Review

Charge
Electron
Proton
Neutron
Quark
Coulomb's law (inverse square)

Current
Voltage
Resistance
Ohm's law (V = I R)

Circuits
Series
Parallel
Brightness problems (based on current, if bulbs are identical)

Schematic symbols
Light bulbs lighting
Batteries

Magnetism
Electromagnetism
Electromagnetic induction

Motors vs. engines
Basics of 2-stroke engines

Einstein 
Special relativity (time changing between observers)
General relativity (gravity caused by distortions of space caused by mass)

Online tonight

Between 8 and 9 this evening (Tuesday), feel free to email me questions for quick responses. Be safe in the snow.

Seanplally@gmail.com

I'll repeat this at some points before the final.

Why do we still care about Einstein?

Worth a read (from an Einstein scholar and former prof of mine):

http://www.pitt.edu/~jdnorton/Goodies/Einstein_and_S/index.html

Notes from class:

And then there was Einstein…

Albert Einstein 1879-1955

http://www.aip.org/history/einstein/index.html

What’s happening around the turn of the 20th century? Physics was set to explode with 30 brilliant years of excitement and unprecedented activity

X-rays – Roentgen

Radioactivity – Becquerel, Marie & Pierre Curie

Blackbody radiation (and the quantum discontinuity) – Planck

1905/6 – Einstein publishes 6 major papers:

a) “On the electrodynamics of moving bodies”

b) “Does the inertia of a body depend upon its energy content?”

c) “On a heuristic point of view about the creation and conversion of light”

d) “On the theory of the Brownian movement”

e) “On the movement of small particles suspended in stationary liquid demanded by the molecular-kinetic theory of heat”

f) “A new determination of molecular dimensions”

What are these about anyway?

a. Special relativity (SR)

b. E = m c2 (actually, L = m c2)

c. Photoelectric effect, light quanta, fluorescence

d. Same as title

e. Brownian motion agan

f. Avagadro’s number, etc.

Now, these are interesting (and very different fields of study), but is this why we revere Uncle Al? Not necessarily. Others (Poincare, Lorentz) were working on what would become SR. Planck had introduced the quantum discontinuity (E = h f) and quantum mechanics (QM) would have many contributors. The photoelectric effect had also several investigators (Lenard, et.al.).

Mostly, Einstein’s legend grows because of General Relativity (GR), which appears 1912-1915 and later and on which he worked largely alone with pad and pen. He forced us to re-examine how we see ourselves in the universe; indeed, how we think of gravitation. All of this around the time his marriage was falling apart (he married young after fathering 1 illegitimate child) and he began an affair with his cousin (whom he would later marry). Also, between 1902 and 1909, Einstein held a modest post in Bern, Switzerland as a Patent Clerk. By 1914, he would be director of the Kaiser Wilhelm Institute (later Max Planck Institute).

Special Relativity

Spaceship – Inside an inertial reference frame (constant velocity), you can’t tell whether or not you’re moving (“Principle of Relativity”)

Biographical notes

1879 – born in Ulm, Germany

1884 – receives first compass

1895 – attempts to gain entrance to Swiss Polytechnic (and finish high school early), but is rejected

1896 – begins Federal Polytechnic (ETH) in Zurich, Switzerland

1898 – meets Mileva Maric

1900 – graduates from ETH

1901 – Einstein becomes Swiss citizen and moves to Bern; Mileva becomes pregnant

1902 – Lieserl born (put up for adoption); Hermann dies

1903 – Albert and Mileva marry

1904 – Hans Albert born

1905 – Einstein’s “Annus Mirabilus”, his miracle year; Ph.D. (Zurich)

1919 – divorces Mileva (having lived apart for 5 years); marries Elsa; GR verified

1921 – awarded the Nobel Prize in Physics "for his services to Theoretical Physics, and especially for his discovery of the law of the photoelectric effect".

