherapy to treat neonatal الوليد jaundice

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/λ, h = Planck’s constant = 6.626 x10-34 (J/sec), f = frequency of light, c =

velocity of light in vacuum and λ = wavelength (i.e., shorter wavelength =

higher energy).

Medium particles oscillate up and down about their individual equilibrium positions as light wave passes

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

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 α 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.

Geometry of reflection and refraction of light rays

Incident

Reflected

Refracted

(Refractive index)

[Incident medium]

[Refractive medium]

(Inci

denc

e surf

ace

)

(a) Regular & (b) Diffuse reflection

θi = θr ≠ θ2

i

r

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 θ1 and θ2 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.

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 α c & n α 1/v

(Incident ray)

(Refracted ray)

(c/v1) (c/v2)

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 θc . 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

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/vIncident Incident

Normal (N)

Rarer medium

Denser mediumn = 1.333

n = 1

Refract tow

ard N

Refract

away from NInterface(Vacuum)

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

Center

Edge

Positive [convex(+)] and negative [concave(-)] lenses

موحب البؤرى بعدها محدبه عدسه البؤرى بعدها مقعره عدسهسالب

= - 0.2 (m)

(+ve, Converging) (-ve, Diverging)

P=(100/20) cm=5 (D)

= 0.2 m

Parallel light from a great distance

.

Front Back

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.

[n = 1.337][n = 1.336]

[n = 1.376]

n =

1.4

06

The eye and the camera

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 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 [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.

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.

14

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 .

Size of image on the retina

On the retina

Focusing by the cornea and crystalline lens

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)

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.

An incident ray parallel to the principal axis after refraction passes through the focus (F2).

An incident ray passing through the focus of the lens (F1) refract parallel to the principal axis

A ray of light passing through the optical center (O) of the lens travels straight without

deviation.

Ray diagrams for a converging lens, showing the

formation of (a) a real image or (b) a virtual image.

1

2

3

4

The straight line joining the center of curvature to the pole is called Principle Axis

Principal axisP

C

Focal length

P

- 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 α 1/f).

يجمع يفرق

(Erect)

(object at different positions)

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 sourced = 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 maker’s 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.

Lensmaker's equation

Light source

General law of lenses

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.

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)

Positive (convex), converging lens مجمعه و محدبه

1

2

3

1

2

3

Incident rays of light which produce image

(Upside down)

Refracted rays of light

Front of the lens Back of the lens

Pole of the lens

.

d

Center of lens

F1

F2

21

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).

22

Normal Eye

Incident (parallel) light photons

Image fo

rmed

on th

e

retin

a

S1 = ∞ S2 = f

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. 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.

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.

بوضوح

Far point: is the distance between the eye and the furthest object that can be brought into focus. The far point is effectively infinity (∞) for normal vision.

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.

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.

(Nearsightedness)

(diverging)

Myopia (short sight)

Image o

f fa

r obje

ctR

etin

a

Focus point

Far object

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).

(a) Hyperopia (b) Its correction

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 isn’t 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)

----------

Focu

s poin

t of

ligh

t from

a

near o

bject

Retin

a

Hypermetropic (Long sight)

Parallel light rays

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 don’t 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.

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.

A- Plano-Convex cylindrical lens

B - Plano-Concave cylindrical lens

In astigmatism the image on the retina is distorted مشوهه

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

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

Summary of various Focusing Problems and Their Characteristics

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.

Concave

Convex

(Curved in one direction,

flat in the other).

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.

cylindrical

Physics of the Eyes and Vision