1Physics 430/530: Optics, Fall 2015
Homework 5, Fresnel Formulae
Due: Oct 15, 2015
1) I claimed in class that when applying the boundary conditions to plane waves at
interfaces between homogeneous media, I got 6 equations, of which 2 are redundant.
(i )
E

Physics 430/530: Optics, Fall 2015
Homework 4, Propagation Models
Due: Oct 6, 2015
1. [Hecht]:
2. Propagation models
Consider a plane wave propagating along in the z axis in air (assume that n=1) so that at
some observation point, it is described by by U

Physics 430/530: Optics, Fall 2015
Homework 3, Disperson and Propagation
Due: Sep 29, 2015
1) Assume we find that our complex permittivity for some material is given by
k
= 0 (1 + + i ) where > 0 . Given 0 0 n(1 + i ) , what is the square of the
absolute

Physics 430/530: Optics, Fall 2015
Homework 7, Geometrical Optics II
Due: Nov 10, 2015
1) Nodal points are a pair of points along the axis of a paraxial optical system. If a ray is
aimed at one nodal point, it will appear to originate from the other nodal

Physics 430/530: Optics, Fall 2015
Homework 6, Geometrical Optics I
Due: Oct 22, 2015
1) A 1 cm tall wire is imaged by a thin convex lens.
a. The real image formed is 2 cm tall. If the lens 50 mm from the wire, what is the
focal length of the lens and whe

Physics 430/530: Optics, Fall 2015
Homework 1, Waves
Due: Sep 8, 2015
1) Consider cylindrically symmetric solutions to the wave equation (f does not depend on
or z).
a) Find the cylindrically symmetric monochromatic waves that satisfy the wave equation
(

Physics 430/530: Optics, Fall 2015
Homework 2, Electrodynamics
Due: Sep 17, 2015
E
and derive the wave equation for
t
the B field, assuming that we are considering a region of space with no charge or current. (If you
get stuck, refer to the slide from cla

Matrix methods for ray tracing
An elegant way of handling ray tracing.
Say we have a flat sheet of glass, so Snells law governs ray tracing.
Paraxially, define y as the height of the ray from the optical axis and the
angle the ray makes WRT that axis:

Fresnel approximation
Rayleigh-Sommerfeld is accurate, but it requires evaluating
for every point in the aperture!
r ( x ) ( y ) z
( x ) ( y )
z
,
r
z
, cos 1
If
max
max ,
2z
2z
2
2
2
01
2
2
01
One more approximation: wavenumber k is
very large, so whe

Energy and momentum in electromagnetic waves
If we want to believe in the conservation of energy and momentum, we need
to assign energy and momentum to waves.
As an example: We know energy from the sun reaches us here on earth.
It takes ~8 minutes to t

Stops
So far weve ignored the diameter of lenses, but in reality, some rays will not
be able to pass through a finite diameter lens.
The region of the lens through which rays can pass is called the clear diameter
of a lens.
Sometimes other apertures ar

Scattering
Light scattered laterally will tend to arrive
with random phase
Path length differences much bigger than
Randomness means interference washes out
Even if two can interfere, the interference
depends on path length difference:
cos(1 t ) cos(

Geometrical optics
Ray-based modeling of light
Gives a rough idea of how light will behave in a system
Does not account rigorously for intensity at a point
Does not account for wave effects (interference, diffraction)
Rigorously, arises in the limit

Electrodynamics
Basic question of electrodynamics: if we have some charges, what forces will
another test charge feel?
Force vector
Source charges
(can be moving)
Test charge
How do we explain that charges exert action at a distance through vacuum?
Elec

APHY 430/530: Optics, Fall 2015
Question: What is light?
Answer: Electromagnetic waves! See Maxwells equations (or QED).
Question: But Maxwells equations are a pain. Isnt there a simpler way of
doing optics?
Answer: Yes, and most of this class will be

Waves in 1D
Height (m)
Wave on a string moving left to right
Position along string (m)
Wave shape defined by a function: g ( ) . Here g denotes height.
, t ) g ( z vt ) for left to right and f ( z=
, t ) g ( z + vt ) for right to left at speed v
Rigid wav