1933 – settles in Princeton, NJ

1936 – Elsa dies

1939 – E. writes FDR

1940 – E. becomes American citizen

1949 – Mileva dies

1955 – E. dies

http://www.aip.org/history/einstein/index.html

http://www.albert-einstein.org/

http://einstein.stanford.edu/

http://en.wikipedia.org/wiki/Einstein

General Relativity

By 1907, E. wanted to advance the SR theory to include non-inertial (accelerated) frames of reference. Around this time, E. has the “happiest thought of my life”. In a uniformly accelerated spaceship, a stationary thing (ball, etc.) would appear to be falling (accelerating) down – it would be indistinguishable from normally accelerated motion. Light, too, follows this idea. Two clocks at different ends of an accelerated spaceship would be out of sync. Gravity is the result of the curvature of space and time?

Why does the Earth follow the Sun? Gravity – the very presence of the Sun causes Earth to veer from its otherwise straight (Newtonian inertial) path. With the Sun, it takes an elliptical path as its natural motion. Getting to this point, and showing that mass alters space and time is the real genius.

There is a breakdown of the observed geometry (Euclidean). E. must use non-Euclidean geometry (Gauss, surfaces, infinitesimal geometry) to consider the behavior of things (rods, etc.) on surfaces. He also considers the shortest distance between 2 points on a sphere (geodesic, great circle). He obtains the mathematical advice of his friend Marcel Grossman and studies (at great length) tensor calculus, differential geometry, Riemann and Minkowski math … it’s all puzzle solving. Soon, the principle of equivalence emerges. Eventually, the gravitational field equations appear (to show how matter “produces” gravity. GR was mostly worked out by 1913

Electromagnetic Induction

Generator - a motor in reverse

Magnetism questions

1. In general, what causes magnetism?

2. What is electromagnetism?

3. What is the peculiarity involving magnetic north?

4. How would you find true north?

5. What is a motor and how does it basically work?

6. How do compasses respond to magnetic fields?

7.  What is electromagnetic induction?

8.  What is a generator?

9.  What is a transformer?

10.  Don't forget to review all of the circuit questions from earlier.  Emphasize:

a.  V, I and R -- know what they are, their units, and how to calculate them (V = I R)
b.  the difference between series and parallel circuits -- particularly, how to calculate currents
c.  related to series and parallel circuits -- know how to ascertain relative bulb brightnesses in circuits

11.  Regarding the earliest stuff (for the final exam) on charge.  Focus on:

a.  what the charge concept means
b.  electron, proton, neutron, quark
c.  Coulomb's law (as an inverse square law)

A few more -

12.  Distinguish between motors and generators.

13.  Explain the basic parts of the speaker.

14.  Differentiate between a motor and an engine.

15.  Explain the basic processes of the 2-stroke engine.

Student help

Folks,

I did not mention this in class - sorry!  A couple of students have requested some help with material in the class.  There is not a formal tutoring process in place for this class, nor do I have a TA or some such.  We'll have to do the next best thing - see if we can formalize a study group before the final exam (Monday, December 16 at class time).

After class tonight, all of you interested in forming a study group should stick around - we'll see if we can put something together to help you all.  I will not be involved directly, but I'll help coordinate the endeavor.  Also, if you agree on a night, maybe we could set up a 1 hour "email hour" wherein you ask questions of me directly.  That could work for everyone, actually.

See you tonight.

SL

Motors are not Engines.

Steam Engines:

http://science.howstuffworks.com/transport/engines-equipment/steam.htm

http://www.animatedengines.com/locomotive.html

Stirling Engines:

http://auto.howstuffworks.com/stirling-engine.htm

http://www.animatedengines.com/vstirling.html

http://www.animatedengines.com/stirling.html

http://www.animatedengines.com/ross.html

2-stroke Engines:

http://science.howstuffworks.com/transport/engines-equipment/two-stroke1.htm

http://science.howstuffworks.com/transport/engines-equipment/two-stroke2.htm

4-cycle Engines:

http://auto.howstuffworks.com/engine1.htm

(single cylinder)

Intake, Compression, Combustion, Exhaust

http://auto.howstuffworks.com/engine2.htm

(more typical, and more complex)

http://auto.howstuffworks.com/engine4.htm

What goes wrong typically?

http://auto.howstuffworks.com/engine3.htm

http://science.howstuffworks.com/transport/engines-equipment/two-stroke1.

