Wave Theory – part 2

Wave Theory – part 2

Electromagnetic Spectrum:

An electromagnetic spectrum is a “map” of the total range of waves. All are forms of “LIGHT”!

Usually, high frequency (low λ) is on the right.Low frequency (high λ) is on the left.

Notice the wide range of waves. We only perceive visible light, a tiny fraction of the whole spectrum...

Speed of Light:

In a vacuum, all electromagnetic waves have a velocity of 300,000,000 m/s! (3x108m/s)

That’s 186,000 miles per second!

• There are a number of wave phenomenon that are characteristic of all Waves:

• #1 – Reflection

• #2 – Refraction

• #3 – Diffraction

• #4 – Interference

• #5 – Resonance

• They all involve the movement of energy in to form of waves – sometimes from 1 material to another!

Moving from one medium to another

Once a wave (incident wave) has reached a change in media, part of the energy is transferred to the medium that is immediately next to it (transmitted wave) and part is reflected backward (reflected wave).The energy transferred depends on the difference between the mediums. If there is a significant difference, almost all the energy will be reflected.

If the mediums are similar, most of the energy will be transferred. However, the reflected waves will be inverted if the medium that comes next is more dense or it won't be inverted if the medium is less dense. •Ex:•sound moving from air to water•light moving into a piece of glass•earthquake waves moving from solid rock to molten rock

#1: Reflection of WavesIf we draw a line perpendicular to a surface, this line is the normal of the surface. When a ray of light hits the surface of an object, part of the light is reflected. If the ray of light is at an angle with the surface, then the angle between the incident ray and the normal [incident angle]will be the same angle between the normal and the reflected ray [reflected angle].

This is called the law of reflection.

Incident Ray

Incident Angle

Reflected Angle

Reflected RayNormal Line

Boundary / Mirror

Most surfaces are not completely flat. When millions of rays of light hit the rough surface of an object, they are reflected in all directions. This is how we can see illuminated objects.

http://library.advanced.org/10796/ch10/ch10.htm

http://micro.magnet.fsu.edu/primer/java/reflection/reflectionangles/index.html

http://micro.magnet.fsu.edu/primer/java/reflection/reflectionangles/index.html

If not absorbed, the light can be reflected from the object.

White Light:White light is not a distinct color. Instead, white light is the combination of all the other colors.

White light

Another discovery by Isaac Newton

Newton’s Prism Work• Before Newton, it was thought that the prism

added color to the light…• Newton tested this idea by breaking the light

into the spectrum, then again dividing a single color of the spectrum with another prism to test if it would again “add” color to the light.

• Once he discovered it did not, he reached the conclusion that the original white light had contained all of the colors that were seen coming from the prism.

http://micro.magnet.fsu.edu/primer/java/scienceopticsu/newton/index.html

http://micro.magnet.fsu.edu/primer/java/scienceopticsu/newton/index.html

Selective Reflection:When we perceive an object to be a particular color, we actually are receiving only one particular color of

light in our eyes.

Ex: A banana looks yellow because it reflects only yellow light. It absorbs all the other colors.

Black:

When an object appears black, it means that all colors ( frequencies) of light are being absorbed by

that object. None are being reflected.

Often, black objects are hotter because they

are absorbing more light/energy.

If a rose were illuminated with a red light, you would see the red rose, but the stem and leaves

would look nearly black. Since they are green, that means they reflect only green light ( absorb red).

reflected

absorbed

#2: Refraction of Waves

• When a wave travels from one medium to a second medium, The original wave is redirected at a different wavelength at a different angle (bend) from the normal to the surface.

• The index of refraction determines the amount of change in wavelength and angle. (bending the wave)http://micro.magnet.fsu.edu/primer/java/scienceopticsu/refraction/index.htmlhttp://www.physics.uoguelph.ca/applets/Intro_physics/refraction/LightRefract.html

Refraction of Water Waves

Refraction of Light Beam

• Refraction occurs at the boundary and is caused by a change in the speed of the light wave upon crossing the boundary.

• Direction of bending depends upon whether light wave speeds up or slows down at the boundary.

Refraction --Refraction -- bending of bending of light wave path as light light wave path as light passes from one material to passes from one material to another material. another material.

Transmission Across a Boundary

• Only time a wave can be transmitted across a boundary, change its speed, and still not refract is when wave approaches boundary in a direction which is perpendicular to it.

Light wave speed Light wave speed changeschangesLight wavelength Light wavelength changes - frequency changes - frequency does not changedoes not change

Ray Diagrams

Optical Density

• Optical density -- tendency of the atoms of a material to hold on to absorbed energy from a photon in the form of vibrating electrons before reemitting it as a new photon

• The more optically dense a material is, the slower a wave will move through the material.

