WEEK 3 FUNDAMENTALS OF PHYSICAL SCIENCE

Section 1: The Inverse Square Law An Inverse Square Law is a mathematical relationship between two quantities where the first quantity is inversely proportional to the square of the second quantity. In physics, this typically will describe how the strength or intensity of something varies inversely with the square of the distance. This relationship will be relevant to all topics covered this week: electricity, magnetism, sound, and light and also applies to last week’s topic of the force of gravity.

For example, if we are talking about light from a camera flash, the illumination (or intensity) of the flash changes when your distance from the flash changes. The illumination gets weaker the further away you are.

Specifically, the intensity of a physical quantity between two objects is inversely proportional to the square of the distance separation those two objects. This relationship is expressed as:

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ELECTRICITY AND MAGNETISM

COURSE NOTES – PART 1

Intensity∝ 1

distance2

WEEK 3 FUNDAMENTALS OF PHYSICAL SCIENCE

Section 2: Electricity Experimenting in the late 1700s, Benjamin Franklin decided that there were two types of “electric fluid” that could be transferred by friction between two substances (like rubbing a rubber balloon on your hair). He named them “positive” and “negative”. Today we know that this “fluid” is not actually a fluid and is called charge. Charge is the property of both electrons and protons, where electrons hold negative charge and protons hold positive charge. These two fundamental particles have exactly equal but opposite amounts of charge.

Electrons are used to create electric fields and magnetic fields. An electric field applies a force to other particles with electric charge. The strength of the electric field is known as voltage and is measured in volts (V).

An area with more electrons is negatively charged and an area with less electrons is positively charged. An electric field will flow from the positively charged region to the negatively charged region.

An electric charge creates an electric field that surrounds it.

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Charge is an intrinsic property of these particles, just as their masses are.

“Invention is the most important product of man’s creative brain. The ultimate purpose is the complete mastery of mind over the material world, the harnessing of human nature to human needs.”

– Nikola Tesla, My Inventions

Nikola Tesla was an inventor who contributed to the development of the alternating-current (AC) electrical system that is widely used today and also discovered the rotating magnetic field, both of which which you will learn about this week!

Important Names: Nikola Tesla

WEEK 3 FUNDAMENTALS OF PHYSICAL SCIENCE

The electric force between two charged particles is given by Coulomb’s Law:

The electric force is directly proportional to the two charged particles and inversely proportional to the square of the distance between them. Coulomb’s Law is an example of the Inverse Square Law!

The fact that electric force gets weaker with distance explains how a charged object (like the comb in the image) can attract an uncharged one (the paper). The charge on the comb induces, or separates, charges on the paper. Positive charges on the paper move closer to the negatively charged comb. Because the positive charges on the paper are closer to the comb than the negative ones, there is a net force toward the comb!

Example:

A charge of -0.26 C lies 2 meters from a charge of +0.45 C. What is the the electric force between them?

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FE = k q1q2 d2

FE = electric force (N) k = Coulomb’s constant (N·m2/C2) = 9×109 q = charge (C) d = distance (m)

FE = k q1q2 d2

FE = (9 ×10 9

N ⋅ m 2

C2 ) (−0.26 C)(0.45 C)

(2 m)2

FE = (9 ×10 9

N ⋅ m 2

C2 ) −0.117 C2

4 m 2

FE = (9 ×10 9

N ⋅ m 2

C2 )(−0.02925

C2

m 2 )

FE = −2.63×10 8 N

k is a physical constant and will always be 9×109

A negative value indicates the electric force is

attractive. A positive value would mean the force is

repulsive.

WEEK 3 FUNDAMENTALS OF PHYSICAL SCIENCE

Electric current is defined as the flow of electrons through materials, usually metals. It is measured in units of Amperes or Amps (A). One Ampere is the rate of flow of one Coulomb of charge per second. There are two types of current: direct current (DC) and alternating current (AC). With direct current, charges flow in one direction and terminals have a set charge of positive or negative. Batteries are a good example of providing direct current. With alternating current, charges alternate in direction and the terminals are constantly changing back and forth from positive to negative. Household outlets provide AC. This is because the power transmits more efficiently from the power station with AC. In North American outlets, positive and negative switches 60 times per second.

