Chapter 14

Light and Reflection

Chapter 14 Objectives

• Identify the nature of light• Calculate the speed of light• Law of Reflection• Ray Diagrams

– Flat mirrors– Concave mirrors– Convex mirrors

• Mirror Equation• Magnification Equation• Color• Polarization

What is Light?

• Sir Isaac Newton first proposed that light was a tiny stream of particles emitted by the light source.

• Thomas Young noticed that given light under certain conditions it could cancel itself due to interference.– Interference is a wave property!

• Einstein took it one step further to explain the photoelectric effect.– Thus creating photons, or tiny particles of energy

that are transferred by a light wave.

Electromagnetic Wave

• For much of our introductory purpose, we will only consider the wave property of light.

• Since we can cancel out the wave property of light but still have energy emitted, there must be more to the wave than just the light.

• This leads to light fitting being an electromagnetic wave.– That is it contains perpendicular electric fields and magnetic

fields that oscillate perpendicular to the wave flow.• So light waves travel as transverse waves.

Speed of Light

• Armand H. L. Fizeau developed the first successful method for measuring the speed of light.– By bouncing a laser off a mirror and

calculating the time it takes to return to the source.

• He also used a toothed wheel to separate the continuous laser into countable pulses.

• v = c = 3 x 108 m/s

c represents the speed of light

Modeling Light Waves

• For our purposes, we will model a light wave as a ray, or vector.– So that is to draw an arrow.

• Sometimes it may be necessary to model light as a set of rays.

• What we do know…– Light will continue in a straight line until it encounters a

boundary between two different materials.– When light encounters that new boundary, anything could

happen!

Intensity of Spherical Light Waves

• Since the waves will travel as a spherical shell, the area that it approaches is equal to the area of a sphere– 4r2

• Due to the spherical nature, as the wave travels the intensity dissipates by a factor of r2.

PI =

4r2

Law of Reflection• Any time a light ray encounters the surface of a new

medium, part of the light ray is reflected.– In a mirror, some light is reflected upon entering the glass

and the rest is reflected when it hits the metallic backing.• The new light rays will now travel parallel together, assuming

the surfaces were smooth.– Reflection from a smooth surface is often called specular

reflection.

– Reflection from a rough surface such as cloth or wood is often called diffuse reflection.

Angle of Reflection

• From observation, the angle of reflection is equal to the angle of incidence.– Incidence indicates the original path of entry.

• However, the angle is measured from a line perpendicular to the surface that we call the normal.– We use the perpendicular line because using the mirror

itself could vary based on the shape and surface quality of the mirror at the incidence point.

1 ’1

Red Eye

• Red eye is often seen in photographs taken with a flash.

• This shows an example of retroreflection.– Retroreflection is reflection that travels back along its original

direction.

• So what you are seeing is the light reflecting off the blood vessels in the retina of your eye and returning back out the lens of the eye.

Reflection Notation• When investigating reflections, there is some notation to

account for:– The original item that is being reflected is called the object.

• The object distance, or the distance the object is from the mirror, is represented by the variable p.

• With a height of h.

– The observed reflection of the object is called the image.• The image distance is represented by the letter q.• With a height of h’.

o i

p q

h h’

Real vs Virtual• An image is real when

– The reflected light rays and the incident light rays actually pass through the image point.

– The image appears to be on the same side of the mirror as the object.

– The image can be displayed on a screen.

• An image is virtual when– The incident light rays

do not pass through the image point.

– The reflected light rays appear to diverge from the image point.

– The image cannot be displayed on a screen.

