Nature of Light
|May 1, 2010
|April 7, 2010
Darryl Meister is a Certified Master Optician, technical marketing manager for Carl Zeiss Vision, technical representative to the VCA and ANSI, has been a key contributor to many important industry initiatives and writes and lectures frequently on ophthalmic optics, lenses and dispensing.
completion of this program the participant should be able to:
- Learn the fundamental principles of light
- Understand the visible spectrum
- Know Snell’s law
- Determine the effects of prisms and reflection
- Understand how mirrors work
- Understand the effects of light and shadows.
This course will present the fundamental principles of light and its interaction
with objects, including a review of the visible spectrum, Snell's law of
refraction, prism, and reflection. This is a technical, intermediate level course
intended for dispensing opticians, laboratory technicians, and paraoptometric
personnel. An understanding of basic mathematics is required.
Since the time of Plato, scientists have theorized about the exact nature of
light. The renowned physicist, Isaac Newton, proposed that light consisted of
streams of minute particles that were emitted from a source. He called these
particles corpuscules, and his theory the corpuscular theory of light. This
theory proposed that light exhibited particle-like nature. In the late 1600s,
Robert Hooke and Christian Huygens each suggested that light emanated
from a source in the form of waves, much like ripples across a pond. This has
become known as the wave theory of light, and suggested that light
exhibited wave-like behavior. At least one of these two theories could be
applied to explain the various phenomena produced by light. Still, neither of
them was able to explain completely every aspect of the complex behavior of
Scientists broke further ground in the 1800s when Thomas Young was able to
substantiate the wave nature of light with his "double-slit experiment."
Another milestone came a few years later when James Maxwell suggested
that light was, in fact, a form of electromagnetic radiation. Maxwell
discovered that certain types of energy traveled through space via waves of electromagnetic radiation that vibrate along their direction of their travel (or propagation).
These continuous waves of electromagnetic radiation are formed by
continuously changing magnetic fields that vibrate perpendicularly to
changing electrical fields. Waves of electromagnetic radiation travel at a
speed of approximately 300,000 kilometers per second (186,000 miles per second) in free space. This discovery integrated the wave theory of light with
the principles of electromagnetism.
These waves are periodic, since they repeat at regular intervals (or
cycles). The distance from crest to crest (or trough to trough) between any
two waves is known as the wavelength. The height of the wave is known as
the amplitude. Frequency describes the number of vibrations of the wave
per unit length of time, or how fast the wave repeats itself. If we know the
velocity (that is, 300,000 km/s) and wavelength of an electromagnetic wave,
we can determine its frequency using:
Frequency = Velocity ÷ Wavelength
Consequently, the frequency of an electromagnetic emanation is inversely
proportional (or inversely related) to its wavelength, and vice versa. This inversely proportional relationship means that, as the wavelength increases,
the frequency decreases—and vice versa. Frequency is usually measured in cycles per second, or Hertz (Hz).
Although the electromagnetic wave explanation of light seemed to be the
most complete, it still failed to account for certain effects produced by light,
like the photoelectric effect. In the early 1900s, Max Planck hypothesized
that radiation wasn't simply produced in continuous waves of energy by the
source, but rather discrete (or individual) packets of energy that he called quanta. A few years later, Albert Einstein extended Planck's quantum theory
to light, and called these packets—or particles—of energy photons. Einstein
proposed that light consisted of streams of these high-speed energy
particles. The energy of a photon is directly proportional (or directly related)
to its frequency; so electromagnetic radiation with a higher frequency also
has a higher energy level:
Energy ~ Frequency
Consequently, if we know the frequency of a wave of light we can determine
the energy of its photons. The total energy produced by waves of light will
also be determined by the number of photons present, which is related to the amplitude of the light wave and its intensity. You can think of this
relationship as Intensity of Light = Amplitude of Wave = Number of
In essence, this new theory of light, which employed particles of energy
called quanta or photons, was simply another form of the earlier corpuscular theory. Today, we say that light has a dual nature, with both particle-like
and wave-like properties. Essentially, light consists of high-speed particles of
energy—or photons—that travel in a wave-like manner.