Resistance describes how much a circuit component resists the passage of electric current and is measured in units of Ohms (Ω). There are several factors that affect electrical resistance:

1. Thickness of wire: Thin wires resist electrical current more than thicker wires, because in a thin wire, there are fewer electrons passing through it.

2. Length of wire: Longer wires resist current more than shorter wires.

3. Material of wire: All materials have resistance, but conductors such as metals will offer lower resistance and allow a higher current than insulators such as rubber.

4. Temperature: Higher temperatures offer more resistance.

Example: A really long wire running to a loudspeaker will have more resistance and therefore less current (it won’t be as loud) as a speaker with a shorter wire. Wires to both speakers should be the same length or they won’t sound equally loud!

Voltage is defined as the amount of potential energy per unit charge flowing through a circuit and is measured in units of volts (V).

We should recall our discussion of gravitational potential energy in Week One. Gravitational potential energy is given to an object when it is lifted to a height off the surface of the Earth (assuming we are on Earth). This object has potential energy because it is being held away from something that it is attracted to. Once that restraint is removed, the object will fall to the surface of the Earth due to the gravitational force and the potential energy will be converted into kinetic energy.

Electric potential energy is also dependent upon position and is given to a charged object whenever it is being held away from something that it is attracted to (the opposite

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WEEK 3 FUNDAMENTALS OF PHYSICAL SCIENCE

charge). The electric force gives an electric charge potential energy depending on the charge’s position. The electric force is another force that can “store” energy as potential energy, just like gravity – except it is very much stronger than gravity.

What is really significant is the difference in potential (voltage) between two points. That will determine how much potential energy the charge gains or loses moving in the electric field.

The relationship between voltage, current, and resistance is called Ohm’s Law. Ohm’s Law relates the current of electrons flowing through a material with resistance, with the voltage from the electric field ‘pushing’ the electrons. Ohm’s Law can be written as:

For a given voltage, if the resistance is high, little current will flow. But if the resistance to the flow of current is low, the amount of current flowing will be higher.

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I = V R

I = Current (A) V = Voltage (V) R = Resistance (Ω)

WEEK 3 FUNDAMENTALS OF PHYSICAL SCIENCE

Example:

A 9-V battery is connected to a lamp and a current of 2 A begins to flow. What is the resistance of the lamp?

When electrical appliances such as lamps, televisions, or computers are connected to a household circuit, they generally get a voltage difference of 110-120 V. Heavy electrical energy users such as clothes driers, stoves, or ovens are on a separate circuit that gives them twice that voltage, 220-240 V. Operating an electrical appliance requires not just energy, but also a certain amount of electrical power, which is the rate at which energy is delivered (energy/time). The rate at which electrical energy is used by an appliance is the power needed by that appliance to operate:

Electric power is measured in Joules per second (J/s) or watts (W).

To operate an electrical appliance, you need to provide an uninterrupted path for the electrons that are being “pushed” by the voltage (from the battery or wall outlet). Any such conducting path is called an electrical circuit. You can turn the appliance on or off by a switch. If the switch is on, the circuit is complete, or closed, and charge flows. If the switch is off, there is a break in the circuit, and the circuit is open. With no conducting path for electrons to move along, no electrons can flow.

Devices connect to a circuit in one of two ways:

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I = V R

2 A = 9 V R

2 A 1

= 9 V R

(2 A)R = (9 V)(1) (2 A)R = 9 V R = 4.5 Ω

P = IV P = Power (W) I = Current (A) V = Voltage (V)

WEEK 3 FUNDAMENTALS OF PHYSICAL SCIENCE

In a series circuit, there is only one way for electrons to travel, so everything in the circuit gets the same current.

Older Christmas lights are connected in series – when one bulb goes out, the circuit is broken, and all the other bulbs go dark.

In a standard flashlight, the circuit connecting the voltage source (battery) and resistor (light bulb) is a series circuit.

Total resistance in a series circuit is calculated by:

Example:

Four light bulbs are connected in series. Each light bulb in this circuit is actually a resistor. The filament in the bulb resists the flow of current, and it gets hot. As a result, the filament glows and gives off light.

If each of the four bulbs has a resistance of 5 ΩΩ, what is the total resistance of this series circuit?

In a series circuit, adding more resistors increases total resistance, so the current flowing through the circuit decreases.

In a parallel circuit, the electrons have more than one path that they can take to complete the circuit.

