Elementary optics discussion

O  P  T  I  C  S    A  N  D    W  A  V  E     E  F  F  E  C  T  S

Light rays are what we deal with in Sections 7.1 – 7.4.  This is geometric optics.  Light is represented by a straight line with an arrow on it to show direction of travel of the light beam or “wavefront.”  Sections 7.5 and 7.6 deal with physical optics, the wave nature of light.

When can you see a reflected image of yourself?  Not in most situations—pages of the book, desktop, walls, floor.  Sometimes you can see a glare, a blurry reflected image of a light source, but these surfaces are not good reflecting surfaces because they are rough-textured as in (b) of fig 7.2.  If a surface is smooth and polished, like a mirror or glass window or even a clean car fender your reflection can be seen.

7.1 Reflection:  The law of reflection is “the angle of reflection is equal to the angle of incidence.”   Snell’s law, dates from about… when?  (Baghdad 984, says Wikipedia.) It applies to all surfaces, but the reflection from most surfaces is diffuse, meaning the individual light rays go off in all directions away from the surface.  When you have a polished surface, it’s “regular reflection” and reflected rays travel parallel to each other.

7.2 Refraction and dispersion: 

Refraction: (get some equipment do demo or lab!)  “the deviation of light from its original path because of a change in speed.” In other words, a beam of light bends when going from one medium to another.  What is a medium?  The substance that a wave travels through.  Electromagnetic radiation can travel in a vacuum, without a medium.  The speed of light in the absence of a medium (in free space) is 299792458 meters per second, a universal constant.

The "index of refraction" of a medium tells how much bending of a light beam will occur when light goes from one medium into another, such as from air into water (making a pencil in a glass of water appear bent).  Index of refraction is defined as (speed of light in vacuum / speed of light in medium), and given by the letter n .

Density variations: oasis and illusion of water on hot roadway = refraction by different air density (due to temperature difference).  Also, just above the surface of a hot object, you can see a shimmering from the changing index of refraction if you look along the surface. 

Reflection by refraction:  also known as total internal reflection.  When going from higher density material to lower density material --- higher n to lower n --- light is refracted “away from the normal.”  Draw a picture.  When incidence angle gets big, the refracted ray can be totally reflected back into the substance, fig. 7.10.

Dispersion:  prisms and rainbows: White light has spectrum of red (longest wavelength) through violet (shortest), with mnemonic ROY G. BIV.  The index of refraction varies with the wavelength of light, so that there is more bending for shorter wavelengths.   The “phenomenon of colors” or the “spectrum” of light is seen.  The different wavelengths are spread out or dispersed, thus giving the effect the name “dispersion.” The higher the index of refraction the more the light is spread out, or dispersed.  Thus a prism made of crown glass or of leaded crystal, both of which have higher n than regular glass, can disperse the colors better.

The best material is diamond, with index of refraction 2.42.  (From comparison, water is 1.33, and normal glass is about 1.5.)  Besides the good separation of the colors, the total internal reflection of diamond is more than for other materials.

Rainbow, see highlight, page 160.  You can see rainbows in the sky when there are enough water droplets and when the sun is in the right position, which is about 42 degrees above the horizon.  Total internal reflection AND refraction are occurring in a rainbow.  Two internal reflections produce a secondary rainbow.  Where else do you see rainbows?  Fooling around with the water hose—spraying fine mist of water.  Oil on water, soap bubbles.

7.3 Spherical Mirrors.  Concave, convex.  Introduction to focal length.  Rays hitting a concave mirror converge at what’s called the focal point.  (Draw it.)  Spherical and parabolic reflectors are used to collect light or radio waves at a point.  Convex mirror = diverges light away from a point.

Ray diagrams.  Won’t do these too muchly.

7.4 Lenses.  Do all this as if it’s an introduction and they will continue on in physics…  no, forget it.

Human eye:  The main thing I want you to know is the lens of the eye, the "crystalline lens,” can change shape and is able to focus light on the retina. Know the difference between nearsightedness and farsightedness in terms of where the image appears—in front of the retina or behind it.  Near: in front of retina.  Far: behind retina.  And know which type lens corrects for each. Diverging for nearsightedness, converging for farsightedness.  Also, what happens to near point with age?  Recedes=gets further away.  Inability of the eye’s lens to focus. 

