SAT II Physics (Gary Graff) Episode 1 Part 6 docx

The law of reflection can be stated as follows: The angle ofincidence equals the angle of reflection.A spherical concave mirror reflects light toward a point on thecentral radius called

The law of reflection can be stated as follows: The angle ofincidence equals the angle of reflection.

A spherical concave mirror reflects light toward a point on thecentral radius called the focal point The radius of curvature is thedistance from the mirror to its center if the mirror were a fullsphere This is called the principal axis

Concave spherical mirrors are important tools in science because

of their ability to focus incident light The point where incidentrays are focused is called the focal point and is one half the radius

of curvature

f =r2

Two rules worth remembering about light rays that strike a cave mirror are:

1 Any light ray that is moving parallel to the principal axis and isincident to the mirror will be reflected though the focal point

2 Any light ray that passes through the focal point and is incident

to the mirror will be reflected parallel to the principal axis

Light rays from objects (O) placed in front of a concave mirror produce images (I).

The images produced may be real (projectable onto a screen)

or virtual (appearing to be located on the other side of the mirror);they may be enlarged (magnified) or shrunk (reduced); or they may

be right side up (erect) or upside down (inverted)

The following diagrams illustrate the position of the imagewhen the object is placed in various locations in front of themirror

Object distance is considered infinite

Light rays are parallel as they approach and strike the mirror

Image is located at f It is reduced, inverted, and real.

Object is located at r.

Image is located at r It is the same size as the object, inverted, and

real

Object is located between r and f.

Image is located beyond r It is magnified, inverted, and real.

Object is located inside f.

Image is located behind the mirror It is reduced, erect, and virtual

The letters I and O are used to represent the height of the image (I) and the height of the object (O) The distance from the mirror to the image is labeled q and the distance from the mirror

to the object is labeled p.

Mirrors are used in a variety of ways throughout the world.Shopkeepers use convex mirrors to keep an eye on the aisles oftheir stores, and sharp corners on roadways have mirrors set out

so drivers can see the road ahead The magnifying capability ofmirrors allows astronomers and laboratory researchers to performtheir work

This capability of a mirror is based upon the set of ratios (ofthe object and image heights) compared to the distance of theobject and the image from the mirror

h h

q p

Object is located in front of the mirror

Image is located behind the mirror and appears to be inside it It isreduced, erect, and virtual

The equation that describes the location of an image in amirror is called the mirror equation

1 1 1

f = +p q

The focal length (f) is positive for concave mirrors and negative for convex mirrors If the image (q) or the object (p) are located in front of the mirror, they are positive If the image (q) and/or the

object is/are located behind the mirror, it is negative

Let’s do a typical reflection problem

Find the location of the image for an object that is placed 37

cm in front of a mirror having a focal length of 3.6 cm Describethe image

1025

The image is located 4 cm from the mirror The object is outside

the radius of curvature (2f = 7.2 cm), and the image is located between r and f It is reduced, inverted, and real.

Now we’ll use the original information from the problemabove, but we’ll replace the concave mirror with a convex mirror

cm cmcm

0027

The image is located 3.29 cm behind the mirror (the negative sign

for q) It is reduced, erect, and virtual.

REFRACTION

Waves that move into a new medium bend as they enter the dium All waves can be refracted, but our discussion here will belimited to light The light beam shown below passes from air into

me-a cube of plme-astic

At the air/plastic boundary, the light ray bends (refracts) towardthe normal when the light ray passes into the plastic The raymoves in a straight line while in the plastic until it reenters the air

At the plastic/air boundary the light ray bends (refracts) awayfrom the normal

When light enters an optically more dense material, it refractstoward the normal When it enters an optically less dense material,

it refracts away from the normal

The mathematical relationship between the velocity of light inone material (usually air) compared to another material was

determined to be

n1sinθ1=n2sinθ2 (Snell’s Law),

where n is the index of refraction of the material through which

light is passing

Example

A typical Snell’s Law problem is one where a scuba diver shines alight upward into the air from under the water The light beammakes an angle of 30° from the vertical What is the angle of thelight beam as it enters the air?

Solution

The index of refraction (n) for water is 1.33 and for air is 1.