If the new medium is more dense, the light bends because it slows down.

How much do you ask? This decrease in speed is given by the formula:

v = c / n where v - is the new speed of light and n is…

Index of Refraction

• Index of Refraction is a measure of optical density

• Represented by n• The higher n is, the

more optically dense the material and the slower light travels in the material

Indices of Refraction

Refraction of light

When a ray of light passes from one medium to another, it bends. Depending of the new medium the light will travel faster or slower. If the light travels faster in the second medium, then this medium is called the rarer medium (or less dense)

Refraction of light

On the other hand, the medium in which the light travels slower, in this case the first one, is called the denser medium. When a ray of light enters a denser medium, it is bent towards the normal. When a ray of light enters a rarer medium, it is bent away from the normal.

http://micro.magnet.fsu.edu/primer/java/scienceopticsu/refraction/index.html

Law of Refraction: Snell’s Law

• There is a formula to predict how much a wave will “bend” as it travels into a new medium:

n1sin1 = n2sin2

http://theory.uwinnipeg.ca/physics/light/node5.html

Angle of Incidence

Angle of Refraction

1 = 40

2 = 32

AIR - n1 = 1.00

? - n2 =

“New” Angle of Incidence

“New” Angle of Refraction

n1 sin 1 = n2 sin 2

(1.00) (0.643) = (x) (0.53)

X = 1.21

At the boundary of 2 media:

Some of the light wave is always reflected. However, when a ray of light goes from a denser medium to a rarer medium, all the light will be reflected if the angle of incidence is greater than the critical angle. The critical angle is the angle of incidence for which the refracted ray is at 90 degrees with the normal. http://micro.magnet.fsu.edu/primer/java/refraction/criticalangle/index.html

#3: Diffraction When a wave travels through a small hole in a barrier, it bends around the edges. This is called diffraction.

• The bending of a wave around an obstacle

http://micro.magnet.fsu.edu/primer/java/diffraction/basicdiffraction/index.html

#4: Interferenceof

Waves

The Addition of waves can add (Constructive) or subtract(Destructive).

Standing waves are a result of waves combining in phasehttp://micro.magnet.fsu.edu/primer/java/interference/doubleslit/index.html

Collision of wavesWhen two waves traveling in opposite directions through the same medium collide, the amplitude of the resulting wave will be the sum of the two initial waves. Remember: the energy of the 2 waves is influencing the motion of the media - the energy “pulls” on the media.The resulting phenomenon is called interference and there are two types:

Collision of waves

Constructive interference is when the amplitudes of the initial waves are in the same direction. The resulting wave will be larger than the original waves. The highest point of a constructive interference is called an antinode. Constructive!

Destructive interference is when the amplitudes of the initial waves are opposite. The amplitude of the resulting wave will be zero. The point in the middle of a destructive interference is called a node and it never moves (in light - it would be a dark spot)

The Principle of

Superposition

When waves “add”

and “subtract

Interference of waves

Summary• Waves are a pulses of energy through a medium

• Waves properties: Speed, amplitude, wavelength, and frequency

• Waves change through mediums by

–Reflection

–Refraction

–Diffraction

–Interference

ORIGIN OF LIGHT Where does light come from? How is it produced? The least complex answer is that light comes from the atom itself - the motion of the electrons around the nucleus. When an electron drops an energy level - a packet of light (photon) is produced.This is the phenomenon that you studied in the online activity.

VISIBLE LIGHT Of all the electromagnetic waves, visible light is the only portion of electromagnetic waves that can be detected by the human eye. It is a very small section of the spectrum and visible wavelengths run from 7.5 x 10-7 m (red) to 3.5 x 10 -7 m (purple).

Luminous and illuminated bodies

Light is produced by a luminous body. A light bulb is a luminous body that emits light in almost every direction. Light travels in straight lines at 299,792,458 m/sec in a vacuum. OR

3.0 X 108 m/s

Luminous and illuminated bodies

When light hits an object OR another medium, it is reflected or refracted . An illuminated body reflects light. When a ray of light reaches our eyes, the receptors in our eyes will produce a different color sensation depending on the wavelength of the light wave.

COLORS Red, green and blue are

known as primary colors, because when they are added together white light is formed. By mixing primary colors in pairs we obtain secondary colors. Blue and red produce magenta, and blue and green produce cyan.

Why the Sky is Blue:

Our sky, atmosphere, is made up of various particles ( mostly N2 and O2 ) that vibrate at

various frequencies.

When hit by light of various frequencies, some react, some don’t.

