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ISNS 3371 - Phenomena of Nature
The Electromagnetic Spectrum
Most wavelengths of light can not be seen by the human eye.
The visible part of the electromagnetic spectrum lies between ultraviolet
and infrared light (between about 400 and 700 nm). The higher the
frequency (shorter the wavelength), the higher the photon energy. Radio
waves are at the long wavelength end of the spectrum and gamma rays
are at the short wavelength end of the spectrum.
ISNS 3371 - Phenomena of Nature
On the moon, there is no atmosphere to scatter light and the sky is black
Atmosphere on Mars too thin to scatter light effectively - sky is reddish from
presence in the atmosphere of reddish dust from surface. On Venus, almost
all blue light scattered away - atmosphere dimly lit and appears reddish
ISNS 3371 - Phenomena of Nature
Additive primary colors - adding light of additive primary colors
produces complementary colors - all colors produces white
Red + Green  Yellow
Red + Blue  Magenta
Green + Blue  Cyan
ISNS 3371 - Phenomena of Nature
Subtractive primary colors - mixing pigments (that absorb light) of
various subtractive primary colors produce complementary colors added all together, produce black.
Yellow + Magenta  Red
Yellow + Cyan  Green
Magenta + Cyan  Blue
ISNS 3371 - Phenomena of Nature
Only four colors are used to print color illustrations and photos: (a)
magenta, (b) yellow, (c) cyan, (e) black. (d) is with all but black, (f) is with
ISNS 3371 - Phenomena of Nature
Four Ways in Which Light can Interact with Matter
emission – matter releases energy as light
absorption – matter takes energy from light
transmission – matter allows light to pass through it
reflection – matter repels light in another direction
- Phenomena
of Nature
of Nature
Properties of Light
Law of Reflection -
Angle of Incidence = Angle of reflection
Law of Refraction - Light beam is bent towards the normal
when passing into a medium of higher Index of Refraction.
Light beam is bent away from the normal
when passing into a medium of lower Index of Refraction.
Index of Refraction -
Speed of light in vacuum
Speed of light in a medium
Inverse square law - Light intensity diminishes with square of
distance from source.
ISNS 3371 - Phenomena of Nature
Mirror reflects light at
angle equal to
incoming angle -
Most materials reflect
light randomly scattering. Movie
screen scatters light
into array of beams
that reaches every
member of the
ISNS 3371 - Phenomena of Nature
Index of Refraction
As light passes from one medium (e.g., air) to another (e.g., glass,
water, plexiglass, etc…), the speed of light changes. This causes to light
to be “bent” or refracted. The amount of refraction is dependent on the
index of refraction of the material and the angle of incidence.
ISNS 3371 - Phenomena of Nature
Imagine that the axles of a car represent wave fronts. If the car crosses
from a smooth to a rough surface at an angle, one tire of the axle will slow
down first while the other continues at normal speed. With one tire traveling
faster the other, the car will turn in the direction of the slow tire. This is how
refraction works.
ISNS 3371 - Phenomena of Nature
The Prism
A prism separates white
light into its component
colors - because index of
refraction is dependent on
wavelength. Blue light
bends (is refracted) more
than red light
Violet Blue
Index (glass) 1.532
Orange Red
Dispersion - “spreading” of a light beam dependent on:
- the angle between the two surfaces
- the direction of incidence on the
first face
- the index of refraction of the prism.
ISNS 3371 - Phenomena of Nature
Water is more dense than air - light is
refracted as it enters and leaves a raindrop
drop - red is bent less, blue more - the light
is dispersed, just like a prism
- some of the light will reflect off the
back of the drop if the angle is larger
than the critical angle for reflection (48°
for water)
- the light is then refracted again as it
leaves the drop, the colors of white light
have been dispersed.
- blue light will leave the drop at an
angle of 40° from the beam of sunlight
- red light will leave the drop at an angle
of 42° from the beam of sunlight
This process generates the primary rainbow.
Naturally the sun must be behind you and
the rain in front of you.
ISNS 3371 - Phenomena of Nature
However, you can not see the blue light and red light refracted from the
same drop - you only see one color (indeed, only one tiny beam of light!)
from each raindrop. So, many drops are involved in producing the rainbow.
The raindrops lower down contribute blue and green light and the
raindrops higher up contribute red and yellow light.
ISNS 3371 - Phenomena of Nature
antisolar point - the point where the
sun is directly opposite of us.
- If we look away from the sun,
the shadow of our head on the
ground marks the antisolar point
- If the sun is in the sky, the
antisolar point is below the
horizon. If the sun has set, the
antisolar point is above the
Tells us is the direction of the sun and
where we can expect the rainbow to
ISNS 3371 - Phenomena of Nature
red light gets refracted back at 42° from
antisolar line - blue light gets refracted
back at about 40° from antisolar line.
Every raindrop within 42° of the antisolar
line is reflecting red light back to your
Look at every raindrop within about 40° of
the antisolar line - see a circle of
raindrops centered on the line - horizon
gets in the way of most of the rain, so we
only get to see an arc or a bow - full
rainbows can be seen from airplanes and
Rain is falling not in a flat sheet, but in
varying distances from you - causes the
"rainbow circle" to be formed at varying
distances - raindrops that contribute to
your rainbow all lie on a cone with its
apex at your eye.
Move to the left or the right - looking
at new raindrops - a new rainbow.
Two people see different rainbows each rainbow is your own.
