Resolution Limits for Single-Slits
and Circular Apertures
 Single source
 Two sources
Example Problem 38.18
A binary star system in the
constellation Orion has an angular
separation of 1.00x10-5 rad. If =500
nm, what is the smallest diameter a
telescope can have to just resolve it?
Diffraction Gratings
Chromatic Resolving Power
If the source (i.e., a star)
is not monochromatic, a
diffraction grating can
perform the same function
as a prism – separate the
different  components
For m=0, all components
are merged
As |m| increases, the order
components separate more
and more
What if 2 and 1 are
close?
1
2
2>1
We define the Chromatic Resolving Power R
needed to distinguish the two wavelengths

where
R

  2  1
  (1  2 ) / 2
For example, in a field of study called
spectroscopy, we want to know the wavelength
of various transitions in atoms or molecules.
Therefore, we need to measure  accurately.
It turns out (without proof), that
R  Nm
where N is the number of slits
illuminated by the source
Therefore, the larger m or N, the better the
resolution
Example Problem 38.27
Three discrete spectral lines occur at angles
of 10.09, 13.71, and 14.77 in the first-order
spectrum of a grating spectrometer. (a) If the
grating has 366 0 slits/cm, what are the
wavelengths of the light? (b) At what angles
are these lines found in the second-order
spectrum? (c) How many slits must be
illuminated in first- and second-order to
resolve lines at 695.5 nm and 695.0 nm?
X-ray Diffraction of
Crystals
Consider the surface of some crystalline
material
It consists of a regular spacing of atoms
with a separation of a in uniform planar
rows with interplanar spacing of d
a and d are ~10-10 m
Radiation is directed at
the surface at an angle
of  (with respect to the
horizontal)
Example Problem 38.38
The first order diffraction maximum is
observed at 12.6 for a crystal in which
the interplanar spacing is 0.240 nm.
How many other orders can be
observed?
Transverse Nature of Light and
Polarization
Light is a transverse wave
- the oscillating property (electric and
magnetic fields) are vectors which are
perpendicular to the propagation direction
Radiation is produced, in general, by
accelerating charges
Atoms in some material are perturbed
The atoms oscillate like a spring-mass system
This produces a time-varying electric field was is
align along the same direction as the atom
motion
Light then propagates away from the atom in
a direction perpendicular to the oscillatory
motion
For a give wave (produced by a given atom),
the direction of the electric field vector
corresponds to a direction of polarization of
the wave
Since atoms are usually oriented randomly,
the light leaving the media is composed of
randomly oriented electric fields
Such light is said to be unpolarized
Polarization
methods
Reflection
Absorption
Example Problem
38.42
Three polarizing disks whose planes are parallel
are centered on a common axis. The
transmission axis of each is given by 1, 2, and
3, all respect to the vertical. A plane-polarized
beam of light with E0 parallel to the vertical is
incident on the first disk with intensity of 10.0.
Calculate the transmitted intensity when
1=20.0, 2=40.0, and 3=60.0.