Introduction/Theory:-
Diffraction Grating:
A diffraction grating is a multiple-slit interference device, an
array of a large number of parallel, closely spaced slits, all with
the same width a and spaced equal distances d between centers,
useful for viewing the color spectrum of a light source and for
analyzing the light.
The rst one was constructed by Fraunhofer using ne wires.
Diffraction patterns of bright and dark fringes occur when
monochromatic light passes through a single or double slit. Fringe
patterns also result when light passes through more than two slits
i.e. through Diffraction grating.
Although the term diffraction is used in the name, it would be
more appropriate to call these devices interference gratings. The
primary effect is that of interference of light coming from
different slits. Although the terms interference and diffraction
are sometimes interchangeable, we usually use interference when
referring to effects of separate slits or openings and diffraction
for effects from a single opening.
A diffraction grating has a very large number of slits very
closely spaced. A good grating may have several hundred slits in
the space of just 1 mm. Precision machines have been designed to
produce these closely spaced slits or lines needed for producing
high quality gratings. A diffraction grating can be manufactured by
scratching glass with a sharp tool in a number of precisely
positioned parallel lines, with the untouched regions acting like
slits. Nowadays, good gratings can be made much more simply using
lasers and holographic techniques. Gratings can also be made by
using a diamond point to scratch many equally spaced grooves on a
glass or metal surface, or by photographic reduction of a pattern
of black and white stripes on paper.
Gratings with as many as 40,000 slits per centimeter can be
made, depending on the production method. In one method a
diamond-tipped cutting tool is used to inscribe closely spaced
parallel lines on a glass plate, the spaces between the lines
serving as the slits. In fact, the number of slits per centimeter
is often quoted as the number of lines per centimeter.
Diffraction gratings work both for transmission of light, and
for reflection of light, as on butterfly wings or on the CD/DVD.
Natural diffraction gratings occur in the feathers of certain
birds. Tiny finger like structures in regular patterns act as
reflection gratings, producing constructive interference that gives
the feathers colors not solely clue to their pigmentation.
In addition to their use as novelty items, diffraction gratings
are commonly used for spectroscopic dispersion and analysis of
light. What makes them particularly useful is the fact that they
form a sharper pattern than double slits do.
By increasing the number of slits in an interference experiment,
an interesting pattern emerges. If the spacing of the slits remains
the same, the bright fringes become brighter and narrower as the
number of slits increases. Because these maxima are so narrow,
their angular position, and hence the wavelength, can be measured
to very high precision.
Diffraction gratings are used to separate and measure the
wavelengths of light in instruments we call spectrometers. They are
a common piece of apparatus in chemistry and physics laboratories.
Holographically produced gratings are now also seen in many novelty
products including space glasses" and reective gift wrappings. The
colorful effects that we see when viewing a compact disc (CD) are
also a grating phenomenon. The disc contains a continuous spiral
track that circles the disc from the inside to the outside.
Adjacent turns of this spiral track are very closely spaced and act
as a reecting diffraction grating.
Figure illustrates how light travels to a distant viewing screen
from each of five slits in a grating and forms the central bright
fringe and the rst-order bright fringes on either side.
Higher-order bright fringes are also formed but are not shown in
the drawing. Each bright fringe is located by an angle relative to
the central fringe. These bright fringes are sometimes called the
principal fringes or principal maxima, since they are places where
the light intensity is a maximum. The term principal distinguishes
them from other, much less bright, fringes that are referred to as
secondary fringes or secondary maxima.
Constructive interference creates the principal fringes. To show
how, we assume the screen is far from the grating, so that the rays
remain nearly parallel while the light travels toward the screen.
In reaching the place on the screen where a first-order maximum is
located, light from slit 2 travels a distance of one wavelength
farther than light from slit 1, as in Figure. Similarly, light from
slit 3 travels one Wavelength farther than light from slit 2 and so
forth, as emphasized by the four colored right triangles on the
right hand side of the drawing. For the first-order maximum, the
blow-up view of slits 1 and 2 shows that constructive interference
occurs when sin, where d is the separation between slits. A
second-order maximum forms when the extra distance traveled by
light from adjacent slits is two wavelengths, so that sin.