Stating Snell’s Law

n n

1 1 2 2 2

1 1 2 2

2

1 33 5

1 655

sin sinsin sin

sin ( )( ) sin

θθ

Lenses are important because they can focus light Convexlenses converge light rays passing through them toward the focal

point f This kind of lens is called convergent Concave lenses

separate light rays passing through them as if the separated lightrays had originated at the focal point This kind of lens is calleddivergent The two light rays of which to take note are:

• A light ray that is parallel to the principal axis and is incident uponthe lens will be refracted through the focal point (on the other side

of the lens)

• A light ray that passes through the focal point and is incident uponthe lens will be refracted parallel to the principal axis (on the otherside).

Light rays from object (O) placed in front of a curved lens produce images (I) The diagrams below illustrate the position of

the image when the object is placed in various positions

Object distance is considered infinite

Light rays are parallel

Image is located at f It is reduced, inverted, and real.

Object distance is outside 2f but not infinite.

Image is located between 2f and f It is reduced, inverted, and real.

Image same side and outside object; magnified, erect, and virtual.

The lens equation 1 1 1

f = +p q is the same as the equation used for

mirrors Remember though, the image distance (q) is positive

when on the opposite side of the lens

Concave lenses produce virtual images.

As with the mirror equation, the lens equations can be used tolocate an image

1 1

125 05 1

1075

f p q

q q q

Polarization is a phenomenon that applies only to transversewaves Light is a transverse wave and is commonly the object ofpolarization Let’s examine polarization by considering a rope tied

to a fixed end Vibrating the rope up and down produces wavesthat travel down the rope

Should we stand beside the rope and hold a meter stick verticallybeside the rope, there is no problem

The rope vibrates on the vertical axis, and the meter stick is ented on the vertical axis If we change the orientation of the stick

ori-to the horizontal axis, the vertical vibrations in the rope strike thehorizontal meter stick

Transverse waves are almost completely stopped when they reachthe meter stick

We can take these results a step further and apply them tolight Light is considered a transverse wave that only differs fromour rope example in that light vibrates 360° around the line path

of the light ray

The polarized eyeglasses many people wear restrict the intensity

of the light that reaches their eyes by using a device (polarizer)that only allows light vibrating on one plane to pass through tothe eye

The result is similar to holding a meter stick over a rope that isvibrating up and down, but with the plane polarizer, every planebut one is polarized at the same time

DIFFRACTION AND INTERFERENCE

Water waves approaching a fixed object in their path tend to movearound the object and continue on their way The ability of waves

to bend around obstacles in their path is called diffraction

Like-wise, waves that strike a barrier in which there are openings havethe ability to pass through the opening The opening acts as a newsource of waves that radiate out from the source

Suppose the barrier has two holes Then each hole acts as a newsource of waves.

The area of waves beyond the barrier is filled with a confusion ofwaves crossing one another A series of peaks and troughs exists

as waves both constructively and destructively interfere with oneanother

Thomas Young (1801) tested light in this manner using a

double slit Since the confused waves were light waves, Youngdecided he could project the results onto a screen Young learnedthat the light waves would interfere with one another in a waythat produced areas of constructive interference (light spots) anddestructive interference (dark spots)

The light traveling from Slit 1 (S1) travels a number of whole

wavelengths (nλ) to reach the screen at P1 Additionally, the light from Slit 2 (S2) would travel the same number of whole wave-

lengths plus one more, nλ + 1 Typically more than one bright spot

on the fringe is visible The central (zeroth) fringe is the fringe

where the light path is exactly equal for both S1 and S2 The firstfringe on either side of the zeroth fringe is called the first orderfringe, the second is the second order fringe, etc The number ofthe fringe is the number of extra wavelengths traveled by the lightray on the longest path

nλ= sind θ

Example

Let’s find the wavelength of the green-yellow mercury spectralline The grating used has a spacing of 1 × 10–6m, and the anglebetween the zeroth and first fringe is 33.l° Write the equation and

remember n = 1 in this case.

and sin

If the angle to the fourth order fringe of a blue light is known to

be 3.9°, and the distance between slits is 0025 cm, find the length of the light

( )

and

cm100cm/m

4

40025

6 8 102

4

4 25 10 7 425

λ = × − or nm

CHAPTER SUMMARY

• Waves are periodic vibrations that carry energy

• Interference can be constructive or destructive

• The velocity of a wave is a product of its frequency and

wavelength v = λ f.

• Sound is a longitudinal wave

• Light is a transverse wave

• Mirrors reflect light

• The law of reflection is stated as ∠i = ∠r.