Light Interaction with Objects
Light is emitted by a luminous—or primary—source, which is a source of
energy that can generate visible radiation. This radiation is often produced by
heat, and such sources include the sun, incandescent light bulbs, fire, and so
on. Most other objects are visible because they reflect light from luminous
sources. These objects are called secondary sources. When light is incident
upon an object, the atoms in the surface of the object essentially "catch" its
energy. At this point, the energy from the incident light can interact with the
object in a variety of ways, and the three most common for lenses include:
- Reflection: Most objects reflect some degree of light, causing it to
"bounce" back. Basically, the atoms in the surface "catch" the energy
and release it back out in the same direction. The reflectance of an
object describes the fraction of incident light that is reflected for a
given angle. Smooth, shiny surfaces have a high reflectance, while
matte, dark surfaces have a low reflectance.
- Absorption: Most objects will absorb some degree of light,
converting it into heat (or another form of energy). Basically, the
atoms in the surface "catch" the energy and convert some of it into
heat and pass the rest along to their adjacent atoms. The absorptance of an object describes the fraction of incident light that
is absorbed for a given thickness. Very dark or opaque objects have a
high absorptance, while relatively clear objects have a low
- Transmission: Objects that are at least slightly transparent (or
clear) will transmit some degree of light, allowing it to pass through
the material. Basically, the atoms in the surface "catch" the energy
and pass it along to their adjacent atoms, until the energy is finally
released out the other side. The transmittance of an object describes
the fraction of incident light that is transmitted for a given thickness.
Highly transparent objects have a high transmittance, while opaque
objects have a low transmittance. In many cases, as the light passes
through the object, it
is refracted, or
deviated from its
For instance, consider a
typical ophthalmic lens with a
slight tint. The surfaces of
the lens will reflect about 8% of the total incident light. The
tint of the lens may absorb
another 20% of the incident
light, converting it into heat—another form of energy.
Finally, the remaining 72% of the incident light will be transmitted through
Other Wave Phenomena
Although less relevant to spectacle lenses, light can also interact with
objects—particularly small objects—in other ways due to its wave-like
behavior. Light can be diffracted, which is the subtle spreading (or bending)
of light at the edge of an object or opening, particularly when the opening is
small relative to the wavelength of light. Essentially, light waves reaching the
edges of the opening act as new point sources for light waves continuing
beyond the opening, allowing these waves to spread out as if they originated
from the opening, itself.
Light can also be scattered by objects that are small relative to the
wavelength of light, redirecting it in many directions. When the particles are
smaller than the wavelength of light, a phenomenon known as Rayleigh
scattering occurs. The amount of light scatter produced by Rayleigh
scattering is inversely proportional to the wavelength (or color) of light, so
that blue light is typically scattered more than red light. This is why the sky
appears blue; small particles in the atmosphere scatter blue light more than
the other colors.
Waves of light that reach the same place at the same time can also
combine to form a new wave pattern without permanently disrupting each
other, a phenomenon known as interference. When the peak of one light
wave combines with the peak of another wave, the amplitudes of these two
waves add to reinforce each
other, resulting in in-phase or constructive interference.
When the peak of one light
wave combines with the trough of another wave, the
amplitudes of these two waves
subtract to cancel each other
out, resulting in out-of-phase or destructive interference.
Antireflection coatings rely on this phenomenon to reduce reflections by employing an optically thin
layer of material that causes two separate waves to combine with each othe
after one wave has been offset in space from the other wave by one-
wavelength. This causes the peaks of the first wave to align with the troughs
of the second wave, resulting in destructive interference, canceling the
amplitude of the reflected light.
Visible Light and Color
The spectrum of electromagnetic radiation includes cosmic rays at one end
and radio waves at the other. We think of light as the visible portion of this electromagnetic spectrum. This means that the radiation can stimulate
the photoreceptors within the retina of the eye, creating a visual sensation.
This region consists of electromagnetic radiation whose waves range from
380 to 760 nanometers (nm)—or one billionth of a meter—in length. This is
only 0.000380 to 0.000760 millimeters! The range of radiation visible to the
human eye is referred to as the visible spectrum, ranging from violet at
one end of the spectrum to red at the other, and represents a small fraction
of the total electromagnetic spectrum.
