What is Physics? First of all, Physics is a Science. So our first question should be: What is a Science?

Science What is a science? Physics is a science. Biology is a science. Is Psychology a science? Is Political Science a science? Is English a science? What makes a field of inquiry into a science?

Scientific Method What makes a field of inquiry into a science? Any field that employs the scientific method can be called a science. So what is the Scientific Method? What are the “steps” to this “method”?

Scientific Method 1. Define the “problem”: what are you studying? 2. Gather information (data). 3. Hypothesize (try to make “sense” of the data by trying to guess why it works or what law it seems to obey). This hypothesis should suggest how other things should work. So this leads to the need to: 4. TEST, but this is really gathering more information (really, back to step 2).

Scientific Method Note one thing about step 3: the predictive power of the hypothesis gives us something else to look for. We are in essence trying to extend our common sense to areas in which we initially have little common sense.

Scientific Method Fascinating Question Is the scientific method really a never ending loop, or do we ever reach “THE TRUTH”?

Scientific Method Is the scientific method really a never ending loop, or do we ever reach “THE TRUTH”? Consider: can we “observe” or “measure” perfectly? If not, then since observations are not perfect, can we perfectly test our theories? If not, can we ever be “CERTAIN” that we’ve reached the whole “TRUTH” ?

Scientific Method If we can’t get to “THE TRUTH”, then why do it at all? We can make better and better observations, so we should be able to know that we are getting closer and closer to “THE TRUTH”. Is it possible to get “close enough”? Look at our applications (engineering): is our current understanding “good enough” to make air conditioners?

Physics Now Physics is a science, but so are Chemistry and Biology. How does Physics differ from these others? It differs in the first step of the method: what it studies. Physics tries to find out how things work at the most basic level. This entails looking at: space, time, motion (how location in space changes with time), forces (causes of motion), and the concept of energy.

Scientific Method and Light To try to show the scientific method in action, we’ll look at light.

Light What is it?

Light What is it? Moving energy There are two basic ways that energy can move from one place to another: particles can carry the energy, or the energy can propogate in waves. Can light be explained as a wave or as a particle?

Light What is it? Moving energy Wave or particle? How do we decide?

Light What is it? Moving energy Wave or particle? How do we decide? If a wave, what is waving? (waving even in a vacuum?)

Light What is it? Moving energy Wave or particle? How do we decide? If a wave, what is waving? (waving even in a vacuum?) Electric & Magnetic Fields

Properties of Light speed of light colors reflection refraction (bending) shadows energy theory absorption of light emission of light

Property 1: Speed of Light particle (photon) prediction?

Property 1: Speed of Light particle (photon) ? no prediction wave (E&M) prediction?

Property 1: Speed of Light particle (photon) ? no prediction wave (E&M) ? For a wave on a string, we can start from Newton’s Second Law and get a wave equation that leads to the relation: v phase =  [T/  ] (speed of wave depends on parameters of the string the wave travels on - T is tension in the string and  is the mass density of the string)

Property 1: Speed of Light particle (photon) ? no prediction wave (E&M) ? Maxwell’s Eqs. In a similar way to the wave on a string, we can get a wave equation from Maxwell’s Eqs for Electromagnetism. This predicts: v phase =  [1/  o  o ] where the  o and  o are the electric and magnetic properties of vacuum.

Property 1: Speed of Light particle (photon) ? no prediction wave (E&M) ? Maxwell’s Eqs. in vacuum: v = [1 / {  o  o }] 1/2 where  o = 1/{4  k} = 1 / {4  * 9x10 9 Nt-m 2 /Coul 2 }  o = 4  * 1x10 -7 T-s /Coul v = [4  *9x10 9 / 4  *1x10 -7 ] 1/2 = 3 x 10 8 m/s = c

Property 1: Speed of Light particle (photon) ? no prediction wave (E&M) ? Maxwell’s Eqs. in material, v phase =  [1/  o  o ]  = K  o, where K>1; and    o ; so v < c According to the wave theory, light should move slower in material than in vacuum.

Property 1: Speed of Light particle (photon) ? no prediction wave (E&M) ? in vacuum, v = c; in material, v < c we’ll come back to this when we look at refraction.