Whenever this path difference is equal to an integer multiple of
the light wavelength, we get a strong bright fringe for that
wavelength. This condition can be expressed as
Where m is an integer having possible values 0, 1, 2, 3 etc.
Since the condition locating the fringes depends on the
wavelength of the light, different wavelengths will appear at
different points on the screen for a given order m. Thus passing
light through a diffraction grating will spread the light into its
spectrum of colors. A good grating produces a wider separation of
colors than a prism and also allows direct computation of the
wavelength from the condition for interference.
When a grating containing hundreds or thousands of slits is
illuminated by a beam of parallel rays of monochromatic light, the
pattern is a series of very sharp lines at different angles. If the
grating is illuminated by white light with a continuous
distribution of wavelengths, each value of m corresponds to a
continuous spectrum in the pattern. The angle for each wavelength
is determined by above equation. For a given value of m, long
wavelengths (the red end of the spectrum) lie at larger angles
(that is, are deviated more from the straight-ahead direction) than
do the shorter wavelengths at the violet end of the spectrum.
As Eq. shows, the sines of the deviation angles of the maxima
are proportional to the ratio . For substantial deviation to occur,
the grating spacing d should be of the same order of magnitude as
the wavelength . Gratings for use with visible light ( from 400 to
700 nm) usually have about 1000 slits per millimeter; the value of
d is the reciprocal of the number of slits per unit length, so d is
of the order of mm = 1000 nm.
In a reflection grating, the array of equally spaced slits is
replaced by an array of equally spaced ridges or grooves on a
reective screen. The reected light has maximum intensity at angles
where the phase difference between light waves reected from
adjacent ridges or grooves is an integral multiple of 2. If light
of wavelength is incident normally on a reection grating with a
spacing d between adjacent ridges or grooves, the reected angles at
which intensity maxima occur are given by above Eq.
The rainbow-colored reections from the surface of a DVD are a
reection grating effect. The grooves are tiny pits 0.12 deep in the
surface of the disc, with a uniform radial spacing of 0.74=740 nm.
Information is coded on the DVD by varying the length of the pits.
The reection-grating aspect of the disc is merely an aesthetic side
benet.
Diffraction involves the interference of light waves coming from
different parts of the same opening. Diffraction from a single slit
produces a bright central fringe with a series of weaker dark and
light fringes on either side of the broader central fringe. A
circular aperture produces a bull's-eye pattern. Making the
aperture smaller causes the diffraction pattern to spread out,
frustrating efforts to narrow a beam of light. A diffraction
grating is a multiple slit interference device that allows us to
separate and measure wavelengths of light.
Diffraction gratings are key components of monochromators used,
for example, in optical imaging of particular wavelengths from
biological or medical samples. A diffraction grating can be chosen
to specifically analyze a wavelength emitted by molecules in
diseased cells in a biopsy sample or to help excite strategic
molecules in the sample with a selected frequency of light. Another
vital use is in optical fiber technologies where fibers are
designed to provide optimum performance at specific wavelengths. A
range of diffraction gratings are available for selecting specific
wavelengths for such use.
Introduction/Theory:
-
Diffraction Grating:
A diffraction grating is a multiple
-
slit interference device
,
a
n
array of
a
large
number of parallel, closely spaced slits
,
all w
ith the same width
a
and spaced
e
qual
distances
d
between centers
,
useful for viewing the color spectrum of a light source
and for analyzing the light.
The
?
rst one
was constructed by
Fraunhofer
using
?
ne wires.
D
iffraction patterns of bright and dark fringes occur when
monochromatic light passes through a
single or double slit. Fringe patterns also result when light
passes through more than two slits i.e. through
Diffraction grating.
Although the term diffraction
is used in the name, it would be more appropriate to call
these
devices interference gratings. The primary effect is that of
interference of light coming from different slits.
Although the terms interference and diffraction are sometimes
interchangeable, w
e usually use
interference when referring to effects of separate slits or
openings and diffraction for effects from a single
opening.