Each path has the same voltage difference driving the electrons. Different paths can have different currents in them.

Disconnecting one appliance does not interrupt the current through the others.

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Rtotal = R1 + R2 + R3 +…+ Rn Rtotal = Total Resistance (Ω) R1,R2,R3,…Rn = Individual Resistances of Resistors (Ω)

Rtotal = R1 + R2 + R3 +…+ Rn Rtotal = 5Ω+5Ω+5Ω+5Ω

Rtotal = 20Ω

WEEK 3 FUNDAMENTALS OF PHYSICAL SCIENCE

Total resistance in a parallel circuit is calculated by:

Example:

Three bulbs are connected in parallel. If each of the bulbs has a resistance of 6 ΩΩ, what is the total resistance of this parallel circuit?

In a parallel circuit, adding more resistors decreases the total resistance, so the current flowing through the circuit increases.

Section 3: Magnetism Magnetism is the force of attraction or repulsion of a magnetic material (such as iron), due to the arrangement of its atoms, particularly its electrons.

Electrons have magnetic fields that create forces, pushing or pulling on each other.

All magnetism is created by electric current (moving charge) either from electrons flowing down a wire or the spinning of electrons in an

atom. The magnetic field of an electron is a vector and has a direction. Antiparallel fields are subtracted from each other, and parallel fields are added together. A net magnetic field is calculated by adding parallel fields and subtracting antiparallel fields. Therefore, a magnet is a material whose electrons have more parallel fields than antiparallel fields (Net Magnetic Field does not equal zero).

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1 Rtotal

= 1 R1 + 1 R2 + 1 R3 +…+

1 Rn

Rtotal = Total Resistance (Ω) R1,R2,R3,…Rn = Individual Resistances of Resistors (Ω)

1 Rtotal

= 1 R1 +

1 R2 +

1 R3

1 Rtotal

= 1

6Ω +

1 6Ω

+ 1

6Ω 1 Rtotal

= 3

6Ω

Rtotal = 6 3 Ω or 2Ω

WEEK 3 FUNDAMENTALS OF PHYSICAL SCIENCE

Magnetic poles are in all magnets, each having a north pole and a south pole. Like poles repel each other, meaning a north pole will repel another north pole, and a south pole will repel another south pole. This is the “push” that is felt between two magnets. Opposite poles attract each other, meaning a north pole will attract a south pole, and a south pole will attract a north pole. This is the”pull” that is felt when two

magnets are brought together. You can’t have one pole without the other. If you cut a magnet in half, each piece will have a north and south pole. If you continue cutting the magnet in half over and over again, you will eventually get down to a single iron atom with a north and south pole.

Examples of magnets include:

1. Simple bar magnets – the poles are at the opposite ends.

2. Horseshoe magnets – bent “U” shape, the poles at the ends.

3. Earth – magnetic field lines of Earth point toward the geographic north pole and away from the geographic south pole. This means that magnetic south is actually in the Arctic north, and magnetic north is in the Antarctic south.

The Connection Between Electricity and Magnetism

When an electric current flows through a wire, a magnetic field forms around the wire in a concentric circle pattern. When the current in the wire reverses direction, the direction of the field lines reverse.

If the wire is bent into a loop, the magnetic field lines become concentrated inside the loop.

If the wire is bent into another loop, the concentration of magnetic field lines inside the double loop is twice that of the single loop.

The magnetic field intensity increases as the number of loops is increased. Thus, a coil of wire becomes an electromagnet when current flows through it. The magnetic field of an electromagnet looks and performs like the magnetic field of an ordinary bar magnet with a north and south pole. Magnetic field lines in an electromagnet reverse direction when the electric current reverses direction – i.e., north and south poles reverse when current is reversed.

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Magnetic field lines point away from the

north pole and point toward the

south pole.

WEEK 3 FUNDAMENTALS OF PHYSICAL SCIENCE

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Electromagnetic induction happens when a voltage is generated in a conductor by an interaction with a magnetic field. It is the main principle involved in producing electricity for the world!

When a magnetic field passes through a conductor, electric charges in the conductor receive a “push” from a force called the Lorentz force. This push generates a voltage in the conductor and causes current to flow through it.

Specifically, the magnetic field passing through the conductor has to change in some way for electromagnetic induction to occur. Any way of changing the strength or direction of the magnetic field relative to the conductor satisfies this:

• moving a magnet toward or away from the coil

• moving the coil into or out of the magnetic field.

