Page 1 of8
Chapter 6: Physics of Vision – Light & the Eye
What is Light?
• Light is a form of radiant energy which stimulates receptors in the eye to evoke a visual sensation.
• Light has speed 3 x 10 m/s, a million times faster than sound. F = C/λ
Light as Rays
• Light normally travels in straight lines or rays from a light source. Light rays are emitted from a point on
a source in all directions. Opaque occluding objects in the path of the rays create shadows.
• Light rays are refracted (change direction) as they pass from one transmitting medium into another,
e.g. air to water, causing a change in the velocity of propagation.
• Lenses refract incident rays so they converge back to a point after passing through. If the source is a
spatially distributed object comprising many points, the lens will form a spatially distributed image of the
object, inverted but with preserved topology.
Light as Particles
• Newton: Light rays consist of a stream of particles. Reflections occur when they bounce off an opaque
surface, and refractions occur when they enter a medium at an oblique angle and are deflected.
Light as Waves
• Huygens: Light propagates from a source in waves.
• Young: Double slit experiment showed that when light passed through
two parallel slits in an opaque screen, a pattern of light and dark bands
was produced on a second screen.
• Passing through the slits, each wave of light spreads laterally to create
new wavefronts in diffraction. These interact in constructive and
destructive interference to create an interference pattern of bright and
• Maxwell: Light is made of transverse oscillating electrical and magnetic
• The electromagnetic spectrum is the full range of frequencies that characterize electromagnetic
radiation, from gamma rays to radio waves.
Wavelengths that stimulate the eye occupy a
narrow range from 400-700nm.
The Duality of Light
• Planck: Radiation is emitted as a stream of
discrete quanta of energy. The energy of a Violet Blue Green Yellow Orange
quantum is proportional to its frequency, by
Planck’s equation E = hf
• Lenard: Photoelectric effect where electrons
are released from a metal surface when struck
by light. Light intensity increases number of electrons emitted, but kinetic energy of electron is only
increased by change in frequency of light, not intensity.
• Einstein: Theory of quantum mechanics – light is both a particle and
• Rays to understand how images are formed; waves to understand
passage through fine scale apertures (pupil); quanta to understand light
emission and absorption. Page 2 of 8
Some Important Properties of Light
• When light strikes the interface between two substances, it may be absorbed, reflected, or transmitted.
• During absorption, light quanta are taken up by the substance and converted into thermal energy.
• Absorption is important for vision because, in order for light to be seen, photoreceptors must absorb
light energy and convert it into electrical signals.
• Light rays are scattered backward at the interface.
• Rays are reflected so angle of incidence = angle of
• Specular Reflection: Occurs when the surface is
smooth, so light rays are reflected regularly in
• Diffuse Reflection: Surface contains large irregularities, with rays ars a whole reflected in random
directions but each ray obeying the law of reflection.
• When light waves are transmitted through media, quanta are
scattered by the molecules they hit. The interference between
the original wave and the scattered wave results in slowing of
• Refraction is the change in direction of the path of light rays
as they enter a transmitting medium. The refractive index of a
medium refers to the degree to which it slows down light rays,
and consequently alters their direction.
• Air has a refractive index of 1.0, so light is retarded very little;
glass has an index of 1.5. Moving to a denser medium, light is
bent towards the normal.
• Refraction is important for lens image formation. The lens is curved so parallel light rays entering the
lens converge at a point behind the lens. The distance of this point of focus from the lens is the focal
• Refraction depends on wavelength: short wavelength blue
light is bent more than long red light.
• The rainbow we see are due to light refraction through
multiple droplets of water bending different wavelengths of
light at different angles.
• Short blue light (400nm) gets scattered more than long red
light (700nm). Rayleigh scattering is proportional to 1/λ .
• As light approaches Toronto near sunset, the short blue
wavelengths are scattered more by the atmosphere and
don’t reach Toronto. Therefore only the red wavelengths do, making the sky look red.
• The intensity of a light source depends on the number of quanta emitted/unit time, measured
using radiometric units of intensity (radiance). Page 3 of8
• Photometric units take into account the sensitivity of the human visual system for some wavelengths
over others, in luminance given in candelas/square metre (cd/m ). 2
• Different light sources have a wide range of intensities, e.g. 0.0003 cd/m of paper in starlight (1013
photons) to 40,000 cd/m of paper in sunlight (10 photons).
• Photons/quanta emitted are not equivalent to photons reaching eye receptors, but reduced by a factor
of 10 . At dimmest conditions, each receptor receives only 0.01 quanta/second, so minutes may elapse
before successive strikes on any one receptor.