7.5 Polarization:  Light is a transverse wave, its oscillation is perpendicular to its direction of travel.  Looking at this wave I draw on the board, you can see its oscillation is up and down in the plane of the board.  That means it is polarized vertically.  Most light in the room is unpolarized—no preferred direction of oscillation.  P. 171, fig 7.28. Polarization is the preferential orientation of the field’s oscillation  (book says field vectors). 

A Polaroid or polymer sheet will block all polarization directions except one.  The light coming out of a Polaroid will be linearly polarized, as shown in fig. 7.29

"Crossed" Polaroids will block all the incoming light.  Polaroid sunglasses reduce glare off of water and off of car windshields because in both cases reflected light is horizontally polarized and the sunglass lenses only pass light with a vertical polarization. 

7.6  Diffraction and Interference

Diffraction—formation of a new wave front because of waves striking a small object or going through a small opening.

Interference—the addition of the amplitudes of two or more waves.  Constructive and destructive.

Kinetic theory, thermodynamics; wave terminology

(Dr. Evil doesn't "do" phases, but in physics we do, in two different contexts--phases of matter, and the phase relations between waves.)

Phases of matter.  Show diagram at top of page 109.  Gas, liquid, solid. And what the process of converting from one to another is called.   What determines whether a given substance is in the solid, liquid or gas phase?  The temp and pressure! 

Solid has a definite volume and shape. Liquid has definite volume but no definite shape.  A gas has no definite volume or definite shape. 

Most solids have a microscopic crystalline structure (lattice), and some have a MACROscopic, visible crystalline structure—quartz crystal, diamonds, other gems.  Two substances mentioned in book that have “amorphous” structure are glass and asphalt.  Don’t have a particular melting temp, where bonds are broken and solid becomes liquid.   Remember melting and latent heat of fusion. 

Kinetic theory of gases.  How do you smell perfume, by some kind of smell rays being emitted by the liquid?  No, by individual molecules of the perfume being deposited in your nasal passages/olfactory glands.  How do the molecules get there?  By being converted from liquid to gas and bouncing in all directions off air molecules.   Some of these bounce into your nose.

Kinetic Theory describes a gas as consisting of molecules (or atoms) moving independently in all directions at high speeds.  Confined gas molecules bounces off walls of container, and molecules bounce off each other. See pages 116 and 117.

Four variables needed: pressure, volume, temp and number of molecules in the container.   How does the pressure of the gas vary as V, T, and N are varying?  Well,  using the symbol α as shorthand for “is proportional to,”  we have:   P α N,    P α T,    and    P α 1/V.

Combining these gives  P α NT/V,    the ideal gas law, which can be written as an equation if Bolzmann’s constant k is used:  P = kNT/V.  Kicking V over to the left side gives the familiar

                                                                                PV = kNT 

“Ideal gas” means a model of a gas in which no forces act between the molecules or atoms constituting the gas, they merely collide with each other like billiard balls and collide with the walls of the container and go on their merry way.  (But, of course, like billiard balls, where the bounce of a collision is ultimately due to electromagnetic forces, there must be some very short range electromagnetic or other force acting in a collision, or the molecules/atoms would not even sense each other’s presence.)

Thermodynamics:  1^st law and heat engines; 2^nd law (Entropy); 3^rd law.   

Thermodynamics is about the dynamics of heat.  It deals with heat production, heat flow, and the conversion of heat to work.  In dynamics or mechanics, we have Newton’s 3 laws.  In thermoshermo, we have also three laws.  Nobody alone discovered them all, though.  Several people contributed to each one, actually, over the course of 50 to 60 years in the 19^th century.

The first law of thermodynamics is THE CONSERVATION OF ENERGY.  In all processes, including thermodynamic ones, energy is neither created nor destroyed.  When heat is added to a closed system it is converted into either the internal energy of the system or into doing work.  Can be written as simple equation: 

H = ΔE_i + W.  