White light is composed of all the wavelengths in the visible spectrum.
Individual wavelengths within the visible spectrum, by themselves, create
different color sensations. These are the spectral colors. Remember that
colors with shorter wavelengths, like blue and violet, have higher
frequencies. Beyond the blue end of the visible spectrum lies ultraviolet
radiation, while infrared radiation—which is often associated with heat—
lies beyond the red end. These two forms of radiation are not visible to the
200 to 380
380 to 450
450 to 490
490 to 560
560 to 590
590 to 620
620 to 760
760 to 1,000,000
Recall that most objects are visible because they reflect light from
luminous (primary) sources. For instance, you can see a red car down the
road because it is absorbing every color of white light from the sun, except
red. The color red is reflected off the car, which then serves as a secondary
source for observers.
Although white light from the sun is a continuous spectrum of colors, white
light can be effectively reproduced by combining equal amounts of three
specific colors of light: red, green, and blue. These colors are referred to as
the additive primary colors, and any color from the visible spectrum can
be reproduced by combining various quantities of these three colors of light.
When no light is present, black (darkness) is produced. This is possible since
the human eye only has three unique photoreceptors for color, called cones,
which can each be stimulated by one of these three "primary" colors. This is
concept is referred to as the trichromatic (three-color) theory of color
Consequently, equal amounts of red, green, and blue light will stimulate all
three of these cones equally—just as white light from the sun would—giving
the sensation of white. Television sets and computer monitors are common
devices that use these three colors of light, in the form of excited phosphors,
to produce a complete spectrum of colors. It is important to note that
additive primary colors are produced by luminous or primary sources of light
that emit colors.
It is also possible to duplicate various colors of light by reflection, which
is the basis for paint pigments and dyes. These would be secondary
sources of light. The color black can effectively be reproduced by combining
equal amounts of three specific colors: cyan, magenta, and yellow. These
colors are referred to as the subtractive primary colors, and any color can
be reproduced by combining various quantities of these three colors—which
are often in the form of
pigments or dyes.
These two sets of primary
colors are also related in
another way. Cyan is the
"opposite" or complementary
color of red, and is produced b
combining blue and green. Magenta is the complementary
color of green, and is produced
by combining blue and red. Yellow is the complementary color of blue, and is produced by combining red
A color printer is a common device that use these three (subtractive) color
pigments to produce a full range of colors. When no colors are present, the color is assumed to be white. It is interesting to note that the three particular
paint pigments used in printing do not produce a perfect black so a fourt
perfectly black pigment is often used (which represents the 'K' in CMYK
The substance through which waves of light travel is referred to as the medium. Media can include empty space, air, lens materials, and so on.
Recall that waves of light travel at a constant velocity of approximately
300,000 km/s in free space. In other transparent media, including lens
materials, waves of light will travel at a slower rate. The velocity of light in
her media will vary as a function of the refractive index for that material.
The refractive index of a transparent medium is essentially a measure of
the "optical resistance" of the material to light, and is defined as the ratio o
the velocity of light in air compared to the velocity of light in the material:
Refractive Index = Velocity in Air ÷ Velocity in Material
For example, consider a wave of light traveling at a velocity of 200,000 km/s
through a particular lens material. The refractive index for th
uld be equal to 300,000 km/s ÷ 200,000 km/s = 1.500.
The refractive index of a material is often abbreviated 'n.' Except for air,
which has a refractive index of 1, the refractive index of most substances is greater than 1 (n > 1). Water, for instance, has a refractive index of 1.3
Spectacle lens materials are available in a variety of refractive indices, ranging from 1.497 to 1.886. Some common materials are shown below.
Hard Resin (CR-39®)
The higher the refractive index of a
lens material, the slower the ligh
travel through it. In reality, the
refractive index of any material
varies slightly as a function of the
wavelength. This means that various
colors of light will each actually have
a slightly different refractive i
the same lens material! This
phenomenon is responsible for chromatic dispersion, or the
breaking up of white light into its component colors by prisms and lenses.