• rotating the coil relative to the magnet

It doesn’t matter how the change in the magnetic field is produced. Whether a charged particle moves across the magnetic field lines or the magnetic field lines move across the particle – either way, the particle gets a push.

Changing the net magnetic field in any way across a closed conducting circuit produces an electric current in that circuit.

WEEK 3 FUNDAMENTALS OF PHYSICAL SCIENCE

Section 4: Sound and Waves Imagine attaching one end of a rope to a wall and then oscillating the other end up and down with your hand. It is easy to imagine that you would create a wave of what we call crests and troughs that propagate from your hand, through the rope, and towards the wall. All waves, whether they be waves along a length of rope, ocean waves, or even sound waves, have several basic properties that we have labeled below.

The medium of a wave is the source of atoms/molecules through which the wave propagates. The rope was the medium in the previous example. Below is an illustration of a slinky (or spring) being used as the medium of propagation:

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SOUND AND LIGHT WAVES

COURSE NOTES – PART 2

WEEK 3 FUNDAMENTALS OF PHYSICAL SCIENCE

Imagine that we were interested in knowing how many wavelengths pass some point (say the half way point between our hand and the wall) during some unit of time (in one second, for instance). This is a measure of the waves’ frequency in Hertz (Hz) and would be equivalent to knowing how many times a particle in the medium completes one cycle (moves up, down, then back up again) in one second. Obviously, the frequency will depend both on the wavelength and the wave speed and can be calculated as:

Sound waves are longitudinal waves which propagate through a source of atoms or molecules (most often the molecules that make up the air we breathe). The frequency of these waves must be between 20 and 20,000 Hz in order to be audible to the human ear.

The creation of sound waves is much like the creation of longitudinal waves in the slinky, only on a much smaller scale. Like your hand, the prongs of the tuning fork

begin vibrating. As a prong moves to the right, it collides with air molecules, knocking them out of the way. These molecules in turn collide with other molecules, resulting in a pulse of high pressure, or a compression, which propagates through the air. As the fork continues to vibrate, it produces a series of high pressure/low pressure regions (compressions/rarefactions) in the air, resulting in continuous ringing sound.

Sound travels at different speeds depending on the medium generally moving faster through denser materials:

Example:

A traffic signal in a congested intersection turns red 20 times in 5 minutes. What is the frequency of the traffic light in Hertz (Hz)?

Solution:

Because Hz is a unit of cycles per second. We can start by converting the 5 minutes to seconds:

We can now simply use our frequency equation to find the frequency of the light:

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frequency = cycles second

= wave speed wavelength

5 min = 5⋅ 60 sec = 300 sec

frequency = cycles

sec =

20 cycles 300 sec

= 0.067 Hz

WEEK 3 FUNDAMENTALS OF PHYSICAL SCIENCE

Example:

The key of “middle C” on a piano produces a sound wave with a frequency of roughly 262 Hz. If the air temperature is 20 degree Celsius (about 70 fahrenheit), what is the sound waves’ wavelength?

Solution:

Using the table on the previous page, we know that the sound wave will have a speed of 343 meter per second. We can use our frequency equation again to solve for wavelength.

When a wave encounters a boundary between two mediums (i.e. air to water, air to glass, or vice versa) the wave can be reflected, transmitted, and absorbed. The fraction of the wave that undergoes each of these interactions depends on the properties of the wave as well as the properties of the two mediums.

Reflection occurs when the wave strikes the surface of a different medium and is returned to the original medium.

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frequency = wave speed wavelength

wavelength = wave speed frequency

wavelength = 342 m/s 262/sec

wavelength =1.3 m or 4.27 ft

WEEK 3 FUNDAMENTALS OF PHYSICAL SCIENCE

Wave interference is a process in which two or more waves overlap to form a resulting wave of greater (constructive interference) or lesser amplitude (destructive interference).

The phase difference between two waves is the degree to which the crests and troughs of one wave overlap the crests and troughs of the second wave.

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If the crests and troughs of each wave overlap, they are said to be

in phase.

If the crests of one wave overlap the troughs of the second wave and vice versa, they are said to

be completely out of phase.

Constructive Destructive

WEEK 3 FUNDAMENTALS OF PHYSICAL SCIENCE

The Doppler effect is the apparent change in frequency of a wave due to relative motion between observer and the wave source.

