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Figure a is a photograph of an opal pendant reflecting various colours. Figure b is the photograph of a butterfly.
(a) This Australian opal and (b) butterfly wings have rows of reflectors that act like reflection gratings, reflecting different colors at different angles. (credit b: modification of work by “whologwhy”/Flickr)

Applications of diffraction gratings

Where are diffraction gratings used in applications? 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. That is, their bright fringes are narrower and brighter while their dark regions are darker. 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 wavelength 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 wavelengths for such use.

Calculating typical diffraction grating effects

Diffraction gratings with 10,000 lines per centimeter are readily available. Suppose you have one, and you send a beam of white light through it to a screen 2.00 m away. (a) Find the angles for the first-order diffraction of the shortest and longest wavelengths of visible light (380 and 760 nm, respectively). (b) What is the distance between the ends of the rainbow of visible light produced on the screen for first-order interference? (See [link] .)

A vertical line on the left is labeled grating and one on the right is labeled screen. They are a distance x equal to 2 meters apart. Four arrows radiate from the grating to the screen. The first and second from the top make angles theta R and theta V respectively with the central axis. The points where they fall on the screen are at distances yR and yV respectively from the central axis. Rainbows are formed on the screen between the first and second arrow and between the third and fourth arrow.
(a) The diffraction grating considered in this example produces a rainbow of colors on a screen a distance x = 2.00 m from the grating. The distances along the screen are measured perpendicular to the x -direction. In other words, the rainbow pattern extends out of the page.
(b) In a bird’s-eye view, the rainbow pattern can be seen on a table where the equipment is placed.

Strategy

Once a value for the diffraction grating’s slit spacing d has been determined, the angles for the sharp lines can be found using the equation

d sin θ = m λ for m = 0 , ± 1 , ± 2 , ... .

Since there are 10,000 lines per centimeter, each line is separated by 1/10,000 of a centimeter. Once we know the angles, we an find the distances along the screen by using simple trigonometry.

Solution

  1. The distance between slits is d = ( 1 cm ) / 10 , 000 = 1.00 × 10 −4 cm or 1.00 × 10 −6 m . Let us call the two angles θ V for violet (380 nm) and θ R for red (760 nm). Solving the equation d sin θ V = m λ for sin θ V ,
    sin θ V = m λ V d ,

    where m = 1 for the first-order and λ V = 380 nm = 3.80 × 10 −7 m . Substituting these values gives
    sin θ V = 3.80 × 10 −7 m 1.00 × 10 −6 m = 0.380 .

    Thus the angle θ V is
    θ V = sin −1 0.380 = 22.33 ° .

    Similarly,
    sin θ R = 7.60 × 10 −7 m 1.00 × 10 −6 m = 0.760 .

    Thus the angle θ R is
    θ R = sin −1 0.760 = 49.46 ° .

    Notice that in both equations, we reported the results of these intermediate calculations to four significant figures to use with the calculation in part (b).
  2. The distances on the secreen are labeled y V and y R in [link] . Notice that tan θ = y / x . We can solve for y V and y R . That is,
    y V = x tan θ V = ( 2.00 m ) ( tan 22.33 ° ) = 0.815 m

    and
    y R = x tan θ R = ( 2.00 m ) ( tan 49.46 ° ) = 2.338 m .

    The distance between them is therefore
    y R y V = 1.523 m .

Questions & Answers

How does, ray of light coming form focus, behaves in concave mirror after refraction?
Bishesh Reply
Refraction does not occur in concave mirror. If refraction occurs then I don't know about this.
Sushant
What is motion
Izevbogie Reply
Anything which changes itself with respect to time or surrounding
Sushant
good
Chemist
and what's time? is time everywhere same
Chemist
No
Sushant
how can u say that
Chemist
do u know about black hole
Chemist
Not so more
Sushant
Radioactive substance
DHEERAJ
These substance create harmful radiation like alpha particle radiation, beta particle radiation, gamma particle radiation
Sushant
But ask anything changes itself with respect to time or surrounding A Not any harmful radiation
DHEERAJ
explain cavendish experiment to determine the value of gravitational concept.
Celine Reply
For the question about the scuba instructor's head above the pool, how did you arrive at this answer? What is the process?
Evan Reply
as a free falling object increases speed what is happening to the acceleration
Success Reply
of course g is constant
Alwielland
acceleration also inc
Usman
which paper will be subjective and which one objective
jay
normal distributiin of errors report
Dennis
normal distribution of errors
Dennis
photo electrons doesn't emmit when electrons are free to move on surface of metal why?
Rafi Reply
What would be the minimum work function of a metal have to be for visible light(400-700)nm to ejected photoelectrons?
Mohammed Reply
give any fix value to wave length
Rafi
40 cm into change mm
Arhaan Reply
40cm=40.0×10^-2m =400.0×10^-3m =400mm. that cap(^) I have used above is to the power.
Prema
i.e. 10to the power -2 in the first line and 10 to the power -3 in the the second line.
Prema
there is mistake in my first msg correction is 40cm=40.0×10^-2m =400.0×10^-3m =400mm. sorry for the mistake friends.
Prema
40cm=40.0×10^-2m =400.0×10^-3m =400mm.
Prema
this msg is out of mistake. sorry friends​.
Prema
what is physics?
sisay Reply
why we have physics
Anil Reply
because is the study of mater and natural world
John
because physics is nature. it explains the laws of nature. some laws already discovered. some laws yet to be discovered.
Yoblaze
physics is the study of non living things if we added it with biology it becomes biophysics and bio is the study of living things tell me please what is this?
tahreem
physics is the study of matter,energy and their interactions
Buvanes
all living things are matter
Buvanes
why rolling friction is less than sliding friction
tahreem
thanks buvanas
tahreem
is this a physics forum
Physics Reply
explain l-s coupling
Depk Reply
how can we say dirac equation is also called a relativistic equation in one word
preeti Reply
what is the electronic configration of Al
usman Reply
what's the signeficance of dirac equetion.?
Sibghat Reply
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Source:  OpenStax, University physics volume 3. OpenStax CNX. Nov 04, 2016 Download for free at http://cnx.org/content/col12067/1.4
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