The images formed through any alteration of light can be classified in two ways:

o i

p q

Magnification

• The lateral magnification, M, is defined as the ratio of the image height to the object height.

o i

p q

M = image heightobject height =

h’h

h’h

Rules for Flat Mirrors

1. The image is as far behind the mirror as the object is in front.

2. The image is unmagnified, virtual, and upright.(Upright means the object and image remain in the same orientation.)

2. Although, a flat mirror will encounter a right-left reversal according to the observer.

o i

p q p = q

h’hh = h’

Drawing Reflections• The basic drawing of a reflection

consists of some essential components:

– mirror• location• height

– object• distance• orientation

• and also the drawn in components

– incident light rays– reflected light rays– image

1. Draw the location of the mirror and indicate the object distance.

2. Draw the object with some indication of its orientationand height (upright, inverted, etc.).

3. Draw an incident light ray parallel to the object distance from the top of the object to the mirror.

3. Reflect the ray appropriately.

4. Draw another incident light ray from the top of the object through the center of curvature until it hits the mirror.

4. Reflect the ray appropriately.

5. Extend both reflected rays through the other side of the mirror to obtain the virtual image location, if necessary.

5. The real image will exist if all rays intersect on the same side of the mirror as the object originally was.o i

p q

Spherical Mirrors

• If the reflecting surface is concave, then it is called a concave mirror.

• If the reflecting surface is convex, then it is called a convex mirror.

Spherical Mirror Components• A spherical mirror is a small arc of a spherical shell.• So with that we identify parts of a spherical mirror based

on it circular nature:– The center of curvature, C, is the point at which all the

radii of the mirror intersect.– The radius of curvature, R, is the distance from the mirror

to the center of curvature.– When the radius of curvature is drawn as a perpendicular

bisector of the mirror, it is called the principle axis.

C

R

Magnification of Concave Mirror• Using a little geometry, you will notice that the distance to

the mirror is directly related to the height of the object.– Using your theorems for similar triangles as well as some

trigonometry, you notice we are concerned with the tangent ratio of our triangle sides.

M = image heightobject height =

h’h

= qp

–

Negative sign shows the image is inverted.

p is always positive, that way it acts as our point of reference.

q is negative for a virtual image,and positive for a real image.

Mirror Equation

• Using some complex algebra with the similar triangles will create an equation that can calculate the image distance by knowing the object distance and the radius of curvature of the mirror.

1p

+ 1q

= 2R

Focal Point

• If we consider our light source to be an infinite distance away, we observe the following:– We can treat the light as a series of individual, parallel light rays– All of which reflect to intersect at one common point.

• That common point of intersection is called the focal point, F, of the mirror.

Focal Length

• Since p is very large (), then the mirror equation relies more on the image distance than the object distance.– So solving for q results in:

• q = R/2

• Because we are attempting to find the focal point, our image distance is now called the focal length, ƒ.

• And from the above work we see that the focal length will always be half the radius of curvature.

1

p+

1

q=

2

R

ƒ = R2

Revised Mirror Equation• Recognizing that the focal length is

half the radius of curvature, we can conclude the following:

• This is the more common and useful form of the mirror equation.

1p

+ 1q

= 1ƒ

ƒ = R2

2R

Sign Conventions for Spherical Mirrors

• p is positive if the object is in front of the mirror. (real object)

• p is negative if the object is behind the mirror. (virtual object)

• q is positive if the image is in front of the mirror. (real image)

• q is negative if the image is behind the mirror. (virtual image)

• Both ƒ and R are positive if the center of curvature is in front of the mirror. (concave mirror)

• Both ƒ and R are negative if the center of curvature is behind the mirror. (convex mirror)

• If M is positive, the image is upright.• If M is negative, the image is inverted.

Drawing Ray Diagrams for Spherical Mirrors

• First draw a ray parallel to the principal axis that will be reflected back through the focal point.

• Remember that all straight rays that encounter a curved mirror reflect through the focal point.

• The second ray should be drawn through the focal point, and then reflected parallel to the principal axis.

• A concave mirror will go through the focal point and then hit the mirror.• A convex mirror will hit the mirror while on line to the focal point, but the reflection

that needs to be accounted for will be parallel to the principal axis.