• The visual system copes with this range of light levels to adjust the operating range of photoreceptors
appropriately, in light and dark adaptation.
Contrast & Reflectance
• Reflectance: The proportion of incident light reflected from a
surface. Highly reflecting surfaces appear whitish and have
values approaching 1, whereas surfaces with low reflectance
appear dark and have values near 0.
• Radiance = Irradiance x Reflectance; Luminance = Illuminance
• Colour perception is based on reflectance, not absolute
luminance: A checkerboard white square in shadow may have
same luminance as checkerboard black square in light, but we
still see them as different colours.
• Contrast: Measure f difference between the highest luminance
and lowest luminance emitted/reflected from a surface; Contrast is independent of the absolute level of
illumination. C = (Lmax– Lmin(L max+ Lmin
• Contrast provides information about surface reflectance, more so than absolute luminance.
Wavelength & Spectral Power/Reflectance
• Humans can detect wavelengths between 400 and 700nm.
Red light has a shorter frequency and longer wavelength.
From 700 nm to 400 nm, color varies through the sequence
• Spectral Power Distribution: The wavelength composition
of a light source. Incandescent lamps have more energy in
the yellow-red end, whereas daylight is more evenly
distributed, slightly favouring blue.
• Fluorescent light bulbs and helium-neon lasers have
discrete spectra; the laser is monochromatic red light.
• Spectral Reflectance: Surface reflectance varying as a
function of wavelength. E.g. Snow reflects a high proportion
of light at all wavelengths, grass reflects a lot of green.
Natural surfaces tend to reflect more light at longer wavelengths (reds).
• Spectral reflectance is the inverse of spectral absorption.
• Objects look a certain colour because that colour light is reflected off it,
into our photoreceptors (red box reflects red light, absorbes the rest)
• Spectral power distribution of light reflected from a surface depends
both on the spectral power distribution of the illuminant, and on spectral
reflectance of the surface.
The Eye Page 4 of 8
• The eye catches photons, and directs them onto photoreceptor
• For a light receptor to be called an eye, an image must be formed on a sheet of photoreceptors which
preserves the spatial arrangement of points in space from which the light emanated.
Structure of the Human Eye
• The human eye is a roughly spherical, light-tight chamber, the inside of which is lined with a sheet of
• Light passes through the transparent membrane of
• It enters the pupil, an aperture controlled by the iris
muscles, which determine eye colour.
• Light passes through the lens, whose shape is
controlled by ciliary muscles and zonule fibres.
Contraction of ciliary muscles loosen zonule fibres,
allowing the lens to naturalize to its round shape.
• Light strikes the retina, covered with photoreceptors.
• The interior of the eye is filled with vitreous humor in
the posterior chamber, which maintains the shape of the
eye and holds the retina in the correct position.
• It also contains aqueous humor, which nourishes the lens and keeps the eye inflated (in through ciliary
process, out through canal of Schlemm) in the small anterior chamber. This fluid is replenished every 45
• The photoreceptors send signals down the optic nerve, which leaves the eye through the optic disk,
creating a blind spot (13° temporal of fovea, diameter of 6°).
• Photoreceptors on the retina are arranged inversely, with ganglion, other cells, and blood vessels in
front of the photoreceptors. Therefore, at the retina there can be no photoreceptors when the ganglion
nerves need to exit.
• Visual Angle: The angle an object subtends at the centre of a lens (nodal point), depends on both the
size of the object and its viewing distance.
• For small angles 10° or less: TanƟ = S/d where Ɵ is visual angle, S is size of object, and D is viewing
• One degree is divided into 60 minutes (60’, and one minute into
60’’ seconds). 0.25° is 60/4 = 15’, 0.01° is 36’’.
• The nodal point is the point the light rays pass through without
• The angle subtended by the image on the retina is equal to the
angle subtended by the object at the nodal point. The farther
away the retina from the lens, the larger the retinal image; one
degree of visual angle is 0.288 mm on the retina.
Cornea & Lens: Optical Power
• Refraction occurs at four surfaces in the eye where there is a
change in medium: front corneal surface, back corneal surface,
front lens surface, back lens surface. Page 5 of 8
• The greatest refraction occurs at the interface between air and cornea (1.0 vs. 1.376). This creates an
optical system with a focal length of 16.8 mm, about the distance between the lens and the retina.
• Optical power is expressed in diopters (D) = 1/focal length (metres); the power of the eye is 59.52D.
Cornea & Lens: Accommodations
• In a relaxed state the eye pr