Final exam topics

Final exam topics / Final exam is Thursday (May 17) at 5:30.

What happens when light hits lenses and mirrors
Convex and concave lenses
Convex and concave mirrors
Plane mirrors
Real and virtual images
Focal length
Total internal reflection - fiber optics
Basics of the eye and camera
Basics of interference and holography
Static electricity - likes repel, opposites attract
Fundamental charge
Coulomb's law (and how an "inverse square law" functions)
Electrons, protons, neutrons, quarks
Current
Voltage
Resistance
Basic circuits (and schematics)
V = I R (Ohm's Law)
Series circuit
Parallel circuit
Magnetism - natural (magnetite, Earth)
Compasses
Electromagnetism
Electromagnetic induction - generators

final exam etc.

My apologies for missing yesterday's class - an emergency happened.  It couldn't be helped.

During our final class (Tuesday) I will discuss magnetism (electromagnetic induction) for part of the class, and take some time for review.

Our final exam is Thursday, 5/17, at 5:30 PM.

Magnetism

Some ideas from the Magnetism sessions

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

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

Like poles repel.
Opposite poles attract.
Each magnet MUST have at least one north and one south pole.
Magnetic fields are real, though the field lines are imaginary. Field lines indicate the direction that a compass needle would take in the vicinity of the magnet.

Magnetic north on the Earth is near Ellesmere Island in Northern Canada, several hundred miles from true (geographic) North - the North Pole.

For gory detail:

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

To find true/geographic North, it has historically been done by following Polaris (the pole-star, the lodestar, the North star). Polaris is actually not all that bright (though in the top 50). You need to find the Big Dipper (the rear end of Ursa Major) and follow the two pointer stars at the end of the scoop - these point to Polaris (which is in Ursa Minor). [If you were to follow the "arc" of the handle, it would take you to the bright star Arcturus, as in "follow the arc to Arcturus".]

FYI - "Star Hopping" is a great way to learn your way around the sky. I like the free star chart site:

http://www.skymaps.com/

Magnetic fields are related to electron spins. Electrons act like miniature (extremely miniature) spinning tops. There is a magnetic element associated with their spins. If spins align, more or less, an object can be said to be somewhat magnetic. More spin alignments (domains) means more magnetism. Materials that do this well are said to be ferromagnetic.

As it turns out, metals do this best, as they often have 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 travel through a wire, electrons can be thought of as moving together - this causes a magnetic field. The magnetic field generated 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 them) can produce quite a strong electromagnet. Understanding electromagnets allows us to understand motors.

Current causes magnetism - something shown in the earth 19th century by Hans Oersted. As it happens, the reverse is also true: magnetism can causes current, but it must be a CHANGE in the magnetic field. The magnet (or conductor/coil through which it travels) must move. There must be some relative change between coil and magnet - either the coil must move or the magnet must move.

This is referred to as electromagnetic induction, and it is the secret to understanding generators. If a coil moves in a magnetic field, a current is generated inside it. Imagine turbines at the bottom of Niagara Falls (or any waterfall) - water hits the turbine and makes it spin. Inside the turbines are large coils of wire, free to rotate. These coils spin within a permanent magnetic field inside the turbine - this generate large amounts of current. Similarly, you can burn fossil fuels to heat water and generate steam. The steam is fed into a turbine, also generating large amounts of current.

It's all about moving conductors in magnetic fields!

Circuit questions

1.  What exactly is voltage, current and resistance?
2.  What is Ohm's law?
3.  Consider a 9-V battery connected to a 6-ohm resistor.  What is the current through the resistor?
4.  Consider 2 batteries (1.5 V each).  They are connected in series to 2 resistors (10 and 30 ohms).  Find the current through each resistor.
5.  In the problem above, what would happen if one of the resistors was removed from the circuit?

Series and Parallel Circuits

Series and Parallel Circuits

Electrical current

Thus far, we have discussed static charges. Static charges alone are useful, but not nearly as much as charges in motion. As you recall, electrons are most easily moved. However, for sake of ease in sign convention (keeping things positive, where positive), 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 also define other new quantities in electricity: voltage, resistance, power

voltage (V) - the amount of available energy per coulomb of charge

V = E/Q

resistance (R) - the amount by which the voltage is "dropped" per ampere of current

R = V/I

You can also think of resistance of that which "resists" current. Typically, resistors are made of things that are semi-conductors (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 a volt per ampere, defined as an ohm (Greek symbol, omega).