Magnetism notes

Some ideas from the Magnetism classes:

Similar to the case of charge, magnetic poles are divided into North and South poles.

A North magnetic pole is one that points toward the Earth's magnetic north pole.  This means that the Earth's magnetic north is ACTUALLY A SOUTH POLE (magnetically speaking).

Also:

- Like poles repel
- Opposite poles attract
- Each magnet must have at least one North and one South pole (though they may have more than one of each).  There is NO such thing as a magnetic monopole.
- Magnetic fields are real, but the lines are imaginary - Field lines indicate the direction that a compass needle would take in the vicinity of the magnetic field.

Magnetic north on the Earth is near Ellesmere Island in Northern Canada, several hundred miles from true (geographic) North (the North Pole).  It is moving toward Russia at several miles per year.

For gory detail:

http://en.wikipedia.org/wiki/North_Magnetic_Pole

To find True/Geographic north, it is easiest to find Polaris (the current north star).  Polaris is actually not all that bright, though in the top 50 brightest stars in the night sky.  You need to find the Big Dipper (asterism at the rear end of Ursa Major).  Follow the “pointer stars” at the end of the dipper.  These visually lead you to Polaris.  [If you were to follow the “arc” of the handle, you’d come to a bright star, Arcturus – “Follow the arc to Arcturus.”]

 

 

 

FYI:

http://skymaps.com/

How do we get magnetism?

Magnetic fields are related to electrons spins.  Electrons act like tiny magnetic  spinning tops.  There is a tiny magnetic element associated with each electron spin.  If the spins align, more or less, the object is said to be somewhat magnetic.  More spin alignments (domains) means more magnetism.  Materials that do this easily are generally said to be ferromagnetic.  

As it happens, metals do this best (free electrons).  In the core of the Earth, molten metal convects (rises and falls), giving the Earth a good magnetic field – measurable from the surface and beyond.  Several planets have magnetic fields.

In general, the motion of charges leads to magnetic fields.  If you have charge traveling through a wire, electrons can be thought of as moving together – this causes a magnetic field, also known as electromagnetism.  The magnetic field caused by a current passing through a wire is often small, but if you coil the wire upon itself, the magnetic fields “add up”.  Several hundred turns of wire (with current running through it) can produced quite a strong electromagnet. 

A coil with current running through it can naturally react to a permanent magnet – if this is engineered well, we have a motor.  See illustrations and demos in class.

 

Electromagnetic Induction

Current causes magnetism – something shown in the early 19^th century by Hans Oersted.  As it happens, the reverse is also true – magnetism can cause current, but there must be some relative CHANGE in the magnetic field or location of conductor.   There must be relative change – either coil or magnet must move, relative to the other.

This phenomenon, wherein a change in magnetic field relative to a conductor, generates electric current is called “electromagnetic induction.”  It is the secret to understanding generators.  If something, say moving water from Niagara Falls, can cause a coil of wire (in a turbine) to spin, current is generated.  More spins of wire means more current.

It’s all about moving conductors in magnetic fields

In conclusion:

Electromagnetism:

Current (moving charges) à  Magnetic Field

Electromagnetic Induction:

Change in magnetic field (through conductor), or vice versa à electric current

 

Power in Circuits

Power - the rate at which energy is "consumed"

P = E / t

Energy (in joules) per time (in seconds)
- new unit (joule/sec) is called a watt (W)

For electricity:

P = E/t
But recall that V = E/q

So....

P = V q / t

And since q/t = I

P = V I

Or

P = I^2 R

In other words, the power of a light bulb depends on its resistance.

For identical light bulbs in a circuit, only the current will matter when trying to determine brightness.

Consider:

- 2 bulbs in series vs 2 bulbs in parallel. Which are brighter?

