PHYS 252 Part 1: Light what is light?

Light what is light: moving energy wave or particle?

Light what is light: 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) ?

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

Property 1: Speed of Light particle (photon): no prediction wave (E&M): Maxwell’s Eqs. wave equation from Maxwell’s Eqs:

Property 1: Speed of Light particle (photon): no prediction wave (E&M): Maxwell’s Eqs. wave equation from Maxwell’s Eqs: is similar to the wave equation for a string: where y = y(x+/- vt) and v = [T/μ] 1/2

Property 1: Speed of Light particle (photon): no prediction wave (E&M): Maxwell’s Eqs. wave equation from Maxwell’s Eqs predicts: E = E(x +/- vt) where

Property 1: Speed of Light particle (photon): no prediction wave (E&M): Maxwell’s Eqs. in vacuum: v = [1/(μ o ε o )] 1/2 where μ o = 4π x T*m/A and ε o = 1 / [4πk] = 1 / [4π x (9 x 10 9 Nt-m 2 /C 2 )] so v = c = [1 / {(4π x )/ (4π x 9 x 10 9 }] 1/2 m/s = [9 x ] 1/2 m/s = 3 x 10 8 m/s = 670 million miles/hour

Property 1: Speed of Light particle (photon): no prediction wave (E&M): Maxwell’s Eqs. in material, v = [1/(με)] 1/2

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 property 4 (refraction) and in Part 4 of the course when we look at Special Relativity.

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

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 Experiment: –visible order: red orange yellow green blue violet

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)

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

Reflection Does a white paper reflect the light, or does a white paper emit from itself the light? - Obviously, the white paper reflects the light. Does a mirror reflect light? Of course. What is the difference between white paper and a mirror?

Reflection A white paper is rough on a microscopic level, and so a beam of light is reflected in all directions: A mirror is smooth on a microscopic level, and so a beam of light is all reflected in just one direction. rough paper smooth mirror Red is incoming, blue is outgoing

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 xa v ya v xw v yw v xa = v xw v ya < v yw therefore v a < v w

Refraction: particle theory Since v 1x = v 2x, using the angles between the normal (the vertical) and the light rays, we have: v x1 = v x2, or v 1 sin(  1 ) = v 2 sin(  2 ), and we have the Pythagorean Theorem: [v 2 sin(  2 )] 2 + [v 2 cos(  2 )] 2 = v 2 2, or [v 2 sin(  2 )] 2 = v [v 2 cos(  2 )] 2, so if we substitute the first equation in the second, we get [v 1 sin(  1 )] 2 = v [v 2 cos(  2 )] 2 or [v 1 sin(  1 )] 2 = v 2 2 [1 - cos(  2 )] 2 = [v 2 sin(   )] 2 or v 1 sin(  1 ) = v 2 sin(   ) (faster speed means smaller angle)

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

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

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): 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  a >  w, need v a > v w 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): nicer form: 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 wave theory works! particle theory fails!

Properties 1, 2 & 4 Speed, Color and Refraction Speed of light changes in different materials Speed is related to frequency and wavelength: v = f If speed changes, does wavelength change, frequency change, or BOTH?

Properties 1, 2 & 4 Speed, Color and Refraction Speed of light changes in different materials Speed is related to frequency and wavelength: v = f What changes with speed: –Frequency remains constant regardless of speed –Wavelength changes with speed

Property 4: Refraction Snell’s Law: n a sin(  a ) = n w sin(  w ) Note that angles are measured from the normal, not the surface. Note that the index of refraction is bigger for slower speeds.

Property 4: Refraction Snell’s Law: n 1 sin(  1 ) = n 2 sin(  2 ) NOTE: If n 1 > n 2, THEN  1 <  2. NOTE: All  1 values between 0 & 90 degrees work fine. NOTE: Not all values of  2 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.

Property 4: Refraction The computer homework program (entitled Snell’s Law, vol. 5, #1) will give you practice is using Snell’s Law. We will now halt our look at light’s different properties, and look at some important applications of Refraction for the rest of Part 1. We will continue looking at other properties in Part 2 of the course.