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Topic #18: The Properties of Light and Optics
Part I: Reflection and Refraction
1. The Law of Reflection
2. Diffuse and Regular Reflection (included in #1 above)
3. Refraction of Light
4. Snell's Law
5. Index of Refraction and the Speed of Light
6. Total Internal Reflection
7. Effects of Refraction
8. Dispersion of Light
Part II: Topic Mirrors and Lenses
1. Plane Mirrors
2. Concave Mirrors
3. Spherical Aberration
4. Real and Virtual Image
5. Real Images Formed by Concave Mirrors
6. Virtual Images Formed by Concave Mirrors
7. Virtual Images formed by Convex Mirrors
8. Lenses
9. Real Images formed by Convex Lenses
10. Virtual Images formed by Convex Lenses
11. Virtual Images formed by Concave Lenses
12. Derivation of the Lens Equation (not covered here)
13. Chromatic Aberration
14. Optical Devices (not covered here)
Part III: Diffraction and Interference
1. Diffraction and Interference Patterns
2. Measuring the Wavelength of a Light Wave
3. Single Slit Diffraction
4. Diffraction Grating
5. Resolving Power of Lenses
Notes should include:
Part I: Reflection and Refraction
The Law of Reflection: Reflection is the process of light rays bouncing off of the surface of an
object. The law of reflection says that the angle at which a light ray is reflected is equal to the
angle at which the light ray struck the surface in the first place. The term for this angle is the
angle of incidence. The angles of incidence and the angles of reflection are both measured from a
line called a normal. The normal is an imaginary line perpendicular to the surface from which
angles of incidence and reflection are measured. Light is reflected off of many objects, but only a
few objects such as mirrors allow you to see a reflection. Whether a reflection is to be seen in the
surface of an object depends upon the smoothness of the surface. A highly polished smooth
surface is more likely to show a reflection than a rough uneven surface. Think of water as an
example. When light rays strike a rough uneven surface the light rays are scattered in many
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directions. This is called diffuse reflection. On the other hand, when light rays strike a smooth
surface, one that is quite smooth even at the microscopic level, the rays are not scattered but
rather all of the rays are reflected at the same angle parallel to one another producing an image in
the surface. This is called regular reflection and the image is simply called a reflection.
The angle of incidence is represented by the symbol i, while the angle of reflection is often
represented by the symbol R. A lower case r is usually reserved for the angle of refraction.
Refraction of Light: When light enters a medium through which it can travel the light rays are
bent as they cross the boundary between the material they were in and the material they are
entering. This bending of light rays at a boundary between two media is called refraction. As with
reflection, the angles of incidence and in this case the angles of refraction are measured from the
normal. The symbol for angle of incidence is i, while the symbol for angle of refraction is r. The
optical density of a medium determines the speed at which light travels through the medium. The
more optically dense a material is the slower the speed of light through that material. In general,
if light travels from a less dense into a denser medium, the light rays are bent towards the normal.
On the other hand, if the light travels from a denser medium into a less dense medium, the light
rays are bent away from the normal.
Snell's Law: The Dutch Scientist Willebrord Snell found a relationship between the angle of
incidence and the angle of refraction. He found that the ratio of the sine of the angle of incidence
to the sine of the angle of refraction was constant for a material. He called this ratio value the
index of refraction. Each material that transmits light has an index of refraction. This relationship
is called Snell's Law. In equation form his law is written as n = sin i / sin r. When Snell’s law is
applied to a light ray traveling from one medium to another, the equation takes the following
form: n1 sin 1 = n2 sin 2.
Index of Refraction and the Speed of Light: The index of refraction for a material is a means
of measuring the degree of bending that occurs when light enters the material. The index of
refraction can be expressed as a ratio of the speed of light in a vaccum to the speed of light in the
medium it has entered. The equation for this ratio is written as ns = c / vs. In this equation the c
represents the speed of light in a vacuum, 3 x 108 m/s, and the vs represents the speed of light in
the material it has entered. The ns is the index of refraction value of the substance.
