Physics of the Human Eye

Charlie Chen, Kevin Sun, Alborz Kia, Vince Milczek, Alan An

McGill University Department of Physics

Supervisors: Michael Hilke

March 10, 2017

1 Introduction

The human eyes are the organs responsible for reacting to light and colours and forming

images that are then interpreted by the brain. The biology of the eye permits light to enter

through the pupil and be bent by a number of biological structures which are used to focus

light onto the retina. The purpose of this paper is to answer the question as to how the optics

and biology work together to form an image which is able to be interpreted by the brain. We

begin by outlining the basic structures of the eye and their individual purposes as well as the

phototransduction mechanism. We then move onto the electromagnetic properties of light in

vacuum as well as its propagation and activity through different media. Using these concepts

we will be able to explain the propagation of light through the eye, and subsequent image

formation onto the retina. Evidently, there are situations where the eye cannot produce a

focused image and we examine how these eye defects are corrected using corrective eye-wear

or laser eye surgery.

2 Biology

The eye is unique due to the result of what occurs when it reacts to light and pressure.

The various structures of the eye work cooperatively to accept incoming light rays in order

to focus an image onto the retina. The human eye is comprised of many components as is

seen in the diagram below, and we outline some of the most important features necessary for

image formation as well as some other structures necessary for electrical impulse production

and structural integrity.

1

Figure 1: A cross sectional view of the eye with various structures labeled.

The light rays entering the eye first encounters the cornea which is the transparent layer

covering the pupil. The cornea itself is composed of five layers: The epithelium, Bowman’s

layer, the stroma, Descemet’s membrane, and finally the endothelium. The epithelium is the

first line of defense and it is also responsible for the absorption of nutrients and oxygen from

tears and conveys it to the rest of the Cornea. The opening to the inner eye is called the pupil

and this is responsible for controlling the amount of light entering the eye. The iris (ring

shaped membrane surrounding the eye composed of muscle fibers) does this by constricting

or dilating the pupil.

Once past the pupil, the light rays entering the inner eye are bent by the crystalline

lens. The lens is an instrumental tool which works cooperatively with the cornea to bend

and focus light. In order to accommodate for different object distances, the lens is able to

change shape, via the action of the ciliary muscle in order to change the focal point of the

lens, which is the point at which all of the light rays collect. Ideally the light rays would

collect on the inner wall of the eye known as the retina on a point called the fovea. The

Fovea are layers of the retina, which are spread aside to let light fall directly on the sensory

cells. This area contains the cone and rod photoreceptors which are used to perceive light

and colour and converts the light into electrical impulses. Of particular importance on this

bed of photoreceptors is the optic disk, or the region of the fovea where the nerve bundles for

2

the optic nerve are gathered, connecting this to the retina, and rendering this a blind spot on

the retina – as well as the converse of this, the fovea centralis. The latter serves as the point

on the retina where images are processed to the highest acuity, and is in close proximity to

the optic disk.

The organization of the retina is of fundamental importance in generating visual infor-

mation. In the majority of the region that is spanned by the retina, there is a systemic

organization of both rods and cones which are involved in signal transduction and subse-

quent neurotransmitter release, followed by a second layer constituted almost exclusively of

bipolar cells and amacrine cells, both of which process and converge the visual information

towards the ganglion cells. The foray of information is fed into the ganglion cells that con-

verge onto the optic disk to form the optic nerve – this then travels, via the optic tract, to

the visual cortex located in the occipital lobe of both hemispheres of the brain. An exception

to the arrangement in the retina is the fovea centralis, wherein the retinal circuitry is shifted

out of the way to maximize image acuity.

A brief outline of phototransduction offers a glimpse into the biochemical processes at

play – within a rod cell, for example, which is responsible for sight at nighttime, and in low

light conditions, there is a single opsin molecule (visual pigment) called rhodopsin that is

manifested in billions of tiny stacked structures that are highly sensitive to faint light. Nor-

mally in rods, the membrane is depolarized as the sodium channels are open to allow influx

of Na+ ions into the cytoplasm, and neurotransmitter release. However, once chromophores

become active, as during light exposure, rhodopsin triggers a G-protein cascade, that con-

verts cGMP to GMP in the rod cytoplasm, resulting in cessation of Na+ ions coming in by

opening of Na+ ion channels and hyperpolarization of the cell. This is what occurs in cones,

which also contain 3 chromatic opsins that enable us to distinguish the colors around us.

