Light what is it?

Light what is it: moving energy particle or wave?

Light what is it: moving energy particle or wave? how do we decide?

Light what is it: moving energy particle or wave? how do we decide? if a wave, what is waving? (waving even in a vacuum?)

Light what is it: moving energy particle or wave? 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

Properties of Light speed of lightProperty #1 colorsProperty #2 reflectionProperty #3 refraction (bending)Property #4 shadowsProperty #5 energy theory consider in Part 4 absorption of light consider in Part 4 emission of light consider in Part 4

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 units: [(Nt-m 2 /C 2 )*(C/[T-s])] 1/2 = [({kg*m/s 2 }*m 2 /C 2 )*(C/[{Nt-s/C-m}*s])] 1/2 = m/s

Property 1: Speed of Light particle (photon): no prediction wave (E&M): Maxwell’s Eqs. in material, v phase =  [1/  ]  = 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 later in this part.

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 (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)

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) ?

Reflection particle (photon): bounces “nicely” wave (E&M): bounces “nicely” experiment: 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 refracted ray incident 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 =  a =  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 ), 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

Refraction: wave theory 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 or (1/v 1 ) sin(   ) = (1/v 2 ) sin(   ) (faster speed means bigger angle) NOTE: since  a >  w, need v a > v w which agrees with wave prediction of Property 1 on speed! Note: This is opposite to the prediction of the particle theory: v 1 sin(   ) = v 2 sin(   ) with v a < v w.

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

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? Does color change with speed? (does color depend on frequency or wavelength?)

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 –Color remains constant (so color depends on frequency, not wavelength)

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 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 in using Snell’s Law. We will now temporarily halt our look at light’s different properties, and look at some important applications of Refraction.