Total Internal Reflection: Have you ever been near a window at night when it is quite dark
outside but there are lights on in the room you are in? Chances are, if you have been in this
situation, you noticed that the room, itself, was reflected by the window glass and you didn't see
much of what was outside. The idea of light reflecting back off of the boundary where two
transparent medium meet, called an interface, is illustrated by the model just described. Normally,
window glass transmits light and does not act as a mirror, but under the right lighting conditions
and perhaps more importantly at the correct angle it acts more like a mirror. Like any model our
model has its limitations. However, it is a common enough experience to help you understand
what is meant by internal reflection. Swimmers who go under water that is relatively calm see an
example of internal reflection. Often the bottom of the pool is reflected downwards off of the top
of the water where the air and water boundary occurs. Anyone under the water at the correct
angle will see this reflection rather than what is above the water. This is called total internal
reflection and occurs when the light falls on the surface of a less optically dense medium at an
angle so large, measured from the normal, that there is no refracted ray. (This large angle is what
is meant by the phrase critical angle described in this passage.) The critical angle is the angle of
incidence sufficiently large that the angle of refraction would be 90o and the refracted light rays
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lie along the surface of the water and never actually leave the water. The light rays that do not
leave the water will experience reflection back down into the water. Total internal reflection
occurs when the angle of incidence has reached the value of the critical angle. To find the critical
angle you use the form of the Snell's law equation that is written as n1 sin 1 = n2 sin 2, where n1
is the index of refraction of the material in which the internal refraction will occur, 1 is the
critical angle, n2 is 1.00 (the index of refraction of a vacuum), and 2 is 90 degrees (the angle of
refraction, if total internal reflection is to occur). An example of total internal reflection that
reflects upon today’s technology (pun intended) is fiber optics.
Effects of Refraction: Have you ever seen a mirage? You probably have, if in the summer you
though you saw water on the pavement ahead while riding in a car, only to discover when you got
there that the pavement was dry and the apparent puddle had moved further along the road up
ahead. This is caused by the fact that the air is hotter near the road surface than the air further
above the pavement. As light rays approach the surface of the road, they pass through air of
decreasing indexes of refraction, because hotter air is less dense than cooler air it refracts light to
a lesser degree. The refraction caused by this layering of air by temperature produces light rays
that resemble the light rays that reflect off of puddles of water.
Refraction also makes objects appear to be where they are not. Placing a pencil in a glass of water
such that it is partially submerged usually results in the pencil appearing bent and in a different
position below the water line than it actually is. An object placed below the waters surface, such
as a coin lying on the bottom of a pan of water, will appear to be in a different position when
viewed from above the surface of the water than they are actually in. The day as in amount of
daylight per day is actually extended due to refraction. Because light travels a little slower in the
atmosphere (air) than in the vacuum of space, light from the sun is bent, making the sun appear
on the horizon a little before it has actually reached that point. This phenomenon also occurs in
the evening when the sun actually goes below the horizon as it sets we see it for a little while
longer, because of refraction. This has an interesting impact on the traditional explanation of the
spring (vernal) and the fall (autumnal) equinoxes. People usually say that on the equinox we have
essentially equal amounts of daylight and darkness, but that is simply based on the position of the
earth with respect to the sun. The effects of refraction on the amount of daylight are not figured in
to the explanation of the equinoxes. If the refraction of sunlight were taken into account, the
actual amount of time the sun was visible in the sky on the equinoxes would probably be a little
more than the exact 12 hours often cited. If you factor in twilight, the time between first light and
the actual rising of the sun and the time between the actual setting of the sun and last light, the
amount of daylight is noticeably longer than the 12 hours stated.
Dispersion of Light - Using Prisms to Separate Light Into Colors: Regardless of wavelength
all light waves travel at the same maximum speed through a vacuum, 3 x 108 m/s. In the vacuum
the frequency is simply a function of the wavelength. In transparent materials, however, each
wavelength (color) of light travels at the different speed. Red light has the longest wavelength and
the highest speed for any color of light in a medium. Violet light has the shortest wavelength and
the lowest speed for any color of light in a medium. When white light passes through a prism,
each color of light slows down to its respective speed and experiences bending, that is, each
frequency is refracted by a different amount and the results are that the colors become separated.