The violet/blue light is reflected/scattered the most, so

we see those colors.

Our eye cones aren’t as sensitive to violet, so we see a

predominantly blue sky.

LIGHT ORIGIN REVIEW QUIZ1. WHERE DOES LIGHT COME FROM? - EXPLAIN THE MECHANISM.

2. WHY DO WE SEE COLORS? - HOW IS IT WE SEE COLORS?

3. WHAT ARE THE COLORS OF THE VISIBLE SPECTRUM?

4. NAME AT LEAST 4 OTHER FORMS OF ELECTROMAGNETIC RADIATION.

LIGHT WAVES VISUAL DEVICE CRITERIA

1. MUST USE AT LEAST 1 REGULAR SIZE PIECE OF CONSTRUCTION PAPER2. AESTICHALLY PLEASING3. USE MIND-MAP DESIGN OR FLOW CHART DESIGN4. MUST INCLUDE THE FOLLOWING ITEMS: - ORIGIN OF LIGHT

- BOHR ATOM- EMISSION & ABSOPTION SPECTRA ORIGINS- TRANSFER OF ENERGY- TYPE OF WAVE MOTION- ELECTROMAGNETIC SPECTRUM

Apparent Depth

• Light exits into medium (air) of lower index of refraction, and turns left.

Spear-Fishing

• Spear-fishing is made more difficult by the bending of light.

• To spear the fish in the figure, one must aim at a spot in front of the apparent location of the fish.

Delayed Sunset

• The sun actually falls below below the horizon

• It "sets", a few seconds before we see it set.

Green Flash

Broken Pencil

Water on the Road Mirage

Palm Tree Mirage

Sometimes an object may have a very different appearance depending on the wavelength of light you are using to observe it. Ex: visible

light and infrared picture of the constellation Orion

The Human Eye:

Our eyes are remarkable organs designed to detect visible light. The design of a camera is very similar to

our eye.

Light passes through the clear cornea of your eye. The cornea bends light so that you have

a wide field of view.

Then light goes through the pupil, which is the variable black opening in the iris

( colored part) of your eye.

The lens focuses the light onto the sensitive retina of your eye.

Color Vision:

There are two types of vision receptors in the eye: Rods and Cones

Color vision is possible because of the Cones.

Animals without color vision have only Rods.

In general, females have better color vision than males.

In fact, a high % of males have some degree of color blindness.

This doesn’t mean that they see the world in B&W, but instead their color vision isn’t as vivid.

You should see a “25” in the dot pattern. The following tests will be more difficult if you are

color blind…

Normal color vision: 45

Red/Green color blindness: no pattern

Normal color vision: 6

Red/Green color blindness: no pattern

Optical Illusions:Here are some illusions to illustrate how our

eye/brain makes judgements. The light our eyes receive may be objective, but we often interpret

this data subjectively. Our vision perception is not always very “scientific”.

Are the horizontal lines bent?

What do you see?

A dalmation?

What do you see?

A man’s face, or the word liar written in

cursive.

Do you see the spiral?Actually they are concentric circles.

The square inscribed in the circle is NOT kinked.

How many black dots do you see? None

Two faces?

Wine goblet?

What do you see?? Scene with tree, or baby?

Selective Transmission:

Not all objects reflect light (opaque), some let light pass through them ( transparent). In this case, if a transparent object looks blue,

this means that all colors except blue are being absorbed.

Mixing Colored Light:

The sun is a pretty good source of white light. Below is a curve showing the relative proportions of

the visible light it produces:

R O Y G B I V

Infra-red ultraviolet

The colors of white light are often simplified into three components: Red, Green, Blue

These are often called the additive primary colors

In a TV, these three colors are used to create all the various images you view. Look closely at

your TV screen and you’ll see….

When the three additive primary colors of light are mixed, the following results are obtained:

Cyan (light blue)White

YellowMagenta

If a golf ball were illuminated with RBG lamps, could you explain the following result?

Pigments:

If you have ever used play-dough, you’ve noticed that if you mix R,B,G colors of clay, you don’t get

white as a result!

This is an example of mixing pigments, not light. Different results are obvious here.

In a lump of clay, you see the light that is reflected (leftover), after the rest has been

absorbed.

For this reason, in painting and printing, magenta, cyan, and yellow are called the

subtractive primary colors.

They are often referred to loosely as red, yellow, and blue.

In a color ink jet printer, you often have a color cartidge with cyan, magneta, and

yellow colors. (CMY)

These small dots are used to create any image needed. An additional black cartridge

is often included.