Property 2: Color experiment ? particle (photon) ? wave (E&M) ?

Property 2: Color experiment ? visible order: red orange yellow green blue violet

Property 2: Color experiment ? invisible as well as visible total spectrum order: radio microwave IR visible UV x-ray and gamma ray

Property 2: Color particle (photon) ? amount of energy per photon determines “color”

Property 2: Color particle (photon) ? amount of energy among different types: x-ray - most energy; radio - least in visible portion: violet - most energy; red - least

Property 2: Color particle (photon) ? amount of energy wave (E&M) ?

Property 2: Color particle (photon) ? amount of energy wave (E&M) ? frequency among different types of “light”: low frequency is radio (AM is KHz) high frequency is x-ray & gamma ray in visible spectrum: red is lowest frequency (just above IR) violet is highest frequency (just below UV)

Colors: frequencies & wavelengths (in vacuum) AM radio  1 MHz 100’s of m FM radio  100 MHz m’s microwave  10 GHzcm - mm Infrared (IR) x10 14 Hzmm nm visible 4x x nm -400nm Ultraviolet (UV) 7.5x nm - 1 nm x-ray &  ray > Hz < 1 nm [This slide will be repeated after we see how we get these values.]

Property 3: Reflection particle (photon) ? wave (E&M) ?

Property 3: Reflection particle (photon) ? bounces “nicely” wave (E&M) ? bounces “nicely” bounces nicely means: angle incident = angle reflected

Property 4: Refraction experiment ? particle (photon)? wave (E&M) ?

Property 4: Refraction experiment: objects in water seem closer than they really are when viewed from air air water real object apparent location eye

Property 4: Refraction particle (photon) ? water air surface incident ray refracted ray

Property 4: Refraction particle (photon) ? water air surface incident ray refracted ray v xi v yi v xr v yr v xi = v xr v yi < v yr therefore v i < v r

Property 4: Refraction wave (E&M) ? surface air water incident wave refracted wave normal line surfac e

Property 4: Refraction wave (E&M) ? surface air water incident wave refracted wave crest of wave crest of preceding wave x a w normal line crest of following wave a w

Property 4: Refraction wave (E&M) ?  +  = 90 o  +  = 90 o surface air water incident wave refracted wave crest of wave crest of preceding wave x a w normal line sin(  ) = a /x sin(  ) = w /x

Property 4: Refraction wave (E&M) ? Snell’s Law sin(  a ) = a /x and sin(  w ) = w /x eliminate x: a /sin(  a ) = w /sin(  w ) and use: f = v (or = v/f) to get f sin(  a ) / v a = f sin(  w ) / v w NOTE: since  w <  a, need v w < v a which is opposite to the prediction of the particle theory but agrees with wave prediction of Property 1 on speed!

Property 4: Refraction wave (E&M) ? Snell’s Law nicer form for Snell’s Law: f sin(  a ) / v a = f sin(  w ) / v w Multiply thru by c/f to get (c/v a ) sin(  a ) = (c/v w ) sin(  w ) and use definition of index of refraction: n = c/v to get n a sin(  a ) = n w sin(  w ) Snell’s Law

Property 4: Refraction particle (photon) theory: v w > v a wave (E&M) theory: v w < v a experiment ?

Property 4: Refraction particle (photon) theory: v w > v a wave (E&M) theory: v w < v a experiment: v w < v a particle theory fails! wave theory works!

Property 4: Refraction Snell’s Law: n 1 sin(  1 ) = n 2 sin(  2 ) NOTE: If n 1 > n 2 (v 1 < v 2 ), THEN  1 <  2. NOTE: All  2 values (angles in the faster medium) between 0 & 90 degrees work fine. NOTE: Not all values of  1 (angles in the slower medium) work! Example: If n 1 = 1.33, n 2 = 1, and  1 = 75 o, then  2 = inv sin [n 1 sin(  1 ) / n 2 ] = inv sin [1.28] = ERROR

Property 4: Refraction Snell’s Law: n 1 sin(  1 ) = n 2 sin(  2 ) If n 1 sin(  1 ) / n 2 > 1 THEN there is NO value of  2 that can satisfy Snell’s law (unless you count imaginary angles!). The math is trying to tell us that there is NO transmitted ray. This is called TOTAL INTERNAL REFLECTION.

