light what is it?. light what is it: moving energy particle or wave?

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 light Property #1• colors Property #2• reflection Property #3• refraction (bending) Property #4• shadows Property #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:

vphase = [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: vphase = [1/oo]

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/{4k} = 1 / {4 * 9x109 Nt-m2/Coul2}

o = 4 * 1x10-7 T-s /Coul

v = [4*9x109 / 4*1x10-7 ]1/2 = 3 x 108 m/s = cunits: [(Nt-m2/C2)*(C/[T-s])]1/2 = [({kg*m/s2}*m2/C2)*(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,

vphase = [1/]

= Ko , where K>1; and o ; sov < 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): frequencyamong different types of “light”: low frequency is radio (AM is 500-1500 KHz) high frequency is x-ray & gamma rayin 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 GHz cm - mm

Infrared (IR) 1012 - 4x1014Hz mm - 700 nm

visible 4x1014 - 7.5x1014 700nm -400nm

Ultraviolet (UV) 7.5x1014 - 1017 400 nm - 1 nm

x-ray & ray > 1017 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?

ReflectionA 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

apparentlocation

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

vxa

vya

vxw

vyw

vxa = vxw

vya < vyw

therefore

va < vw

= a

= w

Refraction: particle theory

Since v1x = v2x, using the angles between the normal (the vertical) and the light rays, we have: vx1 = vx2, or v1 sin(1) = v2 sin(2) ,

v1 sin(1) = v2 sin() (faster speed means smaller angle)

Property 4: Refraction

• wave (E&M) ?

surface

air

water

incident wave

refracted wavenormal 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 linecrest of following wave

Property 4: Refraction

wave (E&M): + = 90o

+ = 90o

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 theorywave (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) / va = f sin(w) / vw or

(1/v1) sin() = (1/v2) sin()

(faster speed means bigger angle)

NOTE: since a > w, need va > vw which agrees with

wave prediction of Property 1 on speed!

Note: This is opposite to the prediction of the particle

theory: v1 sin() = v2 sin() with va < vw .

Property 4: Refraction

wave (E&M): Snell’s Lawnicer form for Snell’s Law:

f sin(a) / va = f sin(w) / vw

Multiply thru by c/f to get

(c/va) sin(a) = (c/vw) sin(w)

and use definition of index of refraction:

n = c/v to get

na sin(a) = nw sin(w) Snell’s Law

Properties 1, 2 & 4

Speed, Color and RefractionSpeed 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 RefractionSpeed of light changes in different materialsSpeed 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: vw > va

• wave (E&M) theory: vw < va

• experiment ?

Property 4: Refraction

• particle (photon) theory: vw > va

• wave (E&M) theory: vw < va

• experiment: vw < va

particle theory fails!

wave theory works!

Property 4: Refraction

Snell’s Law:

na sin(a) = nw 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: n1 sin(1) = n2 sin(2)• NOTE: If n1 > n2, THEN 1 < 2 .

• NOTE: All 1 values between 0 & 90 degrees work fine.

• NOTE: Not all values of 2 work!

Example: If n1 = 1.33, n2 = 1, and 1 = 75o, then

2 = inv sin [n1 sin(1) / n2] = inv sin [1.28] = ERROR

Property 4: Refraction

Snell’s Law: n1 sin(1) = n2 sin(2)

If n1 sin(1) / n2 > 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.