Transcript q 1 - Helios

Electromagnetic Waves
Physics 202
Professor Lee Carkner
Lecture 21
PAL #20 EM Radiation
Acceleration of lightsail craft
F = ma = prA
a = prA/m
pr = 2I/c
I = Ps/4pr2 = (3.9X1026)/(4p(1.5X1011)2) = 1379 W
pr = (2)(1379)/(3X108) = 9.2X10-6 N/m2
a = (9.2X10-6)(2.25X108)/5000 = 0.41 m/s2
Time to get to moon
d = ½at2
t = (2d/a)½ = [(2)(3.8X108)/(0.41)] ½
t = 43054 sec ~ 12 hours
Problems
Sunlight only pushes in one direction
How do you stop or go back?
Gravity and inherited motion also important
Consider a dust grain near a star. If the
grain is perfectly balanced between
light pressure out and gravity in, what
happens to the grain if the mass
doubles (but the size stays the same)?
A) Goes in
B) Goes out
C) Stays put
Consider a dust grain near a star. If the
grain is perfectly balanced between
light pressure out and gravity in, what
happens to the grain if the mass
doubles and the surface area doubles?
A) Goes in
B) Goes out
C) Stays put
Consider a dust grain near a star. If the
grain is perfectly balanced between
light pressure out and gravity in, what
happens to the grain if the distance
from the star doubles?
A) Goes in
B) Goes out
C) Stays put
Polarization

 The plane containing the E
vectors is called the plane
of oscillation

 Most light sources are
unpolarized
 Any given wave has a
random plane of oscillation
Polaroid

 Polaroid is a sheet of material
that will only pass through
the components of the E
vectors in a certain direction

 If you put a horizontal
Polaroid sheet on top of a
vertical Polaroid sheet no
light gets through
Polarization and Intensity

The sum of all of the y components should be
equal to the sum of all of the z components

I = ½ I0
This is true only when the incident light is
completed unpolarized
What about polarized light hitting Polaroid?
Incident Polarized Light
 For polarized light incident on a
sheet of Polaroid, the resultant
intensity depends on the angle q
between the original direction of
polarization and the sheet

E = E0 cos q

I = I0 cos2 q

 For unpolarized light that pass
through two polarizing sheets, q
is the angle between the two
sheets
Multiple Sheets
Sheet Angles
Means of Polarization

This alignment permits only the components in that
direction to pass

The dust grains are partially aligned by the galactic
magnetic field and so the light is partially polarized
Light can also be polarized by reflection
Reflection and Refraction
When light passes from one medium to another
(e.g. from air to water) it will generally experience
both reflection and refraction

Refraction is the bending of the portion of the light
that does penetrate the surface
Geometry

 Angles
 Angle of incidence (q1):
the angle between the
incident ray and the
normal
 Angle of reflection (q1’):
 Angle of refraction (q2):
the angle of the refracted
ray and the normal
Laws
 Law of Reflection

 Law of Refraction

n2 sin q2 = n1 sin q1
 Where n1 and n2 are the indices of refraction of the
mediums involved
Index of Refraction
Every material has an index of
refraction that determines its optical
properties


n is always greater than or equal to 1
Large n means more bending
General Cases
 n2 = n1

 q2 = q1
 e.g. air to air
 n2 > n1

 q2 < q1
 e.g. air to glass
 n2 < n1

 q2 > q1
 e.g. glass to air
Total Internal Reflection
 Consider the case where q2 =
90 degrees

 For angles greater than 90
there is no refraction and the
light is completely reflected

n1 sin qc = n2 sin 90
qc = sin-1 (n2/n1)
 This is the case of total internal
reflection, where no light
escapes the first medium
Chromatic Dispersion

 In general, n is larger for
shorter wavelengths

 Incident white light is
spread out into its
constituent colors
 Chromatic dispersion
with raindrops causes
rainbows
Chromatic
Dispersion
Polarization By Reflection
 Light reflected off of a
surface is generally
polarized

 When unpolarized light
hits a horizontal surface
the reflected light is
partially polarized in
the horizontal direction
and the refracted light
is partially polarized in
the vertical direction
Brewster Angle

At qB the reflected and refracted rays are
perpendicular to each other, so
qB + qr = 90

qB = tan-1 (n2/n1)
If we start out in air n1 = 1 so:
qB = tan-1 n

Next Time
Read: 34.1-34.6
Homework: Ch 33, P: 37, Ch 34, P: 7, 9,
10, 11, 12, 13, 15