- 3 bulbs in series vs 2 in series

- 2 bulbs in parallel, which are then in series with another bulb

Magnetism images

More circuit problems

1.  Consider two resistors, both 10 ohms, connected to a 20-V battery.  Find the current through each if they are connected:

A.  In series

B.  in parallel

2.  Now consider the problem again:  4 and 2 ohm resistors, connected to a 24-V battery.  Find the currents, when connected:

A.  In series

B.  in parallel 

3.  Two identical light bulbs are connected in series. The same bulbs are connected in parallel.  Which are brighter?

4.  Consider 1 bulb connected to a battery vs. 3 identical bulbs in parallel to the same battery.  Which bulb(s) are brighter?

Circuit problems

1.  Describe the difference between voltage, current and resistance.  Give the proper units, too.

2. 10 coulombs of charge flows past a point in a circuit in 5 seconds. What is the current?

3. A 5-ohm resistor is connected to a 10-volt battery. What current passes through the resistor?

4. Two 100-ohm resistors are in series. What is their total resistance?

5.  In general, what is the difference between resistors in series and in parallel?  Recall the light bulb examples. 

6.  Which has more resistance, 2 identical bulbs in series or the same 2 identical bulbs in parallel?

7.  For question 6, which set-up (series or parallel) would kill the battery quicker?

8.  You have 2 bulbs in series - remove one (unscrew it) and what happens?

9.  You have 2 bulbs in parallel - remove one (unscrew) and what happens?

10.  Draw the symbols for battery, resistance and wire.

Circuits

Voltage (V) - amount of available energy per coulomb of charge.  The unit is volt (also V).

Current (I) - how quickly charge travels (or charge per time, q/t).  The unit (a coulomb per second) is called the ampere (or amp, A). 

Resistance (R) - a way of expressing how much charge is resisted through a device.  It is expressed as a ratio of applied voltage to the resulting current (V/I).  The unit (a volt per amp) is called an ohm (represented as the Greek symbol omega).

Often, the relationship between V, I and R is expressed as Ohm's Law:

V = I R

Batteries and other sources (such as wall sockets) "provide" voltage, which is really a difference between TWO points (marked + and - on a battery).  A wall outlet is a bit more complex - there are 2 prongs, but often also a third prong (the "ground", for safety purposes).

Some folks like analogies.  Consider the water analogy discussed in class.  Voltage is like a tank of water (how much water).  Resistance is provided by a drain or faucet.  The rate at which water comes out is the current.  It's only an analogy, but it gets the gist of circuit terminology ok.

What exactly *IS* a circuit?

An electrical circuit can be thought of as a complete "loop" through which charge can travel. Therefore, it actually has to be physically complete - there can be no openings. That is, the current actually has to have a full path to take.

But there is an exception:

If the supplied voltage is high enough, charge can "jump" an "open circuit." This is clearly a dangerous situation, and one way in which a person can get shocked. Think of the unfortunate situation of sticking your finger (or a paper clip, etc.) into an electrical outlet (or something like a toaster, for that matter). You would "bridge" the circuit, becoming in effect, a resistor.

That's bad.

OK, so about regular circuits:

The images represent SERIES CIRCUITS and PARALLEL CIRCUITS.

In a series circuit, the current is constant and is set by the total resistance of the circuit (the sum of the resistors). If you remove one resistor (or light bulb, as in the first image), the current stops. If the resistors were identical bulbs, having more bulbs would result in dimmer bulbs, since the battery voltage is distributed among them.  Note that the sum of the voltages "over" the bulbs is equal to the total voltage provided by the battery (give or take some minor losses).  Identical bulbs (or resistors) have identical voltages "over" them - 3 identical bulbs connected to a 9-V battery would have roughly 3-V each over them.

In parallel circuits, current has multiple paths to take, so the total resistance of the circuit is actually LESS than if the resistors were alone or in series with other resistors. Since the bulbs are connected equally to the battery, they experience the same as the battery voltage - they are, therefore, of equal brightness (and the same brightness they would have if there were only ONE bulb connected). Of course, bulbs in parallel draw more current and thus cause a battery to die sooner.  You could have 10 bulbs or resistors connected in parallel to a battery - each will be as bright as if only 1 were connected to the battery (same voltage over each), though 10 bulbs will kill the battery 10 times faster.