A convenient way to relate all the variables is embodied by Ohm's Law:

V = I R

As in, "Twinkle, twinkle little star, V is equal to I R."
Well, it works for me

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.

more questions

Electrostatics questions

1. What is the difference between an electron and a proton: in terms of charge? In terms of mass? In terms of position in an atom?

2. By "charging" something, what is usually happening? If the object is becoming negatively charged? Positively charged?

3. What is the charge of a proton? An electron?

4. Explain the rotating meter stick demonstration (similar to how a balloon sticks to a wall).

5 What is a Van de Graaff generator?

6. What do you suppose occurs when lightning strikes?

7. What happens to the electrostatic force between two charged objects if the distance between them is doubled? Tripled? Halved?

8.  What do we mean by "fundamental" charge? What charges are fundamental?

practice problems

1. Describe what happens to a light ray as it enters a piece of glass (or tank of water, for that matter) -

a. at a zero degree angle (with respect to the normal)

b. at a non-zero angle

(Though the math may be less comfortable to you, a relationship called Snell's law describes this all perfectly.)

2. Describe the law of reflection.

3. What exactly is the focal length of a lens or mirror? Under what circumstances are images formed AT the focal point?

4. Does a flat/plane mirror have a focal length? Discuss.

5. What is the difference between real and virtual images?

6. Draw what happens when several parallel rays of light hit:

a. convex lens

b. concave lens

c. concave mirror

d. convex mirror

e. plane mirror

7. "An image always forms at the focal length of a lens or mirror." This statement is false. Discuss.

8. A convex lens is similar to a _____. Why?

9. A concave lens is similar to a ______. Why?

10. With a convex lens, a real image is formed everywhere except when the object is located _____.

11. When you are using a magnifying glass or make-up/shaving mirror, where are you placing the object  to get a magnified image? What type of image is this?

12. What is nearsightness and farsightedness?  What types of lenses are used for nearsightness and farsightedness?

13.  What is interference of light?

14.  How is interference related to holography?

Static electricity

Charge
As fundamental to electricity and magnetism as mass is to mechanics

Charge is a concept to quantitatively relate particles to each other, in terms of how they affect each other. Charge is represented by Q.

The basic idea - like charges repel (2 negatives or 2 positives). Opposite charges attract.

Charge is measured in terms on units called coulombs (C). A coulomb is a huge amount of charge - the charge due to 6.2 x 10^18 protons.  That's 6.2 billion billion protons.  A lot of charge, even though this takes up a small amount of actual space..

The charge of a proton is tiny: 1.6 x 10^-19 C.

(By the way, the number above is called the fundamental charge unit (represented by the letter e).  It is the reciprocal of the number of protons in one coulomb.)

Similarly, the charge of an electron is the same value but negative (by definition): -1.6 x 10^-19 C

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

How particles interact with each other is embodied in a physical law called Coulomb's law:

F = k Q1 Q2 / d^2

Or, the force tha exists between 2 particles is proportional to the product of charges divided by the distance squared. A proportionality constant is used to make units work out nicely.

Note that this is an inverse square law like gravitation.

The big 3 of particles are:

Proton
Neutron
Electron

However, of these onl the electron is "fundamental," meaning that it can't be further subdivided. Protons and neutrons can be broken up into quarks.

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

They are exotic particles which typically do not exist alone in nature.

A proton is: 2 ups and a down quark.
A neutron is: 2 downs and an up quark.

Well over 100 particles exist, but few are fundamental.

FYI:  an up quark has a charge of 2/3 e (that's the charge of 2/3 of a proton), and a down quark has the charge of -1/3 a proton (which is like 1/3 of an electron).

Ripple Tank applet revisited.

http://www.falstad.com/ripple/

Choose "2 sources" or "Double slit" to review the phenomena discussed in class.

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 and Diffraction

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.

Camera and Eye