Refraction and Thin Lenses Can use refraction to try to control rays of light to go where we want them to go. Let’s see if we can FOCUS light.

Refraction and Thin Lenses What kind of shape do we need to focus light from a point source to a point? lens with some shape for front & back screen point source of light s = object distance s’ = image distance

Refraction and Thin Lenses Let’s try a simple (easy to make) shape: SPHERICAL. Play with the lens that is handed out Does it act like a magnifying glass?

Refraction and Thin Lenses Let’s try a simple (easy to make) shape: SPHERICAL. Play with the lens that is handed out Does it act like a magnifying glass? Does it focus light from the night light?

Refraction and Thin Lenses Let’s try a simple (easy to make) shape: SPHERICAL Play with the lens that is handed out Does it act like a magnifying glass? Does it focus light from the night light? Does the image distance depend on the shape of the lens? (trade with your neighbor to get a different shaped lens)

Property #5: Light and Shadows Consider what we would expect from particle theory: sharp shadows light dark

Light and Shadows Consider what we would expect from wave theory: shadows NOT sharp light dark dim crest

Double Slit Experiment We will consider this situation but only after we consider another: the DOUBLE SLIT experiment:

Double Slit Experiment Note that along the solid lines are places where crests meets crests and troughs meet troughs. crest on crest followed by trough on trough

Double Slit Experiment Note that along the dotted lines are places where crests meets troughs and troughs meet crests. crest on crest followed by trough on trough crest on trough followed by trough on crest

Double Slit Experiment Our question now is: How is the pattern of bright and dark areas related to the parameters of the situation:, d, x and L? d SCREEN L x bright dim bright

Double slit: an example n = d sin(  ) = d (x/L) d = 0.15 mm = 1.5 x m x = ??? measured in class L = ??? measured in class n = 1 (if x measured between adjacent bright spots) = d x / L = (you do the calculation)

Photoelectric Effect Light hits a metal plate, and electrons are ejected. These electrons are collected in the circuit and form a current. A light + - V ejected electron

Photoelectric Effect The following graphs illustrate what the wave theory predicts will happen: I current I light intensity I current Voltage I current frequency of light

Photoelectric Effect We now show in blue what actually happens: I current I light intensity I current Voltage I current frequency of light V-stop f-co

Photoelectric Effect In addition, we see a connect between V-stop and f above f cutoff : V-stop frequency f cutoff

Photoelectric Effect Einstein received the Nobel Prize for his explanation of this. (He did NOT receive the prize for his theory of relativity.)

Photoelectric Effect Einstein suggested that light consisted of discrete units of energy,  E = hf. Electrons could either get hit with and absorb a whole photon, or they could not. There was no in-between (getting part of a photon). If the energy of the unit of light (photon) was not large enough to let the electron escape from the metal, no electrons would be ejected. (Hence, the existence of f-cutoff.)

Wave-Particle Duality The photo-electric effect can not be understood by the wave theory, but can be understood by the particle theory. Other phenomena also are not described accurately by the wave theory but are by the particle theory: blackbody radiation, Compton scattering, the sprectrum of hydrogen. So, is light a wave or is it a particle? More precisely, does light act like a wave or does it act like a particle?

Wave-Particle Duality Here is a rough analogy. (Remember the strengths but also the weaknesses of analogies.) Are you your mother’s son or daughter? Are you a member of another group (sports team, fraternity, sorority, etc?) Do you act exactly the same way when with your mother and with your group? Are your actions fairly predictable when you are with your mother and when you are with your group?

Wave-Particle Duality We notice that light behaves as a wave when it is moving (refraction, double slit). We also notice that light behaves as a particle when it is created or when it “hits” something (photoelectric effect). Light is very predictable when viewed from the Wave-Particle Duality theory.

Wave-Particle Duality Can this strange wave-particle duality theory “predict” new things to look for? This wave-particle duality theory has been developed to become the Quantum Theory. It has predicted the Heisenberg Uncertainty Principle, it has led to an understanding of the Pauli Exclusion Principle that explains the basis of chemistry: why carbon is so different than nitrogen or oxygen.