Does this have anything to do with holiday lights?

What I've written above is primarily geared toward identical bulbs. In series, add up the resistances to get the total resistance. In parallel, it is more complicated. There is a formula one can use (1/Rp = 1/R1 + 1/R2 + ...), but we will only concern ourselves with the case of identical resistors in parallel. In that case, divide the value of the resistor by the number of resistors to get the total effective resistance. For example, two identical 50-ohm resistors in parallel is the same as one 25-ohm resistor. This seems strange, but it's a little like toll booths - when one toll booth is open, it can get crowded (the current is small). With multiple toll booths open, the resistance is effectively less, so the current can be greater. 

In the images below, the first graphic represents the schematic view of a parallel circuits, with 2 resistors.  Note that 2 possible paths are available for current to take - current runs through EACH path, though there will be more current where there is less resistance.  The total current from the battery is equal to the sum of the currents through the 2 resistors.  It follows V = I R, though the V over each R is the same.  The I through each will therefore be V/R.

The second image illustrates the series circuit concept:  identical resistors in series will effectively give MORE resistance (the sum of the resistances, actually) to the battery, so the current will be LESS (and exactly the same in each resistor or bulb).  It also easily follows V = I R, with more R yielding less I (when V is constant).  Think of V = I R this way:  I = V/R.  More R, less I.

Circuits!

Thus far, we have only discussed "static" (stationary) charges.  Static charges alone are useful, but not nearly as much as charges in motion.  As you recall, electrons are the most easily moved particles.  However, for sake of ease in sign convention (positive vs. negative), we define the following:

Current (I) - the rate at which positive charge "flows"

I = Q/t

The unit is the coulomb per second, defined as an ampere (A).  One ampere (or amp) is a tremendous amount of current - more than enough to kill a person.  In fact, you can feel as little as 0.01 A.  Typical currents in a circuit are on the order of mA (milliamperes).

We need to define other new quantities in electricity:  voltage, resistance, power.

Voltage (V) - the amount of available energy per coulomb of charge.  The unit is the joule per coulomb, called a volt (V, in honor of Allesandro Volta, inventer of the battery).

V = E/Q

Resistance (R) - the ratio of voltage applied to an electrical device to the current that results through the device.  Alternately:  the amount by which the voltage is "dropped" per ampere of current.

R = V/I

You can also think of resistance as that which "resists" current.  Typically, resistors are made of things that are semi-conductive (they conduct current, but less well than conductors and better than insulators).  Resistors are often made of carbon, but can also be made of silicon and other materials.  The unit is the volt per ampere, defined as an ohm (Greek symbol omega)

A convenient way to relate all of the variables is embodied in an expression often called Ohm's Law:

V = I R

But what exactly IS a circuit?

An electrical circuit can be thought of as a complete "loop" through which charge can travel.  Therefore, it actually has to be physically complete - there can be no openings.  That is, the current actually has to have a full path to take.

Also consider electrical power (P).  Power is the rate at which energy is used or expended:  energy per time.  Symbolically:  P = E / t.  The unit is the joule per second, called a watt (W).  In electricity, power is also given by:

P = I V

P = I^2 R

Summary:

Voltage (V) - amount of available energy per coulomb of charge.  The unit is volt (also V).

Current (I) - how quickly charge travels (or charge per time, q/t).  The unit (a coulomb per second) is called the ampere (or amp, A). 

Resistance (R) - a way of expressing how much charge is resisted through a device.  It is expressed as a ratio of applied voltage to the resulting current (V/I).  The unit (a volt per amp) is called an ohm (represented as the Greek symbol omega).

Power (P) - rate at which energy is produced or expended (E/t).  Energy per time.  Unit is the joule per second, called a watt (W).  In electricity:  P = I^2 R

Batteries and other sources (such as wall sockets) "provide" voltage, which is really a difference between TWO points (marked + and - on a battery).  A wall outlet is a bit more complex - there are 2 prongs, but often also a third prong (the "ground", for safety purposes, through which excess charge can travel back to the Earth).