Red light is bent the least and violet light is bent the most. Water drops have a similar effect on
light as does prisms. A combination of refraction and internal reflection produce the rainbow of
colors on the same side of the water droplets as the light source. A prism produces the rainbow on
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the side of the prism opposite the light source. The pattern of colored light produced by passing
the light from a source through the prism is called a spectrum. These patterns often look like
bands of color side by side. A source of light emitting white light produces a continuous
spectrum, the whole rainbow of colors, where all colors appear in the usual order (ROY G BIV).
Other sources of light do not give off a continuous spectrum, but only give off some off the
colors. Such a spectrum has lines of color separated by bands of black (no light waves). Different
substances when heated give off their own unique spectrums which can be used to identify them
when they are in a sample being tested. There are generally two types of spectrum used to
identify substances. One is the emission spectrum, which identifies the colors emitted when a
substance is heated sufficiently. The other spectrum is the absorption spectrum, which identifies
which colors in white light are absorbed by the material, such as when it is dissolved in a solvent.
Emission and absorption spectra are used like fingerprints to identify substances.
Part II: Topic Mirrors and Lenses
Mirrors - Plane mirrors: Mirrored surfaces reflect light. The surface may have been made from a
highly reflective material being polished till it is extremely smooth such as a piece of metal or it
can be the traditional mirror which consists of a sheet of glass with a layer of silvering on the
back side. Plane mirrors are flat mirrors that have no curvature. Such mirrors experience simple
reflection where images are produced and appear to be in the mirror. These images cannot be
projected somewhere else and are referred to as virtual images. (virtual image will be defined a
little later on) The light rays reflected off the mirror are all parallel to the one another as they
come towards the observer. This allows the image to be seen in the mirror much like the image in
a picture. The image is that of objects placed in front of the mirror. Plane mirrors do not focus
light rays, but rather reflect them.
Mirrors - Concave Mirrors: A concave mirror is a mirror that is curved and light is reflected
off of the inside surface. A spherical concave mirror can be thought of as a section of a hollow
sphere with the shiny side on the inside of the sphere. This type of mirror has a geometric center.
A line from this center point to the mirror can be described as the radius of the mirror. A line
placed along the radius of the mirror is called the principal axis of the mirror. The principal axis
is perpendicular to the surface of the mirror where it meets the mirror. Curved mirrors do not
reflect incoming parallel rays back out from the mirror in parallel. Instead all incoming parallel
rays are reflected towards a focal point, which is located in front of the mirror at a distance equal
to one half of the radius of the mirrors curved surface. The focal length of the mirror is the
distance between the focal point and the mirror. This distance is normally measured along the
principle axis. Two characteristics of concave mirrors are: 1. Any light ray parallel to the
principle axis is reflected through the focal point, and 2. Any rays that pass through the focal
point are reflected parallel to the principle axis.
Spherical Aberration: A concave spherical mirror has a curvature that doesn't actually get
every light ray coming in parallel to the principal axis to the exact location of the focal point. As a
consequence of this phenomenon, images produced by this type of mirror tend to be a little fuzzy
around the edges in particular. Likewise, light sent out through the focal point to the mirror will
not result in all the rays reflecting off of the mirror parallel to the principal axis. This problem or
effect is called spherical aberration. To avoid this problem parabolic mirrors are substituted in
place of the spherical mirrors in applications such as flashlights. Solar ovens use parabolic
mirrors. The cooking pot with the food to be heated is placed at the focal point of the mirror.