ISNS 3371 - Phenomena of Nature
In science speak - The rainbow is an optical phenomenon caused by the
refraction and reflection of light by the locus of raindrops between 40.6
and 42° of the observer's antisolar line.
ISNS 3371 - Phenomena of Nature
Light emitted by the sun, a lamp in the classroom, a candle
flame, etc… is unpolarized light - created by electric charges
which vibrate in a variety of directions - an electromagnetic
wave (transverse) which vibrates in a variety of directions.
Helpful to picture unpolarized light as a wave which has an
average of half its vibrations in a horizontal plane and half of its
vibrations in a vertical plane.
Polarized light waves - light waves in which the vibrations occur in a single
Polarization - Process of transforming unpolarized light into polarized light.
Most common method of polarization uses a
Polaroid filter - made of a special material
capable of blocking one of the two planes of
vibration of an electromagnetic wave. When
unpolarized light is transmitted through a
Polaroid filter, it emerges with one-half the
intensity and with vibrations in a single plane;
it emerges as polarized light.
ISNS 3371 - Phenomena of Nature
Two filters with polarization axes perpendicular to each other will
completely block the light.
Light is polarized upon passage through the first filter - say, only vertical
vibrations were able to pass through. These vertical vibrations are then
blocked by the second filter since if its polarization filter is aligned in a
horizontal direction.
Like picket-fence and standing wave on a rope - vibrates in a single plane.
Spaces between the pickets of the fence allow vibrations parallel to the
spacings to pass through while blocking vibrations perpendicular to the
Orient two picket fences
such that the pickets are
both aligned vertically vertical vibrations will pass
through both fences align pickets of second
fence horizontally - the
vertical vibrations which
pass through the first
fence will be blocked by
the second fence.
ISNS 3371 - Phenomena of Nature
Polarization by Reflection
Unpolarized light can also undergo polarization by reflection off of nonmetallic
surfaces - extent dependent upon the angle at which the light approaches the
surface and upon the surface material.
Metallic surfaces reflect light with variety of vibrational directions - unpolarized.
Nonmetallic surfaces (asphalt, snow, water,
paint on a car) reflect light such that there is a
large concentration of vibrations in a plane
parallel to the reflecting surface. A person
viewing objects by means of light reflected off
of nonmetallic surfaces will often perceive a
glare if the extent of polarization is large.
Which pair of glasses is best suited for
automobile drivers, fishermen, snow skiers?
ISNS 3371 - Phenomena of Nature
Adding a third filter with between
two filters polarization axis at 45º to
the other two will allow light though.
Remember, unpolarized light vibrates in all different directions. So not just
the light with horizontal vibrations passes through the first filter, but all light
with a vibrational component in the horizontal direction - in other words, all
but the light with vertical vibrations has some component in the horizontal
direction that gets through.
ISNS 3371 - Phenomena of Nature
Before the middle filter, the light is
horizontally polarized.
The component of horizontally polarized
light along 45º gets through the middle
The component of that light in the vertical
direction then gets though the last filter.
ISNS 3371 - Phenomena of Nature
When light passes through a transparent material such as plastic, internal
(and normally invisible) stresses in the material can rotate the angle of
polarization - different colors will be rotated by different amounts. Place
horizontal polarizer below the object, and a vertical one above it - no light will
be transmitted unless there are stresses inside the object that rotate the light.
Useful in the design of engineering structures - build a model out of plastic,
and view it with crossed polarizers. Put a force on the model - regions of the
model that are stressed the most will show up in color. This way you can
determine which parts of the structure are most likely to break, and the design
can be changed (if necessary) to relieve some of that stress.
ISNS 3371 - Phenomena of Nature
Lenses and Mirrors
(and applications to astronomy)
ISNS 3371 - Phenomena of Nature
Geometry of a Concave Mirror
Principal axis
Focal length
Center of curvature - the center of the circle of which the mirror represents a
small arc
Principal axis - a radius drawn to the mirror surface from the center of
curvature of the mirror - normal to mirror surface
Focus - the point where light rays parallel to principal axis converge; the focus
is always found on the inner part of the "circle" of which the mirror is a small
arc; the focus of a mirror is one-half the radius
Vertex - the point where the mirror crosses the principal axis
Focal length - the distance from the focus to the vertex of the mirror
ISNS 3371 - Phenomena of Nature
Geometry of a Converging (Convex) Lens
Optical axis
Focal length
Optical axis - axis normal to both sides of lens - light is not refracted
along the optical axis
Focus - the point where light rays parallel to optical axis converge; the
focus is always found on the opposite side of the lens from the object
Focal length - the distance from the focus to the centerline of the lens
ISNS 3371 - Phenomena of Nature
Image Magnification Using a Simple Lens
Focal Plane
ISNS 3371 - Phenomena of Nature
The image formed by a single lens is inverted.
ISNS 3371 - Phenomena of Nature
The Eye
The eye consists of pupil that allows light into the eye - it controls the amount
of light allowed in through the lens - acts like a simple glass lens which
focuses the light on the retina - which consists of light sensitive cells that
send signals to the brain via the optic nerve. An eye with perfect vision has its
focus on the retina when the muscles controlling the shape of the lens are
completely relaxed - when viewing an object far away - essentially at infinity.
ISNS 3371 - Phenomena of Nature
When viewing an object not at infinity, the eye muscles contract and
change the shape of the lens so that the focal plane is at the retina (in an
eye with perfect vision). The image is inverted as with a single lens - the
brain interprets the image and rights it.