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 componentsFor m=0, all components are mergedAs |m| increases, the order components separate more and moreWhat if 2 and 1 are close?

1

2

2>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 sourceTherefore, the larger m or N, the better the resolution

1221 2/)(

where

R

NmR

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 materialIt 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 directionRadiation is produced, in general, by accelerating chargesAtoms in some material are perturbed The atoms oscillate like a spring-mass systemThis 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 motionFor a give wave (produced by a given atom), the direction of the electric field vector corresponds to a direction of polarization of the waveSince atoms are usually oriented randomly, the light leaving the media is composed of randomly oriented electric fieldsSuch 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.