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Real and Virtual Images: An image is a real image if the light rays coming from the object
placed in front of the mirror are reflected through the focal point and out to a location in front of
the mirror where an image of the object will appear. A screen must be placed in that location so
the image may be observed. If the mirror projects an image out on to a screen the image on the
screen is said to be a real image. On the other hand, some images are seen to appear in a mirror,
like the plane mirror often found in bathrooms and attached to some dressers. The image seen in
the mirror which cannot be projected outwards on to a screen is called a virtual image. The
virtual image cannot be focused out onto a screen because the reflected light rays do not pass
through a focal point and as a consequence cannot be focused.
Real Images Formed by Concave Mirrors: To best understand how light rays emitted or
reflected are focused by a concave mirror, you should find a ray diagram showing how the rays
are focused by the mirror and how the position of the image is related to both the position of the
object and the position of the focal point. Two equations associated with concave mirrors are
sometimes referred to as the mirror equation and the magnification equation. The mirror equation
is written as 1/do + 1/di = 1/f. The equation involving magnification is written as hi /ho = di /do.
Virtual Images in Curved Mirrors: If an object is placed within the space between the mirror
and the focal point on the inside of a concave spherical mirror, a virtual image will be visible in
the mirror. Negative values will be obtained for the position of the image and the size (height) of
the image. A convex mirror is a spherical mirror that reflects light from its outer surface. Because
convex mirrors cause light rays to diverge, they can never form real images. The image appears in
the mirror and as such is a virtual image. Convex mirrors, because of their curvature, have no
focal point. Any image associated with this kind of mirror is a virtual image and is only seen in
the mirror. Convex mirrors are often seen at the ends of aisles in smaller stores providing a means
for the employees to watch what the customers are doing in the aisles. Now days as the price of
electronics’ surveillance cameras comes down mirrors are not used as often as they used to be.
Lenses - Convex and Concave Lenses: Most lenses are made of glass. Convex lenses are thick
towards the middle and narrow down as you approach the edges. These types of lenses are called
converging lenses, because they refract incoming light rays parallel to the principle axis causing
them to pass through a focal point on the side of the lens opposite the side the object is found on.
There is another kind of lens called a concave lens. Such a lens does not focus light through
convergence of light rays through a focal point such as the convex lens does, but rather causes
light rays to diverge.
Real and Virtual Images: The same equations that were used for the mirrors are also used for
convex lenses. The mirror equation was written as 1/do + 1/di = 1/f and the equation for
magnification is written as hi /ho = di /do. If an object is placed closer to a convex lens than the
focal point a virtual image will be seen in the lens and no real image will be projected outwards.
Concave lenses, lenses thinner in the middle than at the edges produce virtual images.
Chromatic Aberration: When light rays pass through a lens they are dispersed a very small
amount because of each color of light waves being refracted just a little bit differently. When
using a lens to observe an object you are likely to see a ring of color around the object. This is
called chromatic aberration.
Part III: Diffraction and Interference
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Diffraction and Interference Patterns: Diffraction is the bending of light around obstacles.
For example, have you ever noticed how light bends around doorways illuminating a dark room
even if only a little making it possible to navigate through the room without having to turn lights
on. An Italian physicist by the name of Francesco Grimaldi during the 15th century noticed that
shadows appear to have blurred edges. The edges of shadows are not as distinct as they should be,
if light didn't bend around corners. If light did not bend around obstacles shadows should have
crisp distinct edges. He suggested that ordinarily this phenomenon is not noticed because the
wavelengths are so small. However, he suggested that the bending of light would become very
noticeable, if the light passed through very small openings. During the 19th century, a gentleman
by the name of Thomas Young followed up on Gramaldi's work. He hypothesized that, if
diffraction occurred light passed through narrow openings (narrow slits) there should be signs of
interference when a double slit allowed two wave fronts to meet. He confirmed that indeed the
waves coming through two different slits did bend around the openings and override each other as
they moved out away from the slits producing interference patterns which when projected on a
screen appeared as alternating light and dark stripes. He produced the pattern by first placing a
single slit barrier in front of a monochromatic light. (monochromatic light is light having only a
single wavelength) He then placed a second barrier having two slits behind the first barrier.