If it is still a bit unclear how this occurs, focus on the fire truck as it moves toward the man. Imagine the pink lines as being the crests (high pressure regions) of the sound wave. A crest leaves the siren and travels toward the man. However, by the time the next crest leaves the siren, the fire engine has now traveled some distance to the right depending on the trucks speed. So when the next crest leaves the siren, it is now closer to the first crest than if the siren was stationary. Thus the wave in front of the siren has shorter wavelength and higher frequency. Similarly, the crests are spaced further apart behind the siren, producing waves of larger wavelength and lower frequency.

What if the wave source moves at the same speed (right) or faster than (left) the waves it emits?

This results in constructive interference between each wave greatly increasing the amplitude of the waves emitted.

The constructive interference is what creates a sonic boom when a jet travels faster than sound.

The aircraft pushes so much air in front of it, creating a large pressure in front of the craft and low pressure directly behind it. Because lower pressure means lower temperature, water vapor will often times condense into “clouds” along this area of low pressure.

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WEEK 3 FUNDAMENTALS OF PHYSICAL SCIENCE

Example (Sound and the Inverse Square Law):

The loudness, L, of a sound (measured in decibels, dB) is inversely proportional to the square of the distance, d, from the source of the sound. The woman on the porch who is 20 ft from a lawn mower experiences a sound level of 17.5 dB. How loud is the lawn mower for the man pushing the mower who is 6 ft away?

Solution:

Because we know the loudness of sound follows the inverse square law, we may begin with the following equation:

As with any inverse square law, we have a proportionality constant that we call k, that we need to first solve for:

Now that we know the proportionality constant, we may calculate the loudness 6 ft away:

Section 5: Light Light is a packet of oscillating (which is much like vibrating) magnetic and electric fields known as electromagnetic waves. Understanding electromagnetic waves requires us to recall the concepts of electric and magnetic fields from earlier in this text. Both fields can be produced by charged particles, but the charges have to be in motion in order for a magnetic field to be generated. An electric field is generated regardless of whether the charge is moving or not. These fields are a property of the space occupied around the charges and help to predict forces on other charges.

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L(dB)= k d2

k = L ⋅d2

k =17.5 dB⋅(20 ft)2

k = 7000 (dB⋅ ft 2 )

L(dB) = k d2

L(dB) = 7000 (dB⋅ ft 2 )

(6 ft)2

L =194.4 dB Roughly 11 times louder.

WEEK 3 FUNDAMENTALS OF PHYSICAL SCIENCE

When we say “oscillating”, we can picture a charge flowing up and down. A magnetic field will be generated, but will constantly be changing in both magnitude and direction as the charged particle changes direction. A changing magnetic field will generate a voltage in a circuit whose plane is perpendicular to the magnetic field lines. A voltage implies an electric field, even without a circuit present, so a changing magnetic field will generate an electric field at any point in space where the magnetic field is changing. So a symmetry exists in this scenario: a changing magnetic field will generate an electric field and a changing electric field will also generate a magnetic field. A wave involving these fields can propagate through space because they constantly regenerate each other. If there is nothing to slow them down or impede the wave, like in a vacuum, the process can go on forever.

A packet of light is known as a photon. A photon describes the particle properties of an electromagnetic wave instead of the overall wave itself. We can picture an electromagnetic wave being made up of individual particles and that particle is the massless entity known as a photon.

It is important to note that when we refer to light, we are talking about much more than just visible light! Visible light makes up a very small portion of the electromagnetic spectrum. The electromagnetic spectrum makes up the full range of light wave frequencies, which also includes radio waves, microwaves, infrared radiation, ultraviolet radiation, X-rays, and gamma rays.

Frequency is directly proportional to energy in light, meaning the higher the frequency of a light wave means higher energy and lower frequency equals less energy.

It is likely that we are all familiar with what all of these types of radiation are associated. Radio waves are not the waves of sound that you hear from a radio, but rather the waves that are transmitted through space from the radio station to your receiver. Microwaves are used to heat up food, as they are absorbed very well by fats, sugar, and water. Infrared is used in remote controls and night vision goggles. Visible light is all that our eyes can see, and the colors that we perceive are all different frequencies of visible light. Ultraviolet light is what gives a sunburn. X-rays are absorbed to varying degrees by different objects inside our bodies, but are energetic enough to easily pass through the skin. Gamma rays are used to destroy cancer cells, and are also given off by some of the most energetic events in the universe, like supernovae explosions and during the formation of black holes. Every single one of these types of waves is an electromagnetic wave like the light that we can see, but just has a different wavelength, frequency, and energy.