Once the information has been converged onto the middle layer of the retina, bipolar and

amacrine cells are activated by the inverse process – a decrease in release of neurotransmitter

from the first layer is responsible for their functioning

3

Figure 2: A cross sectional view of the mechanism for responsible for phototransduction andthe individual molecules involved.

There are other structures of the eye which are less implicated in image formation. The

inner eye is suspended in a water based fluid known as the vitreous humor. The entire eyeball

is supported by the sclera, which is a white tissue forming the supportive wall of the eyeball.

The eye is supplied with nourishment by the choroid. The Choroid lies between the retina

and the sclera of the eye and contains the vascular layer containing connective tissue. The

choroid’s primary function is to provide a supple of oxygen and nourishment to the outer

layers of the retina, ciliary body and the iris.

3 Physics

To explain how the physics and optics of the eye actually work, the underlying concepts

must be discussed first. The nature of light, how lenses use refraction to bend light and

finally how the eye uses these concepts to produce an image.

3.1 Light Properties

Visible light is just one small section of the much larger electromagnetic spectrum. The

range of wavelengths corresponding to visible light lies in the 400-700 nm range. This also

explains why we perceive different colours, since different colours correspond to different fre-

quencies of light; reddish tones are characterized by longer wavelengths while bluish tones

are characterized by shorter wavelengths. Light itself can be represented as oscillating elec-

4

tric and magnetic fields and can be mathematically represented by the following complex

equation:~E(r, t) = ~Eo(r, t)e

i(~k·~r−ωt−φ) (1)

Equation 1 tells us everything we need to know about that specific wave. The amplitude

is Eo, the direction of propagation is given as the direction of ~r, the polarization of the wave

which is the direction of oscillation is given by the direction of Eo. The wave vector, ~k relates

the direction of propagation and the wavelength of the wave.

Like all electromagnetic waves, light carries energy which is equally distributed in both

the electric and magnetic fields. The amount of energy carried by a light wave is related to

the frequency of the wave as in, where h is known as Plank’s constant:

E = hf (2)

Light can also be described as individual particles which are known to carry momentum

(despite being massless) depending on the conditions, such as the case in the photoelec-

tric effect. Wave-particle duality is captured by the De-Broglie equation which relates the

wavelength of light λ to the momentum of the particle p:

p = h/λ (3)

3.2 Light Propagation

Unlike other types of waves such as sounds waves, light waves do not require any medium

for propagation. In vacuum, the speed of light is a constant, c = 3 × 108 m/s. However in

substances other than vacuum, the speed of light changes according to the properties of the

material. The speed of light in media depends on the permittivity (a measure of “resistance”

of how an electric field is affected by a medium) as well as the permeability (a measure of a

material’s ability to support magnetic transmission).

Upon traversing from one material into a different material, the path of light takes the

5

path of least time, which is known as Fermat’s principle. This means that upon entering

a different material and refracting at the interface between two materials, the light will

take the path which will minimize the time between the start point and end point. Using

Fermat’s principle, we can derive the law of refraction which relates how light behaves upon

encountering a boundary of two materials.

3.3 Refraction

Light traveling through different media are affected differently. Although the speed

of light in a vacuum is a constant denoted c, the speed of light in different media varies

depending on the media itself. Medium with higher index of refraction cause the light to

travel more slowly within that medium. The index of refraction

n =c

v(4)

is the ratio of the speed of light in a vacuum to the speed of light in that medium. Notice

how the index of refraction is always equal to or greater than 1.

When light travels from one medium to another medium, the direction of light prop-

agation changes because of the change in speed upon encountering the interface separating

the two materials.

Figure 3: A depiction of an interface between two materials with different indices of refraction.The medium on the top is of lower index of refraction than the blue medium.

