Download Cutnell Ch 27B

Wave theory predicts diffraction
of light (the spreading of light
into a region behind an
obstruction), but this is not
easily observed unless the
obstruction has dimensions
comparable to the wavelength.
It is possible to see dark
fringes between the thumb
and forefinger when held
very close together. Fresnel
demonstrated in 1816 that
diffraction phenomena are
explained by a wave nature
for light.
Diffraction gratings have as many
as 12,000 equally spaced parallel
grooves. When illuminated with
white light, each slit produces a
new wave front. These wave
fronts interfere and produce
pairs of continuous spectra
equally spaced on opposite
sides of the principle image.
If illuminated with
monochromatic light,
successive pairs of slit images
will appear on either side of the
principle image. The first pair
are called the first-order images,
the second pair are the secondorder images.
Through a series of derivations that I
don’t particularly care to show you, the
following equation emerges:
l = d sinqm /m
or sinq = m•l/d
l = d sinqm /m
d is the distance between the slits, and
is called the grating constant
l is the wavelength
qm is the diffraction angle
A diffraction grating is ruled with
6.50 x 103 lines per centimeter.
The grating produces a secondorder image of a monochromatic
light source at a diffraction angle
of 55.0°. Calculate the
wavelength of the light
source in nanometers.
Ex. 10 - A mixture of violet light
(l = 410 nm in vacuum) and
red light (l = 660 nm in
vacuum) falls on a grating that
4
contains 1.0 x 10 lines/cm.
For each wavelength, find the
angle q that locates the firstorder maxima.
For white light, the ordered
maxima show all colors. At the
first order maxima, the spectrum
would range from 24° to 41°.
For higher orders the spectra
from adjacent orders may
overlap. The central maximum
is still white.