Blue light, which has a higher refractive index than red light, is refracted—
or bent—more than red.
Chromatic dispersion is a result of the fact that colors of light with shorter wavelengths, like blue, travel more slowly through most transparent
materials than colors with longer wavelengths, like red. Therefore, blue light
generally has a higher refractive index than red light. However, this is usually
only a concern for certain high-index lens materials, since the differences in
refractive index between colors is more dramatic.
Nature of Light - Part 2
Vergence of Light
When light is emitted by a luminous source the radiation travels outward in a
wave-like fashion. This is similar to a pebble creating ripples in a pond.
Waves traveling across water are confined to one plane, the surface of the
water, so they travel outward circularly. Light waves from a luminous point
source, however, travel in every direction and form spherical wave fronts.
Each wave front is like a spherical "shell" that envelops all of the waves at
the same distance from the source. Each spherical wave front "expands"
from the source, like a balloon gradually inflating with air. Since these wave
fronts propagate (or travel) away from the point source of light, the source
serves as their common center of curvature.
Point A represents a source with waves of light propagating outward in
every direction. The wave front is the spherical shell that envelops all of
these waves at the same distance from the source. Line AB represents a ray originating from point A, the center. Any ray originating at the center of
curvature of these waves will remain perpendicular to each wave front.
Consequently, for simplicity, we can represent these wave fronts with simple
rays (or lines) traveling through the medium in the direction of the original
The notion that light can be thought of as traveling in straight lines is
referred to as rectilinear propagation. Furthermore, in lens diagrams, rays
of light are always depicted as initially traveling from left to right. Note that
the rays are spreading apart as they travel away from their point source (the
candle flame). When rays or wave fronts of light spread out from their point
source, they are diverging. When rays or wave fronts of light come together
and join or collapse to a point focus, they are converging.
Since these spherical wave fronts expand as they travel from their source,
the size of each spherical shell is directly related to its distance—or radius (r)—from the point source. The longer the distance from the source, the flatter the curvature of the wave front. Conversely, the shorter the distance
from the source, the steeper the curvature of the wave front.
The curvature of the wave front of light, which describes both how steep
or flat the wave front is and how far it is from its source or its focus, is
referred to as its vergence. Vergence is measured in a unit called the diopter (abbreviated 'D'). In air, which has a refractive index of 1, the
vergence of light at a given distance (in meters) is given by:
Vergence = 1 ÷ Distance
Consequently, a wave front will have 1.00 diopters (D) of vergence at a distance of 1.0 meter (m). This
formula shows that vergence is inversely proportional to either
the distance from the source (for diverging light) or the distance
to the focus (for convergering light): As the distance increases, the vergence decreases—and vice versa.
Furthermore, when rays of light
are diverging the vergence is generally considered negative (-), and when rays are converging the
vergence is generally considered positive (+).
For example, consider light rays diverging from a book at a distance of 16"
(0.40 m) from the eyes, which is a typical reading distance (since the light is diverging, we'll use a negative value). The vergence at the eyes is equal to 1
/ -0.40 = -2.50 D.
Wave fronts get flatter and flatter as they get farther from their source. At
some distance, the wave fronts will appear to be perfectly flat and nearly
parallel with each other. The rays of light representing these wave fronts—
and perpendicular to them—will also appear to be parallel with each other.
This distance is called optical infinity, and is usually assumed to be 6
meters in ophthalmic optics. Therefore, rays of light from an infinitely distant object are always drawn parallel to each other.
Refraction of Light
When light travels from one medium into another with a different refractive
index, the velocity of the light will change. When going from a lower-index
medium to a higher-index medium that is more optically dense, such as from
air to a piece of glass, the velocity is reduced. If the rays of light are incident
upon the glass surface perpendicularly, or at a 90° angle to the surface, the
rays will pass through without changing direction.