6

This can be explained through the use of Fermat’s Principle. To minimize the time taken

by the light from point A in air to point B in a medium with a higher index of refraction

than air, the shortest path is no longer a straight line. In fact since light travels faster in air,

it tends to spend more time in the air to make up for the fact that the speed is slower in the

medium. As a result, the light bends upon encountering a material with a different index of

refraction (for reference, vacuum has an index of refraction n=1). If the light travels from

a fast media to a slow media (e.g. air to glass) then the light bends towards the normal to

the interface, whereas if the light travels from a slow media to a fast media then it will bend

away from the normal. In order to mathematically describe the degree of bending, Snell’s

law (derived from Fermat’s principle) is used to relate the angle of incidence and the angle

of transmittance.

n1 sin θ1 = n2 sin θ2 (5)

In this equation n1, n2 are the index of refractions of the media and θ1, θ2 are the respective

angles relative to the normal.

3.4 Optics

In order to bend incoming light rays and focus the light rays, lenses are used to strategi-

cally bend the light rays. Lenses are specially designed shapes composed of materials which

allow the passage of light. There are two main classes of lenses, concave lenses and convex

lenses. The difference between the two lenses (besides their shape) is how they change the

shape of the incoming light rays.

7

Figure 4: The two most commonly categorized type of lenses. Convex lenses focus collimatedor parallel light rays while concave diverge collimated rays.

Lenses are described by a couple of different characteristics: the shape, the radius of

curvature of each side of the lens and the focal length. Since you can shape each side of the

lens to whichever radius of curvature that you like, each side needs to be described. The

focal length of a lens is measured by sending in collimated or parallel rays of light as shown

below.

Figure 5: Convex lens on the left and a concave lens on the right. Notice how the focal lengthf is depicted in the figure.

The focal length for a convex lens can either be defined as the distance away from the lens

in which collimated rays intersect or the distance at which light from a point source becomes

collimated. The focal length for a concave lens is a little different, it is defined as the distance

that rays traced back from collimated rays such that the traced back rays intersect or the

distance at which if a source were placed at the focal length, the traced back rays would be

8

collimated.

The action of convex lenses (the human eye in particular) is used to focus incoming light

rays in order to create an image of the original object. And this is exactly what occurs in

the human eye. The lens in the eye bends the incoming light rays so that the individual

rays collect at the fovea so that a sharp image of the object is formed and can be interpreted

by the brain. To see how a convex lens works to create an image, a ray diagram is used as

demonstrated below. A ray diagram depicts the light rays as arrows.

Figure 6: A depiction of how and where an image is lensed in a standard lens system. Thedistance from the object to the lens is labeled o while the distance from the image to the lensis labeled i.

As the ray diagram above shows, for a convex lens, the light rays originating from the ob-

ject are bent by the lens. The point at which all of the light rays intersect is where the image

is created. This action is identical in the lens, light rays are bent by the lens and are collected

on the retina forming an image on the retina. Furthermore , the image is also upside down

as the ray diagram shows, the brain flips the image right-side up during interpretation. In

order to view objects at different distances, the lens can stretch and change it’s shape in order

to change the focal length of the the crystalline lens and focus the rays at a different location.

There is an equation called the lensmaker’s equation which relates o, i and f .

1

o+

1

i=

1

f(6)

This equation is extremely useful to figure out and compute the characteristics of single and

9

multi lens systems.

One interesting thing about the eye is the presence of the iris. It does not aid in the

actual lensing of the image but has a different purpose. It restricts the amount of light that

can enter the eye. Since the retina is quite fragile to ultra violet light, prolonged exposure

can cause permanent damage and temporary exposure can cause temporary effects. The

restriction of light entering the eye is done by restricting how much of the lens or pupil is

exposed to the light. This iris is also known as the aperture for the eye. It closes when there

is a lot of light present and opens when there is insufficient amounts of light.

Figure 7: The purpose of an aperture is to block some of the refracted light rays from beingdetected by the screen behind.