A diffraction grating has a very large number of slits very
closely spaced. A good grating may have
several hundred slits in the space
of just 1 mm. Precision machines have been designed to produce
these
closely spaced slits or lines needed for producing high quality
gratings.
A diffraction grating can be
manufactured by scratching
glass with a sharp tool in a number of precisely positioned
parallel lines, with
the untouched regions ac
ting like slit
s.
Nowadays, good gratings can be made much more simply using
lasers and
holographic
techniques.
Gratings can
also
be made by using a
diamond point to scratch
many
equally spaced grooves on a glass or metal surface,
or by photographic reduction of a pattern of black an
d
white stripes on paper.
Gratings with as m
any as 40,000 slits per centimeter can be made, depending on the
production
method. In one method a diamond
-
tipped cutting tool is used to inscribe closely spaced parallel
lines on
a glass plate, the spaces between the lines serving as the
slits. In fact,
the number of slits per centimeter
is often quoted as the number of lines per centimeter.
Diffraction gratings work both for transmissio
n of light,
and for reflection of light, as on butterfly
wings
or
on the CD
/DVD
.
Natural diffraction gratings occur in the fea
thers of certain birds. Tiny
f
inger
like
structures in regular patterns act as reflection gratings,
producing constructive interference that gives the
feathers colors not solely clue to their
pigmentation.
In addition to their use as
novelty items, diffraction gratings are commonly used for
spectroscopic
dispersion and analysis of light. What makes them particularly
useful is the
fact that they
form a sharper
pattern than double slits do.
By increasing the
number of slits in an interference experiment, an interesting
pattern emerges.
If the spacing of the sli
ts remains the same, the bright fringes become brighter and
narrower as the
Introduction/Theory:-
Diffraction Grating:
A diffraction grating is a multiple-slit interference device, an
array of a large
number of parallel, closely spaced slits, all with the same
width a and spaced equal
distances d between centers, useful for viewing the color
spectrum of a light source
and for analyzing the light.
The ?rst one was constructed by Fraunhofer using ?ne wires.
Diffraction patterns of bright and dark fringes occur when
monochromatic light passes through a
single or double slit. Fringe patterns also result when light
passes through more than two slits i.e. through
Diffraction grating.
Although the term diffraction is used in the name, it would be
more appropriate to call these
devices interference gratings. The primary effect is that of
interference of light coming from different slits.
Although the terms interference and diffraction are sometimes
interchangeable, we usually use
interference when referring to effects of separate slits or
openings and diffraction for effects from a single
opening.
A diffraction grating has a very large number of slits very
closely spaced. A good grating may have
several hundred slits in the space of just 1 mm. Precision
machines have been designed to produce these
closely spaced slits or lines needed for producing high quality
gratings. A diffraction grating can be
manufactured by scratching glass with a sharp tool in a number
of precisely positioned parallel lines, with
the untouched regions acting like slits. Nowadays, good gratings
can be made much more simply using
lasers and holographic techniques. Gratings can also be made by
using a diamond point to scratch many
equally spaced grooves on a glass or metal surface, or by
photographic reduction of a pattern of black and
white stripes on paper.
Gratings with as many as 40,000 slits per centimeter can be
made, depending on the production
method. In one method a diamond-tipped cutting tool is used to
inscribe closely spaced parallel lines on
a glass plate, the spaces between the lines serving as the
slits. In fact, the number of slits per centimeter
is often quoted as the number of lines per centimeter.
Diffraction gratings work both for transmission of light, and
for reflection of light, as on butterfly
wings or on the CD/DVD. Natural diffraction gratings occur in
the feathers of certain birds. Tiny finger like
structures in regular patterns act as reflection gratings,
producing constructive interference that gives the
feathers colors not solely clue to their pigmentation.
In addition to their use as novelty items, diffraction gratings
are commonly used for spectroscopic
dispersion and analysis of light. What makes them particularly
useful is the fact that they form a sharper
pattern than double slits do.
By increasing the number of slits in an interference experiment,
an interesting pattern emerges.
If the spacing of the slits remains the same, the bright fringes
become brighter and narrower as the