Engines do useful work.  They make something move, whether it’s a generator rotating in a power plant to produce electricity, your car moving down the road, or electrons moving in a wire.  Many, but not all, engines operate by using a source of heat, such as a boiler in an electric power plant or the heat of combustion that moves the pistons in your car.  Electricity supplied by batteries or by electric motors are exceptions—they don’t use heat to do work, they use electrons directly, by forcing the electrons to move and consequently to do work.  In doing work they produce unwanted heat, though, so thermodynamics also applies to them.

Idealized examples of a heat engine and a heat pump are shown in the book.  A heat engine uses heat to do work, and heat pump, such as AC unit, refrigerator, or real heat pump, takes work and uses it to move heat from colder environment to hotter environment.

First law doesn’t rule out heat flowing SPONTANEOUSLY from colder to hotter object.  Common sense does, though!  And in fact, there is also a law that tells what can and can’t happen thermodynamically—the 2^nd Law of Thermodynamics.  Heat can’t spontaneously flow from hotter to colder object. 

The 2^nd law can also be expressed as: the disorder of an isolated system never decreases.  Entropy is a mathematical measure of how much disorder a system has, so the other way of stating the 2^nd law is:  the entropy of an isolated system never decreases.

Entropy has been decreasing on earth, but this is due to energy input from the sun.  For the solar system itself, a good approximation to an isolated system, entropy is increasing.

Third law: it’s impossible to attain a temperature of absolute zero.  Reason:  it would take an infinite amount of work.  This is like trying to reach the speed of light: it takes more and more work to increase the kinetic energy of an object as it approaches the speed of light.  As absolute zero is approached, it takes more work to remove heat and lower the temp.

(There's also a "zeroth law" of thermodynamics.)

Now, on to ...

W             A                  V                   E                   S

And their properties.

Waves carry energy:  a shaking or vibrating of matter—a disturbance, the book says—causes energy to be released in the form of waves.  The energy can be carried in air—or in any gas or liquid—in the form of sound waves.  If the vibrating object is electrically charged, it emits electromagnetic waves, which can travel in a vacuum (empty space).

Waves are of two basic types, longitudinal and transverse.  Longitudinal waves oscillate parallel to their direction of travel.  EX:  Sound waves.  See fig 6.3.  Transverse waves oscillate perpendicular to their direction of travel.  EX: waves on a string and electromagnetic waves.  Fig. 6.4.

Wave characteristics:  wavelength, frequency, period, amplitude, velocity.

Wavelength: the length of one complete wave (thus is measured in meters or other length units).

Frequency:  Number of oscillations that occur during a given time, usually taken to be one second.  Unit is hertz, of Hz: 1 Hz is one oscillation, or one cycle, per second. 

Period: reciprocal of frequency. So  f = 1/T.  The time it takes a wave to travel a distance of one wavelength.

EX:  Let f= 4HZ.  Then 4 wavelengths pass by a point in one second.

Amplitude: the maximum displacement of the wave.

Speed of light:  3x 10^8 m/s or 186,000 miles per second.

Speed of sound in air at room temp, 20 degrees C, is 344 m/s or 770mph.

Doppler effect: increasing frequency as object emitting the waves approaches you, decreasing frequency as object moves away from you. 

Resonance: when an object is made to vibrate at one of its characteristic or natural frequencies. Standing waves are created, as shown in 6.18.

This can be good in the case of making music or singing, because the “resonant cavity” of the instrument or the singer’s throat and nasal cavity will amplify the sound.  It can be bad for a structure like a bridge, a wine glass, a building or moving part on a car.

Oh, yeh, we can't forget phases.  This is the relationship in time or distance of where the peaks and valleys of two or more waves are located relative to each other.  We can have IN phase waves (peaks and valleys of one are lined up with peaks and valleys of another), OUT OF phase waves (peaks of one wave are lined up with valleys of another), and all possibilites in between.