Transcript Reflection and Refraction

Electromagnetic Waves
Physics 202
Professor Vogel
(Professor Carkner’s
notes, ed)
Lecture 12
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
 The new electric field becomes:
E = E0 cos q
 Since I depends on E2 it becomes:
I = I0 cos2 q
 This is only true for polarized light
 For unpolarized light that pass
through two polarizing sheets, q
is the angle between the two
sheets
Multiple Sheets
Sheet Angles
Polarization By Reflection
 Light reflected off of a
surface is generally
polarized
 This is why polarized
sunglasses reduce glare
 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
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
Reflection is the portion of the light that does not
penetrate the second medium but bounces off of
the surface
Refraction is the bending of the portion of the light
that does penetrate the surface
Geometry
 The normal line is a line
perpendicular to the
interface between the
two mediums
 Angles
 Angle of incidence (q1):
the angle between the
incident ray and the
normal
 Angle of reflection (q1’):
the angle of the reflected
ray and the normal
 Angle of refraction (q2):
the angle of the refracted
ray and the normal
Laws
Law of Reflection
The angle of reflection is equal to the angle of
incidence (q1’ = q1)
Law of Refraction
The angle of refraction is related to the angle of
incidence by:
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 = 1 for vacuum
We will approximate air as n = 1 also
n is always greater than or equal to 1
Large n means more bending
General Cases
 n2 = n1
 No bending
 q2 = q1
 e.g. air to air
 n2 > n1
 Light is bent towards the normal
 q2 < q1
 e.g. air to glass
 n2 < n1
 Light is bent away from the normal
 q2 > q1
 e.g. glass to air
Total Internal Reflection
 Consider the case where q2 =
90 degrees
 In this case the refracted light is
bent parallel to the interface
 For angles greater than 90
there is no refraction and the
light is completely reflected
 q2 > 90 when the incident
angle is greater than the
critical angle qc
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
 The index of refraction
depends on the
wavelength of light
 In general, n is larger for
shorter wavelengths
 Blue light bent more than
red
 Incident white light is
spread out into its
constituent colors
 Chromatic dispersion
with raindrops causes
rainbows
Chromatic
Dispersion
Brewster Angle
At a certain angle, known as the Brewster angle, the
reflected light is totally polarized
At qB the reflected and refracted rays are
perpendicular to each other, so
qB + qr = 90
Since n1 sin qB = n2 sin qr we get
qB = tan-1 (n2/n1)
If we start out in air n1 = 1 so:
qB = tan-1 n
This is Brewster’s Law