While the single slit produced a single source of circular waves moving outwards out away from
the first barrier, the two slits produced two circular wave fronts moving out from two separate
sources. These circular waves produced interference patterns which showed as bands or stripes of
alternating bright and dark lines on the screen. There was no doubt about the fact that light waves
were diffracted after this study was done. The dark bands represent nodal lines and the bright
bands represent antinodal lines. If white light is passed through a double slit, a continuous
spectrum is observed instead alternating light and dark bands. A white line is seen in the center of
the pattern and the colors of the rainbow appear as you look to either side of the white line.
Because each color, wavelength, of light is bent a little differently, that is, its diffraction pattern is
a little different, and the bright lines for each color do not fall in exactly the same place, the white
light is being separated into a continuous spectrum of colors on each side of the central bright
line.
Measuring the Wavelength of a Light Wave: Diffraction can be used to measure wavelengths
of light. The wavelength can be found by using the following written equation.  = x d / L,
where d is the distance between the slits (see above notes to describe a two slit interference
pattern), L is the distance from a point exactly centered between the two slits and the position of
the first order line, and x is the distance between the center bright line and the position of the first
order line.
Single Slit diffraction: It is possible to get diffraction by using a single slit. However, the
spacing between the bright lines is not as regular as with two slit diffraction patterns and the
central bright band is not nearly as wide or as bright as compared to double slit diffraction
patterns.
Diffraction Gratings: In studying the diffraction of light, single and double slit barriers are
seldom used. Instead diffraction gratings are used. Diffraction gratings are made by using a fine
diamond point to make very fine parallel lines on glass (or other sturdy transparent medium). The
spaces between the fine parallel lines take the place of slits. Gratings with as many as 12,000
lines per centimeter are used to study the diffraction of light. The gratings allow much more light
to get through and produce stronger images of spectral lines, including those that were not bright
enough to be seen with double slit barriers. Because, it can be easier to measure the angle
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between the central bright line and higher order lines, this approach is used most often to find
the wavelength of a source. The earlier equation  = x d / L can be rewritten as  = d sin .
Resolving Power of Lenses: Lenses can act like a slit. It will cause the light from two sources to
diffract. This is a particular problem when the opening is similar in size to the wavelength of light
passing through the opening. Because of this, the width of a lens affects its ability to distinguish
between two points. One way to get around this is to use a wider lens. Reducing the wavelength
of light being used, if you have control over the light source will also reduce the problem. This is
the means used to deal with the problem in situations where the lens cannot be widened as in a
microscope. In such situation a light source in the shorter wavelengths such as violet light will
often be used.
Vocabulary: Part I: regular reflection, diffuse reflection, angle of reflection, angle of refraction,
Optically dense, Snell’s law, index of refraction, total internal reflection, critical angle,
dispersion; Part II: plane mirror, object, image, virtual image, erect image, concave mirror,
principal axis, focal point, focal length, real image, lens/mirror equation, magnification, spherical
aberration, convex mirror, lens, convex lens, concave lens, chromatic aberration, achromatic lens;
Part 3: interference fringe, monochromatic light, coherent wave, slit, double slit, diffraction
grating, Rayleigh criterion
Skills to be learned:
Construct ray diagrams representing reflection, refraction and diffraction
Solve angle of reflection problems
Solve Snell’s Law index of refraction problems
Solve speed of light in transparent medium problems.
Construct ray diagrams for mirrors and lenses
Solve mirror image and magnification problems
Solve lens image and magnification problems
Solve wavelength of light problems
Assignments:
Textbook: Read / Study / Learn the information in Chapters 17, 18 and 19 pertinent to
this study of light and optics.
WB Exercise(s): PS#17-1, PS#18-1, PS#18-2, PS#19-1
Activities: TBA
Resources:
This Handout and the Overhead and Board Notes discussed in class
Textbook chapters 17, 18 and 19
WB Lessons and Problem Sets
www.physicsphenomena.com - “The Properties of Light and Optics”
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