• The third and final ray is drawn through the center of curvature and reflected back upon itself.

i i

C

o

F C

o

F

Image of a Convex Mirror• Notice the image for a convex mirror will

always be:– Virtual– Upright– Smaller than the object

i

C

o

F

Color• The color of an object is dependent on the

reflecting and absorbing properties of the material.– The color we see is the reflected light from the

material.• So if all the light is reflected off the surface, then the

color we see is the color that was transmitted to the material.

• Some light may be absorbed in the form of heat and some transmitted through the material.

– Remember, every time a wave hits a boundary, some of the wave is reflected and most is transmitted.

Primary Colors v Additive Colors of Light

• Elementary colors are those colors that are split from the rainbow.

• Red, orange, yellow, green, blue, indigo & violet.

• Three of those colors cannot be formed from any other two.

– Red, Yellow, & Blue

• They are called primary colors.

• Since white light can be split into elementary colors, it is safe to assume that elementary colors can be mixed to form other colors.

• Due to the interference and intensity properties of light, yellow and green behave differently than pigments.

– Yellow can actually be created from red and green.

– However, green cannot be formed from anything else.

• So the primary additive colors of light are:

– Red, Green, & Blue

Polarization• Because of the electromagnetic nature of light, a light source can be

thought of as a round point sending off cylindrical beams of light rays.

– This takes into account the wave nature of the electric field created by light rays.

– And it takes into account the perpendicular magnetic field wave that accompanies light rays.

• And since the original light source can be oriented or vibrating in any direction, we assume that light can travel as a cylindrical beam.

• A wave is said to be polarized if its electrical field vibrates in the same direction at all times through a particular point.

Polarization by Selective Absorption

• The most common technique for polarizing light is to use a material that is a good electrical conductor that can alter the electric field plane of the unpolarized light.– This will allow waves whose field vectors vibrate in a plane

parallel to the desired direction to pass through while absorbing those waves that travel perpendicular.

• This can be done by placing sheets of aligned, long-chain hydrocarbons to become the electron transfer molecules that will alter the electric field.– In 1932, E. H. Land discovered this process for material which

he called polaroid.• The material is dipped in iodine to create a better conducting

chain of hydrocarbons.

Polarization Notation• We commonly refer to the direction

perpendicular to the molecular chains as the transmission axis.

• Remember, the molecular chains are responsible for supplying “free” electrons that will alter the electric field.

– In an ideal polarizer, light with an electric field parallel to the transmission axis will pass through.

• So light with an electric field perpendicular to the transmission axis will be absorbed.

Intensity of Light Transmitted by a Polarizer

• To adjust the intensity of polarized light we can send it through two polarizing sheets varying transmission axes.– The first sheet is called the polarizer.

• Its main responsibility is to align all incident light rays along parallel electric fields.

– The second sheet is called the analyzer.• This sheet intercepts the now polarized light beam with a new

transmission axis that is set at an angle of to the axis of the polarizer.

• This is how polarized sunglasses work.– They eliminate glare by absorbing the unwanted incident light

rays and only allow the desire angle of light rays to pass through!• Example: Fishing glasses

How Malus’s Law Works

Polarization by Reflection• Recall that an incident light beam on any boundary will

partially reflect some of its beam.– The reflected ray can become partially polarized,

completely polarized, or stay unpolarized.• The evidence for this is since the wave is reflected we are

altering the electric field(s) that bounce off the surface.

• An angle of incidence between 0o and 90o will become polarized to some extent.– An angle of incidence at 0o or 90o leaves the reflected light

unpolarized.• That is because none of the light transfers into the medium

nor is reflected, it is a straight uninterrupted beam of light.

Polarization by Scattering• A third form of polarization often observed in our atmosphere comes from

the reflection and absorption of light by a system of particles.• This is called polarization by scattering.

– The electrons in the medium can absorb and reradiate the light as it attempts to pass through the medium.

• The electrons are sent into vibration as light energy begins to excite the atom.• When the electron changes state, it will reradiate the light energy and alter its

electrical field.

• So much of the light that we receive from the sun is partially polarized by our atmosphere.

– And some of the sun’s light we never see because it is polarized to a very low intensity.