When rays of light strike a different medium obliquely, or at an angle, they
are refracted, or bent, at the boundary (or interface) between the two
media. When going from a lower-index medium to a higher-index medium
that is more dense, such as from air to a piece of glass, the rays of light are
shifted toward the normal, which is an imaginary line of reference
perpendicular to the surface at the point of incidence. When going from a
higher-index medium to a lower-index medium that is less dense, such as
from a piece of glass to air, the reverse occurs and the rays of light are
shifted away from the normal of the surface. This process can be better
visualized by considering the wave form of light.
Wave fronts entering the glass medium perpendicularly are slowed down
uniformly, but there is no change in their direction. Now consider wave fronts
entering the glass obliquely... Side A of the approaching wave fronts strikes
the glass before side B, causing
side A to slow first. As a result, the
waves are refracted, or bent,
toward the slower side as they
enter the medium. The opposite
situation occurs when the wave
fronts exit the glass.
If the glass slab has parallel faces, the waves of light will
emerge from the other side
parallel to their original path, but
slightly displaced. We can also
consider the principle of refraction using a common analogy... Consider a car
(the light) driving along a smooth highway (the air). If the right passenger side of the vehicle strays into the rough shoulder (the lens material) adjacent
to the road, the right side of the vehicle starts to drag. Consequently, since
the left side of the vehicle is traveling faster than its right side, the vehicle
veers towards the shoulder (or material).
Wave fronts refracted through an "optical element" (such as a lens or
prism) with parallel faces (such as a glass slab) will emerge parallel to their
original path, but slightly displaced. The amount of displacement will depend
upon the refractive index and thickness of the slab. Consider a ray of light
traveling from one medium, such as air, into another medium with a differing
refractive index, such as a lens material. The ray of light will be refracted at
the boundary between these two media as it passes from the first medium
into the second medium, if it strikes the boundary at an angle. Snell's law
of refraction is used to determine how much refraction (or bending)
occurs as light passes through the boundary between two media with
different refractive indices, and is fundamental to the study of optics.
To use Snell's law, we will fist label the refractive index of the first medium
as (n) and the refractive index of the second medium as (n'). We will then
label the angle of incidence (i) in the first medium, which is the angle
between the initial, incident ray of light and the normal to the boundary
interface (that is, a line perpendicular to the surface). Lastly, we will label the angle of refraction (i'), which is the angle between the refracted ray of
light and the the normal to the boundary interface. Snell's law tells us that
the product of the sine of the angle of incidence (i) and the refractive index
(n) of the first medium is equal to the product of the sine of the angle of refraction (i') and the refractive index (n') of the second medium.
Mathematically, Snell's law is given by:
n × sin i = n' × sin i'
Both the angle of incidence and the angle of refraction are measured from
the normal, the imaginary reference line perpendicular to the surface or
boundary at the point of incidence.
A third angle, the angle of deviation (d), lies between the refracted ray
and the direction of its original path. This angle represents the shift of the
ray from its original path. Consequently, the angle of deviation is equal to
the difference between the angles of incidence and refraction, or d = i - i'.
Recall that as the ray passes back into the lower-index medium, it is again
deviated—this time, away from the normal. Snell's law mathematically establishes how much rays of light will be
deviated from their original paths as they pass between various media. The
greater the difference between the refractive indices of the two media, the
greater the amount of refraction.
Reflection of Light
It was mentioned earlier that we see most objects simply because light
"bounces off" them. More specifically, some of the light is absorbed by the
surface of an object and then re-emitted backwards. This process is known
as reflection. The amount and color of light reflected from an object will
depend upon the nature of the reflecting material and the angle that the light
strikes it. Reflection can be described with a simple relationship, known as
the law of reflection, which states that the angle of incidence (i) of the
incident light is equal to the angle of reflection (r) of the reflected light.
Mathematically, the law of reflection is given by:
i = r
Angle of Incidence = Angle of Refraction
As with refraction, both angles are measured from the normal to the
boundary (that is, a line perpendicular to the surface). This concept is
analogous to a ball striking a wall at an angle and bouncing off that wall at
the same angle. There are two primary kinds of reflection:
- Specular reflection: Occurs when light is reflected off a smooth
surface in an orderly fashion, such as polished glass.
- Diffuse reflection: Occurs when light is reflected off a rough surface
in all directions, such as concrete.
