PHYS 252 Part 1: Light what is light?. Light what is light: moving energy wave or particle?

PHYS 252Part 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?


• if a wave, what is waving?

(waving even in a vacuum?)

Light

what is it? moving energy• wave or particle?


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) ?


particle (photon): no prediction

• wave (E&M) ?



wave (E&M): Maxwell’s Eqs.

wave equation from Maxwell’s Eqs:

E / x = t2 2 2 2 E /

Property 1: Speed of Lightparticle (photon): no prediction


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

v x = t2 2 2 2 2 y y/ /

F T x = t ory2 2 2 2 ma y y / /




wave equation from Maxwell’s Eqs predicts:

v = 1 / ( )o

E / x = t2 2 2 2 E /

E = E(x +/- vt) where




in vacuum: v = [1/(μoεo)]1/2 where

μo = 4π x 10-6 T*m/A and

εo = 1 / [4πk] = 1 / [4π x (9 x 109 Nt-m2/C2)] sov = c = [1 / {(4π x 10-7)/ (4π x 9 x 109}]1/2 m/s = [9 x 1016]1/2 m/s = 3 x 108 m/s

= 670 million miles/hour




in material, v = [1/(με)]1/2

= K , K > 1 ; so

v (in material) < c (in vacuum)



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 ?


• 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


• wave (E&M) ?

Property 2: Color


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)

Property 3: Reflection


• 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?

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) ?


experiment: objects in water seem closer than they really are when viewed from air

air

water

real object

apparentlocation

eye



water

air

surface

incident ray

refracted ray


particle (photon):

water

air

surface

incident ray

refracted ray

vxa

vya

vxw

vyw

vxa = vxw

vya < vyw

therefore

va < vw

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) , and we have the Pythagorean Theorem: [v2 sin(2)]2 + [v2 cos(2)]2 = v2

2 , or [v2 sin(2)]2 = v2

2 - [v2 cos(2)]2 , so if we substitute the first equation in the second, we get [v1 sin(1)]2 = v2

2 - [v2 cos(2)]2 or[v1 sin(1)]2 = v2

2 [1 - cos(2)]2 = [v2 sin()]2 or

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


• wave (E&M) ?

surface

air

water

incident wave

refracted wavenormal line


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


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


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) / va = f sin(w) / vw

NOTE: since a > w, need va > vw

which is opposite to the prediction of the particle theory but agrees with wave prediction of Property 1 on speed!


wave (E&M):

nicer form: 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


particle (photon) theory: vw > va

wave (E&M) theory: vw < va

• experiment ?


particle (photon) theory: vw > va

wave (E&M) theory: vw < va

experiment: vw < va

wave theory works!

particle theory fails!

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?

Properties 1, 2 & 4

Speed, Color and RefractionSpeed 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


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.


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


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.


• 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.

PHYS 252 Part 1: Light what is light?. Light what is light: moving energy wave or particle?

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