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WEEK 3 FUNDAMENTALS OF PHYSICAL SCIENCE

When photons of any light collide with matter, the can be transmitted, absorbed, or reflected.

Transmission is when the photons of light pass through a material. Transmitted photons are passed from one atom to the next, like a relay baton being passed from runner to runner.

Transparent materials transmit light through them, while opaque materials do not transmit light. If a transparent object is colored, it is because some colors (energies of visible light) are not being transmitted, but other colors are transmitted.

The speed of light is 300,000,000 m/s in a vacuum. This is the universal speed limit, as nothing travels faster than light in a vacuum. This is fast enough to travel around the Earth eight times in a single second!

When light enters a material, it interacts with every atom of that material. The transmission of photons from atom to atom takes time, so the speed of light is lowered while passing through a transparent material.

Light travels slower through denser materials and faster through less dense materials. Note that this is the exact opposite of sound waves, that travel fastest through denser materials!

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The Speed of Light and the Size of the Universe

The Moon is approximately 240,000 miles away from Earth, and it takes light only 1.2 seconds to travel from Earth to the Moon. The Sun is 93 million miles from the Earth, and it takes 8.5 minutes for light to travel from Sun to Earth. This means that if the Sun suddenly went dark, we would still receive light from it for 8.5 minutes!

Our galaxy, the Milky Way, is 5.75 x 1017 miles across, and it would take light, traveling at 300,000,000 m/s, about 100,000 years to travel

from one end to the other. Consider the implications of this statement – this means that even if humans could develop a means of space travel

that moved as fast as the speed of light, it would take thousands of generations of humans with our current lifespan to make it from one

end of the Galaxy to the other!

In our local view, the Milky Way is incredibly large, but in the grand scheme of the universe, it is very, very small. The picture below was taken by the Hubble telescope and is one of the Hubble Ultra Deep Field images. It focuses on a small region of space in the Constellation, Fornax. Each illuminated area is a galaxy. The estimated number of galaxies contained in this picture is 10,000. This picture is only .00000000000000001% of the observable universe!

WEEK 3 FUNDAMENTALS OF PHYSICAL SCIENCE

When a light wave encounters a smooth, reflecting surface like a flat mirror, the waves are reflected away from the mirror with the same speed that they had before encountering the surface. The angle of reflection is equal to the angle of incidence, as stated in the Law of Reflection.

The image formed by a plane mirror is called a virtual image because the light never actually passes through the point where the image is located. Although the image appears “in the mirror” as far

behind the mirror as the object is in front of the mirror, the light never actually gets behind the mirror, it just appears to come from points behind the mirror as it is reflected. The image can be characterized as being right side up and the same size as the object. There is a reversal, however, of right and left: what appears to be the right hand of your mirror image is actual the image of your left hand. The virtual images are located at the position where the extended reflected rays converge.

Curved mirrors will form a different virtual image than a flat mirror. Convex mirrors are curved outward and the virtual image is smaller and closer to the mirror than the object. Concave mirrors are curved inward and the virtual image is larger and farther away than the object.

When light waves encounter a surface that is not smooth, it is reflected in many different directions. This phenomena is called diffuse reflection. Light bounces off textured walls to fill a room with light, but these walls or bumpy. The Law of Reflection still holds true, but the normal is affected by these bumps.

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Law of Reflection

When light is reflected from a smooth reflecting surface, the angle the reflected ray makes with the

surface normal is equal to the angle the incident ray makes with the surface normal.

WEEK 3 FUNDAMENTALS OF PHYSICAL SCIENCE

The visibility of objects is primarily caused by diffuse reflection. Diffusely-scattered light forms the image of the object in the observer’s eye.

Most objects you see are not emitting their own light, but reflecting light. The color of the object we see is not the color (wavelength) of light the object absorbs, but the color it reflects. This process is known as selective reflection, meaning that the pigment of the object reflects specific frequencies of light while the rest is absorbed. This is how we see different colors.