Some folks like analogies.  Consider a water analogy.  Voltage is like a tank of water (how much water).  Resistance is provided by a drain or faucet.  The rate at which water comes out is the current.  It's only an analogy, but it gets the gist of circuit terminology ok.

More about charge

Charge is difficult to define.  It is property of particles that describes how particles interact with other particles. 

In general, the terms are negative and positive, with differing amounts of each, quantified as some multiple of the fundamental charge value (e):

e = 1.6 x 10^-19 C

That's hard to visualize, since a coulomb (c) is a huge amount of charge.  One coulomb, for example, is the charge due to:

1 coulomb = charge due to 6.3 x 10^18 protons

A typical cloud prior to lightning may have a few hundred coulombs of charge - that's an enormous amount of excess charge.

If the charge is negative (-), the excess charge is electrons.

If the charge is positive (+), the excess charge is protons - however, we can NOT easily move protons.  That usually takes a particle accelerator.  Typically, things are charged positively by REMOVING electrons, leaving a net charge of positive.

Other things to remember:

Neutral matter contains an equal number of protons and electrons.

The nucleus of any atom contains protons and (usually) neutrons (which carry no charge).  The number of protons in the nucleus is called the atomic number, and it defines the element (H = 1, He = 2, Li = 3).

Electrons "travel" around the nucleus in "orbitals."  See chemistry for details.  The bulk of the atom is empty space.

Like types of charge repel.  Opposite types of charge attract.

The proton is around 2000 times the mass of the electron and makes up (with the neutrons) the bulk of the atom.  This mass difference also explains why the electron orbits the proton, and not the other way around.

Protons in the nucleus of an atom should, one would imagine, repel each other greatly.  As it happens, the nucleus of an atom is held together by the strong nuclear force (particles which are spring-like, called gluons, keep it together).  This also provides what chemists called binding energy, which can be released in nuclear reactions.

Static Electricity

Charge

- as fundamental to electricity & magnetism as mass is to mechanics

Charge is a concept used to quantatively related "particles" to other particles, in terms of how they affect each other - do they attract or repel?  If so, with what force?

Charge is represented by letter Q.

The basic idea - likes charges repel (- and -, or + and +) and opposite charges attract (+ and -).

Charge is measured in units called coulombs (C).  A coulomb is a huge amount of charge, but a typical particle has a tiny amount of charge:

- the charge of a proton is 1.6 x 10^-19 C.  Similarly, the charge of an electron is the same number, but negative, by definition (-1.6 x 10^-19 C).  The negative sign distinguishes particles from each other, in terms of whether or not they will attract or repel.  The actual sign is arbitrarily chosen.

The charge of a neutron is 0 C, or neutral.

How particles interact with each other is governed by a physical relationship called Coulomb's Law:

F = k Q1 Q2 / d^2

Or, the force (of attraction or repulsion) is given by a physical constant times the product of the charges, divided by their distance of separation squared.  The proportionality constant (k) is used to make the units work out to measurable amounts.

Note that this is an inverse square relationship, just like gravity.

The "big 3" particles you've heard of are:

proton
neutron
electron

However, only 1 of these (the electron) is "fundamental".  The others are made of fundamental particles called "quarks""

proton = 2 "up quarks" + 1 "down quark"
neutron = 2 "down quarks" + 1 "up quark"

There are actually 6 types of quarks:  up, down, charm, strange, top, & bottom.  The names mean nothing.

Many particles exist, but few are fundamental - incapable of being broken up further.

In addition, "force-carrying" particles called "bosons" exist -- photons, gluons, W and Z particles.

The Standard Model of Particles and Interactions:

http://www.pha.jhu.edu/~dfehling/particle.gif

some answers.

