phys 252 part 1: light what is light?. light what is light: moving energy wave or particle?
TRANSCRIPT
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): no prediction
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 (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
v x = t2 2 2 2 2 y y/ /
F T x = t ory2 2 2 2 ma y y / /
Property 1: Speed of Light
particle (photon): no prediction
wave (E&M): Maxwell’s Eqs.
wave equation from Maxwell’s Eqs predicts:
v = 1 / ( )o
E / x = t2 2 2 2 E /
E = E(x +/- vt) where
Property 1: Speed of Light
particle (photon): no prediction
wave (E&M): Maxwell’s Eqs.
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
Property 1: Speed of Light
particle (photon): no prediction
wave (E&M): Maxwell’s Eqs.
in material, v = [1/(με)]1/2
= K , K > 1 ; so
v (in material) < c (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 property 4 (refraction) and in Part 4 of the course when we look at Special Relativity.
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
• 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): 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
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: 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
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)
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): + = 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
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) / 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!
Property 4: Refraction
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
Property 4: Refraction
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
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 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.