4 Eye Conditions

A perfectly healthy eye would perfectly focus the incoming light rays at the fovea, how-

ever there are certain conditions which causes the image to become unfocused and some of

these eye defects are discussed in this section.

4.1 Nearsightedness (Myopia)

Nearsightedness is characterized by blurriness when trying to view distant objects. The

reason behind this condition is that due to irregularities in the cornea and the crystalline

lens, the light rays from distant objects focus before the retina as shown in the top picture

of figure 8. To correct for myopia, a concave lens is used to diverge the incoming light rays

so that they focus on the retina as shown in the bottom image of figure 8.

10

Figure 8: The effect of myopia on image formation and the concave lens used to correctmyopic conditions.

There is no strong evidence as to the cause of myopia, but there are a few hypotheses. The

"near work" hypothesis states that near work strains the eyes and increases the risk of myopia.

The "visual stimuli" hypothesis states that lack of normal stimuli (natural environment)

causes improper development in the eyeball.

4.2 Farsightedness (Hyperopia)

The opposite condition to nearsightedness is known as hyperopia. This condition is

characterized by an inability to focus on nearby objects. The cause of this is due to the

cornea or crystalline lens being too short so that incoming light from nearby objects are

focused behind the retina, as shown in the top image of figure 9. To correct for hyperopia,

a convex lens in placed in front of the cornea so that incoming light rays are focused before

reaching the eye.

11

Figure 9: The effect of hyperopia on image formation and the convex lens used to correcthyperopic conditions.

The causes of hyperopia are largely genetic and thus are less common than myopia.

4.3 Other Eye Conditions

Some other common conditions of the human eye include astigmatism, presbyopia, and

cataracts. Astigmatism occurs as a result of an aspherical lens or the cornea, resulting in

distorted or blurred vision- this can be corrected using contact lenses that focus light evenly

on a focal point on the retina. Presbyopia and cataracts become markedly more pronounced

with age – while presbyopia is a result of the stiffness of the lens and/or ciliary muscle,

rendering the eye unable to accommodate changes to near vision, cataracts is a ‘cloudiness’

of the lens wherein the lens changes color. While presbyopia is commonly treated with

eyeglasses, specifically bifocal lenses (which have an upper portion for distance viewing, and

a lower portion for reading and closer viewing), cataracts, in its more progressed stages, is

treated by cataract surgery, a popular option owing to its largely successful results in treated

patients in improving vision.

4.4 Laser Eye Surgery

Instead of correcting myopic and hyperopic conditions, laser eye surgery can be used in

order to treat the condition altogether. Laser eye surgery involves making small incisions in

12

the surface layers of the cornea in order to gain access to the inner layers of the cornea. A

laser in then used to reshape the cornea. Applying concepts from the optics discussed above,

the cornea is reshaped so that incoming light rays are focused on the retina in instead of in

front of the retina (myopic patients) or behind the retina (hyperopic patients)

5 Conclusion

As a result, we have discovered that there are significant properties that are infinitesi-

mally important and further more instrumental which pertain to the underlying principles

of how an eye works. The Anatomy of the eye, Biophysics, Physics and Optics; all serve a

purpose on how we are able to understand how the eye works. The anatomical components of

the eye all have specific purposes as either structural support or function. The rod and cone

cells that are instrumental for absorbing the light. In a nut shell the biochemical reaction

happens through an influx of Na+ ions which are released into the cells cytoplasm. This

results in a neurotransmitter release this triggers a chemical reaction in the rod cell cyto-

plasm; and ends with the cell being hyperpolarized. The direct result it the cone cell begins

to distinguish colors around us. Once the information has been converged onto the middle

layer of the retina, bipolar and amacrine cells are activated by the inverse process a decrease

in the release of neurotransmitter from the first layer is responsible for their functioning. The

physics of the eye help describe mathematically what occurs in the eye while light penetrates

through it. Henceforth leading into the subject of optics. The optics of how the eye interprets

light is provided in detail of how light is affected when it comes into contact with a concave or

convex shape. In the circumstances of the human eye, we will use a convex shape to examine

how light reacts to the eye. The action is identical in the lens, light rays are bent by the lens

and are collected on the retina, henceforth forming an image on the retina. Keep in mind

the image is upside down until the brain interprets the information from the eye and inverts

the image making it right side up. Finally, under the circumstances as of health issues the

eye must require medical attention in order to find a curable solution.