Review Questions:

+ =

+ =

+ =

Magenta

Yellow

Cyan

+ + = White

Review Questions:

Keeping the previous concepts in mind, try the following question:

+ =Green Magenta White

Since magenta is equivalent to blue and red, its just like combining RBG

to get white!

So, each of the following is also true because in each case you are adding the equivalent of RGB

together to get white:

White

White

+ =Yellow Blue

+ =Cyan Red

Complimentary Colors:

When two colors are added together to produce white, they are called complimentary colors.

The previous two slides contain examples of complimentary colors.

Magenta + Green

Yellow + Blue

Cyan + Red

Subtracting Colors?With the previous color “rules” in mind, you can

also subtract colors:

- =White Red Cyan

White is equivalent to RGB combined. When you subtract the R, you are left with G and B.

As learned previously, these two combine to make cyan!

Using all the information you now have, try the following question:

- =White Blue Yellow

To correctly answer this, you need to

recall that R & G produce yellow:

Why are Sunsets Red:Q: If the sky is blue here on Earth, why do we see sunsets

as orange/red?

A: In the previous description, we said the atmosphere scatters or reflects the blue light the

most. This leaves the red light to continue through the atmosphere.

Air molecules

When the sun is low on the horizon, the light is passing through a lot of the atmosphere. The blue is scattered (subtracted), and orange/red

light is leftover.

The blueness of the sky, or the redness of a sunset depends on many factors like humidity and air pollution.

In 1883, Mt. Krakatoa erupted. The addition of many small particles produced more spectacular sunsets/rises around the world.

Why is the Ocean Green/Blue?

Again, the answer has to do with absorbtion and transmission.

Water resonates or vibrates at infrared and red frequencies. This means it absorbs the red light. If the red light is taken away, the

remaining green & blue light ( cyan ), remains!

Once again, the exact color of the water depends on many factors.

Review Question:

Q: Why does the blood of an injured deep sea diver look greenish-black when photographed with

natural light, but red when a flash is used?

Deep in the water, most of the red light has already been absorbed. Thus, with no red

light reflecting off the normally red blood, it looks black. With a flashbulb, there is a new

source of red light to be reflected!

Can you say the color of each word without reading the actual word?

For example, for the first word you would say: “green” since the letters are green.


THE ELECTROMAGNETIC SPECTRUM


CONVERGING (CONVEX)LENS - GENERAL IMAGEFORMATION

DIVERGING (CONCAVE)LENS - GENERAL IMAGEFORMATION

CONVERGING LENSES

CONVERGING LENSES

The diagrams above shows that in each case, the image is •located behind the lens •a virtual image •an upright image •reduced in size (i.e., smaller than the object)

LENS EQUATION

Sample Problem #1A 4.0-cm tall light bulb is placed a distance of 45.7 cm from a double convex lens having a focal length of 15.2 cm. Determine the image distance and the image size.


ho = 4.0 cm do = 45.7 cm f = 15.2 cm

1/f = 1/do + 1/di

1/(15.2 cm) = 1/(45.7 cm) + 1/di

0.0658 cm-1 = 0.0219 cm-1 + 1/di

0.0439 cm-1 = 1/di

di = 22.8 cm


ho = 4.0 cm do = 45.7 cm f = 15.2 cm

hi/ho = - di/do

hi /(4.0 cm) = - (22.8 cm)/(45.7 cm)

hi = - (4.0 cm) * (22.8 cm)/(45.7 cm)

hi = -1.99 cm

Sample Problem #2A 4.0-cm tall light bulb is placed a distance of 8.3 cm from a double convex lens having a focal length of 15.2 cm. (NOTE: this is the same object and the same lens, only this time the object is placed closer to the lens.) Determine the image distance and the image size

ho = 4.0 cm do = 8.3 cm f = 15.2 cm 1/f = 1/do + 1/di

1/(15.2 cm) = 1/(8.3 cm) + 1/di

0.0658 cm-1 = 0.120 cm-1 + 1/di

-0.0547 cm-1 = 1/di

di = -18.3 cm

Sample Problem #2A 4.0-cm tall light bulb is placed a distance of 8.3 cm from a double convex lens having a focal length of 15.2 cm. (NOTE: this is the same object and the same lens, only this time the object is placed closer to the lens.) Determine the image distance and the image size

ho = 4.0 cm do = 8.3 cm f = 15.2 cm hi/ho = - di/do

hi /(4.0 cm) = - (-18.2 cm)/(8.3 cm)

hi = - (4.0 cm) * (-18.2 cm)/(8.3 cm)

hi = 8.8 cm

http://www.glenbrook.k12.il.us/gbssci/phys/Class/refrn/u14l5f.html

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Wave Theory – part 2