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

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

Effects through the eye Effects through the skin

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.

Bright light therapy is a common treatment for other diseases.

A newborn infant undergoing light phototherapy to treat neonatal jaundice

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)

Angle of incidence = Angle of reflection

The angle of reflection is formed between the

reflected ray and the normal.

The angle of incidence is formed between the incident ray and the

normal.

When a wave reaches a boundary it is:Partially reflected (bounces off surface)Partially transmitted through surface

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

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:

)sin()sin( 2211 nn

n1

n2

1

2

The incident ray, the normal to the incidence point and the refracted ray are all in one plane

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

Incident Incident

Normal (N)

Rarer medium

Denser medium

n = 1.333

n = 1

Refract tow

ard N

Refract

away from NInterface(Vacuum)

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

• the critical angle ( c) is defined as the angle of incidence that provides an angle of refraction of 90-degrees.

• Medical Applications: endoscopy

n1

n2

c

2= 90

1

2)sin(n

nc

Problem-1Determine 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-2Determine 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.

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

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 DiopterMagnification of the formed image is M = - (S2/S1) (has no measuring unit)

Positive (convex), converging lens

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

Image Object

Upright Enlarged VirtualInside f

Image

Object

Inverted Enlarged RealBetweenf & 2f

Object

Image Inverted Reduced Real

An example is the human eye

f is the focal length of the length

Past 2f

Three cases for converging (Convex) lensThree cases for converging (Convex) lens

f

f

f

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

= - 0.2 (m)

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

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

= 0.2 m

Parallel light from a great distance

.

Front Back

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).

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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.

[n = 1.337]

[n = 1.336]

[n = 1.376]

n =

1.4

06

Eye as an optical system

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.

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.

19

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.

Size of image on the retina

S2

On the retina

Focusing by the cornea and crystalline lens

O/I= S1/S2 S2

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)

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Normal Eye

Incident (parallel) light photons

Image form

ed on the retina

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.

The distance between the farthest and nearest points which an eye can see distinctly and without strain is called range of accommodation.

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 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 corneaAbnormal 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 objects3 -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 objects2“ -Can see far” – no difficulty focusing on distant objects

3 -Images of nearby objects are formed at a location BEHIND the retina4 -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