13

6 Individual Contributions

Charlie Chen - Wrote half of the physics section as well as the introduction, also formatted

the final PDF document.

Kevin Sun - Wrote half of the physics section and also formatted the final PDF document.

Alan An - Researched and wrote about Myopia and Hyperopia as well as the laser eye surgery

section.

Vince Milczek - Researched the entire biology of the eye as well as wrote the conclusion.

Alborz Kia - Researched the mechanism by which phototransduction occurs and other eye

conditions.

7 References

7.1 Images

1. https://clipartfox.com/categories/view/a14655f7d34ba88c78695533b6033881471c49ff/eyeball-diagram.html

2. http://formulas.tutorvista.com/physics/snell-s-law-formula.html

3. https://researchthetopic.wikispaces.com/What+are+concave+and+convex+lenses

4. http://hyperphysics.phy-astr.gsu.edu/hbase/geoopt/imggo/foclen.gif

5. http://hyperphysics.phy-astr.gsu.edu/hbase/geoopt/raydiag.html

6. https://en.wikipedia.org/wiki/Near-sightedness

7. https://en.wikipedia.org/wiki/Far-sightedness

8. http://photo.stackexchange.com/questions/2559/how-does-aperture-work-without-cropping-the-image-

hitting-the-sensor

7.2 Sources

1. Alan Litke. "Biophysics Approach to the Eye". <http://www.hep.yorku.ca/menary/biophysics/eye.html>

2. Antonio Zamora. "Anatomy and Structure of Human Sense Organs".

<http://www.scientificpsychic.com/workbook/chapter2.html>

3. Healthline Medical Team. "Cornea Function". <http://www.healthline.com/human-body-maps/cornea>

14

4. MedicineNet. "Medical Definition of Pupil". <http://www.medicinenet.com/script/main/art.asp?articlekey=5135>

5. Healthline Medical Team. "Iris". <http://www.healthline.com/human-body-maps/iris-eye>

6. MedicineNet. "Medical Definition of Aqueous Humor".

<http://www.medicinenet.com/script/main/art.asp?articlekey=10588>

7. Healthline Medical Team. "Lens". <http://www.healthline.com/human-body-maps/lens>

8. Linda J. Vorvick. "Ciliary Body". <https://medlineplus.gov/ency/article/002319.htm>

9. Heathline Medical Team. "Sclera". <http://www.healthline.com/human-body-maps/sclera>

10. Wikipedia. "Choroid". <https://en.wikipedia.org/wiki/Choroid>

11. MedicineNet. "Fovea". <http://www.medicinenet.com/script/main/art.asp?articlekey=24120>

12. MedicineNet. "Optic Nerve". <http://www.medicinenet.com/script/main/art.asp?articlekey=4653>

13. Healthline Medical Team. "Vitreous Humor". <http://www.healthline.com/human-body-maps/vitreous-

humor>

14. MedicineNet. "Retina". <http://www.medicinenet.com/script/main/art.asp?articlekey=7931>

15. Healthline Medical Team. "Central Retinal Artery". <http://www.healthline.com/human-body-

maps/central-retinal-artery >

16. Eugene Hecht. "Optics". <https://physics.wustl.edu/classinfo/316/Theory/Light.pdf>

17. Wikipedia. "Permeability". <https://en.wikipedia.org/wiki/Permeability(electromagnetism)>

18. Wikipedia. "Permittivity". <https://en.wikipedia.org/wiki/Permeability(electromagnetism)>

19. Wikipedia. "Nearsightedness". <https://en.wikipedia.org/wiki/Near-sightedness>

20. Wikipedia. "Farsightedness". <https://en.wikipedia.org/wiki/Far-sightedness>

21. Chris Woodford. "Laser Eye Surgery". <http://www.explainthatstuff.com/lasereyesurgery.html>

22. Previous/Current course notes from Physiology, and physics courses

15