Mirrors are a common example of specular reflection; the source of the
reflected light is still visible from the mirror because the orderly reflection
creates an image. No image is created by diffuse reflection.Some degree of reflection generally occurs at the boundary (or interface)
between two different refractive media, such as air and glass. The fraction of
incident light that is reflected is known as the reflectance. For light reaching
the interface between two different media with refractive indices of (n) and
(n'), the reflectance is given by Fresnel's formula:
Reflectance = (n - n')2 ÷ (n + n')2
To express the reflectance as a percentage, simply multiply it by 100.
Consequently, as the refractive index of the lens material increases, the
amount of light reflected increases. In reality, the actual amount of
reflectance between two media will depend upon the initial angle of incidence
at their boundary.
For example, consider light that is incident upon a transparent medium
with a refractive index of 1.500, surrounded by air (with a refractive index of
1). The reflectance is equal to (1.500 - 1)2 ÷ (1.500 + 1)2 = 0.04 (or 4%).
Each surface of common glass and plastic lens materials reflects at least 4 to
5% of the light incident upon the lens. Between both surfaces, this
represents a total reflectance of at least 8%. Conversely, a completely clear
lens (with little or no absorption) can only transmit 92% of the light passing
through it. Thin coatings can be applied to a lens surface to reduce this
reflectance to almost nothing—thereby increasing the transmittance of the
Refraction by Prisms
We can now apply the concept of refraction to "optical elements" designed to
manipulate light. One of the simplest optical elements is the prism, which is
simply a wedge-shaped piece of refracting material. More specifically, a prism is a refracting medium bound by two non-parallel sides (that is, they
are at an angle to each other). Like a triangle, the thickest edge of the prism
is referred to as the base, while the thinnest edge of the prism is referred to
as the apex. This wedge-shaped element changes the direction of light
without necessarily changing its vergence.
A prism displaces, or bends, light passing through it towards the base of
the prism. This is the thicker end of the prism. In the simplest case, a ray of
light strikes the first surface at a normal (perpendicular) incidence, and
remains undeviated. Upon reaching the second surface, the ray is refracted
away from the normal to the surface, according to Snell's law of refraction,
and towards the base of the
Although a prism displaces
light towards its base, when the
refracted light is projected
backwards it makes the object
appear as though it originated in
the opposite direction of this
displacement. Consequently, we
say that the image created by a
prism is displaced towards the apex of the prism. This point is
extremely important and worth reiterating: A prism deviates light towards its base and images toward its apex.
For thin prisms, whose thickness and apical angles are negligible, the
amount of displacement will depend upon the refractive index of the material
and the apical angle of the prism, which is the angle of the apex or the "tilt"
between the two faces of the prism. However, the approximate deviation
produced by a thin prism, in degrees, can be determined using:
Deviation = (Index - 1) × Apical Angle
Consequently, the amount of
displacement will depend upon
both the refractive index of the
material and the apical angle of
the prism. Prisms with greater
apical angles are "stronger" and
will deviate light more. The
approximate deviation (d) of the
prism is equal to quantity (n - 1)
times the apical angle (a).
For example, consider a prism with an apical angle of 10° made in a material
that has a refractive index of 1.500. The deviation is equal to (1.500 - 1) ×
10° = 5°.
In practice, the initial angle of incidence of the light reaching the first
surface will also affect the total amount of deviation produced by the prism
slightly. As a result, the exact formula for calculating prism is more
complicated than this.
Light and Shadows
We will conclude our discussion of the basic properties of light by briefly
reviewing shadow formation. Without light, we would only have darkness,
which—strictly speaking—is the absence of light. When a region that would
otherwise be illuminated is blocked from its light source, a shadow—or area
of darkness—results. There are two categories of shadows:
- Umbra: A complete shadow (or umbra), which is a sharply defined shadow, is generally produced by a small, or point, light source.
- Penumbra: A partial shadow (or penumbra), which has some
illumination, is generally produced by a larger, or extended, light
A penumbra occurs when only part of an extended light source is illuminating
a region. In most cases, both an umbra (no illumination) and a penumbra
(partial illumination) are formed.