Doppler and Light problems:

1.  To you, the frequency would appear:
a.  lower
b.  higher
c.  same
d.  higher
e.  lower

2.  expanding universe

3.  light source moving away from or toward you

4.  see notes

5.  a.  320 x 2
b.  320/2
c.  320 x 8
d.  320 x 1.059
e.  320 x 1.059^3

6-7 notes

8.  less than 45

9.  See notes on total internal reflection

10.  notes


Light pt 2

1.  where light converges in a convex lens or concave mirror, when the light rays are initially parallel (which usually happens when the object is very far away)

2.  no.  distance between lens or mirror and object

3.  convex lenses - thicker in middle.  They *can* produce real images on sheets of paper (though not when the object is within f).

concave lenses - thinner in middle.  They never produce real images on screens/paper.

4.  Concave mirrors are like convex lenses.  Like shaving mirrors.

Convex mirrors are like concave lenses.  Like convenience stores mirrors.

5-8.  notes

Diffraction and Holography

Diffraction and Holography

When light passes through small openings or around barriers, it can actually interfere with itself - this is called diffraction. Like interference, patterns can result - and these patterns are related to the opening or barrier that caused the diffraction.

Holography is an interference phenomenon, caused by two beams - a reference beam, coming from the laser, and an object beam (which reflected off the object). This interference pattern is burned into the film emulsion of holographic film. It can be reconstructed when light passes through it again.

Interference

http://surendranath.tripod.com/Applets/Waves/TWave02/TW02.html

http://falstad.com/ripple/

 

Consider 2 waves meeting each other in the same space. Their energies (AKA wave amplitudes) can add (or subtract). This phenomenon is called interference. If you've ever added sine waves on a calculator before, the effect is similar - and sometimes also called superposition.

Crests can add to other crests or cancel with troughs - however, it's usually some combination, depending on the waves in question. And often, beautiful "interference patterns" can result.

Light problems pt. 2

1.  Define "focal point."

2.  Do images always form at the focal point?  If not, what determines if/where an image is formed?

3.  How are convex and concave lenses different?

4.  How are convex and concave mirrors different?

5.  Revisit the final problem from the last problemset.  Draw what happens to parallel rays of light as they pass through:
a.  convex lens
b.  concave lens
c.  convex mirror
d.  concave mirror

6.  Play around with the lens applet used in class to see how image formation depends on the location of the object.

7.  Describe the difference between nearsightedness and farsightedness, and the lenses used to correct each.

8.  Describe the operation of a basic reflecting telescope.

Doppler and Light etc. problems

1.  Doppler effect.  A police car approaches you.  According to the siren's manufacturer, the frequency is 1000 Hz.  How would the frequency change if you were located:
a.  behind the car as it passed you
b.  in front of the car as it approached you
c.  in the car
d.  running toward the car, if it were at rest
e.  running away from the car, if it were at rest

2.  What does the red shift of distant galaxies suggest?

3.  What do red shift and blue shift mean?

4.  Explain the Doppler effect.

5.  Consider a 320 Hz note (E, approximately).  What is the frequency of:
a.  the next E (one octave above)
b.  the E one octave below
c.  an E that is 3 octaves above
d.  an F, one semi-tone above
e.  a G, three semi-tones above

(You don't have to calculate these, but show how it would be done.)

6.  Explain the idea of reflection (of light).  What is the 'law of reflection'?

7.  What happens during refraction?  What changes exactly?  (Hint:  more than one thing could change during refraction.)

8.  Light goes from air into a rectangular piece of glass.  If the light hits the glass at an angle of 45 degrees (with respect to the normal line), how is it refracted inside the glass?  Draw this situation.  Would the refraction angle be greater than, less than or the same as 45 degrees?

9.  Light passes from water into air - basically the opposite of the previous problem.  Light hits the surface of the water (from below) at an angle of 45 degrees.  Revisit the previous problem and answer/draw what is expected.

* Problem 9 can refer to "total internal reflection", or what happens when light hits the surface INSIDE the substance (water, plexiglas, etc.) at angle too great to leave.  This phenomenon allows for fiber optics, as well as strange effects seen when you look into an aquarium.

10.  Draw what is expected when parallel rays of light hit:
a.  convex lens
b.  concave lens
c.  convex mirror
d.  concave mirror
e.  flat mirror