Resolution Limits for Single-Slits and Circular Apertures  Single source  Two sources

Example Problem 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

We define the Chromatic Resolving Power R needed to distinguish the two wavelengths 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 where N is the number of slits illuminated by the source Therefore, the larger m or N, the better the resolution

Example Problem Three discrete spectral lines occur at angles of 10.09, 13.71, and in the first-order spectrum of a grating spectrometer. (a) If the grating has 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 nm and 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 ~ m Radiation is directed at the surface at an angle of  (with respect to the horizontal)

Example Problem The first order diffraction maximum is observed at 12.6  for a crystal in which the interplanar spacing is 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 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 E 0 parallel to the vertical is incident on the first disk with intensity of Calculate the transmitted intensity when  1 =20.0 ,  2 =40.0 , and  3 =60.0 .