• A concave mirror reflects light toward the focal point

• A convex mirror reflects light as if the rays had passedthrough a focal point on the other side of the mirror

• The mirror equation

1 1 1

f = +p q is the same for both concaveand convex mirrors: f is positive for concave mirrors, and f is

negative for convex mirrors

• Light passing between two transparent materials is refracted

at the surface boundary of the materials

• Snell’s Law is n1 sinθ1 = n2 sinθ2 where n is the index of

refrac-tion for the materials, and θ is the angle of refraction

• A convex lens (converging) refracts light toward a focal point

• A concave lens (diverging) refracts light as if it had passedthrough a focal point and the other side of the lens

• The lens equation

1 1 1

f = +p q is identical in form to the mirrorequation However, q is positive when the image is located on the opposite side of the lens from p the object.

• Light that has had all its vibrations eliminated except for those

on a single plane is plane polarized

• Diffraction is the ability of waves to bend around barriersplaced in their way

• Interference is the constructive or the destructive

superposi-Chapter 4

HEA

HEAT T T AND AND AND THERMOD THERMOD THERMODYN YN YNAMICS AMICS

CHAPTER 4

HEA HEAT T T AND AND AND THERMOD THERMOD THERMODYN YN YNAMICS AMICS

TEMPERATURE

The atoms and molecules of which matter is made are constantly inmotion The more energy they contain, the faster they move Thekinetic energy the particles have is called internal energy A hot bodyhas more internal energy than a cold body The measure of the inter-nal energy of a body is called temperature The temperature of anobject is not dependent on the amount of the substance present andcan be measured with a thermometer

• Temperature scales are the method by which the heat energy ofbodies can be compared They are often based on an arbitrarypoint

• The Fahrenheit scale was devised to read 0°F as the coldest perature reached on earth and 100°F as the hottest material tem-perature on the earth The freezing point of water is 32°F and itsboiling point is 212°F

tem-• The Celsius scale was devised to measure between the freezing andboiling points of water The freezing point of water on the Celsius

scale is 0°C, and the boiling point of water is 100°C.

• The Kelvin or absolute scale places 0K at the point where there is

no heat, thus no lower temperature is possible Zero on the Kelvinscale is absolute, thus absolute zero means no heat energy is

present Note the degree sign is not used on the Kelvin or lute scale.

abso-• There are 180 degrees between the freezing and boiling points ofwater on the Fahrenheit scale

• There are 100degrees between the freezing and boiling points ofwater on the Celsius scale

• The Kelvin scale places the freezing point of water at 273K and the boiling point of water at 373K, which is also a 100-unit difference.

The Celsius and the Kelvin scales have a 1:1 relationship Thus to

change °C to K, all that’s necessary is to add 273 to the Celsius

temperature

THERMAL PROPERTIES OF MATTER

Thermal energy is the energy substances possess when their ture is greater than absolute zero As energy is added, most sub-stances expand You have probably seen the open joints in concrete

tempera-or on bridges—they are there to allow room ftempera-or the expansion of theconcrete as the seasons change Continued addition of heat energycan cause solids to change into liquids or liquids to change to gases.These are called phase changes

• Solids change to liquids by melting

• Liquids change to solids by freezing

• Liquids change to gases by evaporation

• Gases change to liquids by condensation

Above is a generalized heat and temperature graph for materials.Note the increase in temperature in the substance until a phasechange begins to occur During a phase change all the heat energyadded to the material is converting the substance from one phase toanother The temperature remains constant The temperature doesnot begin to rise again until the phase change is complete Reversingthe process means removing heat Should we apply the graph towater, we can say that during the freezing/melting phase, both liquidwater and ice are present Likewise, during the condensation/evapo-ration phase, both liquid water and steam are present The graph isflat during these processes, showing that no temperature changeoccurs during a phase change.

The heat required to change a substance from a solid to a liquid

is called heat of fusion The heat required to change a substance from

a liquid to a gas is called heat of vaporization Typically the heat of

vaporization is greater than the heat of fusion for a given substance

Expansion and ContractionWhen the temperature of a substance is raised, the atoms and mol-ecules of the substance have more energy This causes the distancebetween the atoms and molecules to increase As a result, the materialexpands Lowering the temperature of a substance causes the dis-tance between atoms and molecules to decrease or shrink

Heat Heat TTTrrrrransfansfansfererHeat can be transferred between substances in several ways Everycase of heat transfer involves the movement of heat from an area ofhigh heat content to an area of low heat content