Recall that the speed of light is lower through denser materials than it is through empty space. Light travels at different speeds in different materials. Refraction is the bending of a light ray due to a change in speed of the wave when it changes mediums. If the ray is not perpendicular to the surface, it is refracted. The angle of refraction is the angle between the refracted ray and the normal.

The difference in the speed of light in different materials is usually described by a quantity called the index of refraction, which is represented by the letter n. The index of

refraction is defined as the ratio of the speed of light in a vacuum, c, to the speed of light, v, in some material.

The amount of bending a light ray experiences depends on both the angle of incidence and the indices of refraction of the materials involved, which determine the change in speed. A larger difference in speeds will produce a greater difference in how far the ray travels in the two materials. A larger difference in indices of refraction of the two materials therefore produces a larger bend in the ray of light.

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Diffuse reflection is why it is easier to see on a dry road than a wet road.

n = c v

n = index of refraction c = speed of light in a vacuum (m/s) v = speed of light through material (m/s)

WEEK 3 FUNDAMENTALS OF PHYSICAL SCIENCE

Absorption is when the electrons in a material take some or all of the energy from the incident light and neither transmit nor reflect it. This absorbed energy can cause the material to heat up. Light can be transmitted, reflected, refracted, and absorbed to varying degrees depending on the material it encounters.

Visible Light, Colors, and Vision

The visible light spectrum is the very narrow portion of the electromagnetic spectrum that stimulates the retina of our eyes and allows us to see. This region consists of a spectrum of wavelengths from 400-700 nanometers and contains all the different colors of the rainbow. Each individual frequency and wavelength of the visible light spectrum corresponds with a particular color. So when light of that particular wavelength strikes the retina of our eye, we perceive that specific color.

We know that we do not only see the colors of the rainbow (ROYGBIV) – the human brain can interpret over 20,000 different hues of color, and all of these different shades that we see are related to different wavelengths of light, the properties of different materials, and how our eyes see. When you look at an object and perceive a certain color, you are usually not just seeing a single frequency of light; there may be several frequencies striking your eye with varying degrees of intensity. Your eyes and brain interpret the frequencies that strike your eye and the object is determined by your brain as being a certain color.

When all the wavelengths of the visible light spectrum strike your eye at the same time, white light is perceived. So white is not a color at all, but a combination of all the colors of the visible light spectrum. Black, then, also is not defined as a color because it is the absence of all of the wavelengths of the visible light spectrum.

There are other ways to produce white light. One way is by combining only three distinct frequencies of light: red, green, and blue. Red, green, and blue are known as primary additive colors. (Please note that this is different than the primary colors you may have learned about in art class! Those colors are referring to pigments, whereas here we are referring to light.)

The addition of any of these primary colors of light with varying degrees of intensity can produce a wide range of other colors. Many television sets and computer monitors take advantage of this by the use of red, green, and blue light-emitting phosphors.

Adding together any two of the primary colors at the same intensity will give us the primary subtractive colors: cyan, magenta, and yellow.

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WEEK 3 FUNDAMENTALS OF PHYSICAL SCIENCE

The subtractive colors can also be created by subtracting any of the primary additive colors from white light.

Since cyan = white minus red, it makes sense that cyan + red would equal white. This makes cyan and red complementary colors. Complementary colors are two colors of light that combine to make white light. Following the same logic, this means that the other complementary c o m b i n a t i o n s a r e m a g e n t a / g r e e n a n d yellow/blue.

Since colors of light can be added together to create white light, white light can also be split into all the different wavelengths of colors. Dispersion is the process of separating light into its different

colors. Prisms are a common way of dispersing light into the different colors. As white light passes through a prism, the different colors (or frequencies) are refracted

at different angles. Different frequencies deviate from the original path at different angles: the higher the frequency, the more the deviation. Red will deviate the least, and violet will deviate the most. Rainbows are a natural example of dispersion. Each individual raindrop acts as a prism, and the light passing through it disperse to all the different colors.

Like sound, light will also experience the Doppler effect. This was discovered when studying the light from distant stars. The color of stars moving away from us will shift to red, while the color of stars moving toward us will shift to blue. The Doppler effect can still be defined as the apparent change in frequency due to the motion of t h e s o u r c e o r t h e motion of the observer, b u t t h e d i f f e r e n t frequencies perceived in the case of light will be different colors.

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