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Significance

The large distance between the red and violet ends of the rainbow produced from the white light indicates the potential this diffraction grating has as a spectroscopic tool. The more it can spread out the wavelengths (greater dispersion), the more detail can be seen in a spectrum. This depends on the quality of the diffraction grating—it must be very precisely made in addition to having closely spaced lines.

Check Your Understanding If the line spacing of a diffraction grating d is not precisely known, we can use a light source with a well-determined wavelength to measure it. Suppose the first-order constructive fringe of the H β emission line of hydrogen ( λ = 656.3 nm ) is measured at 11.36 ° using a spectrometer with a diffraction grating. What is the line spacing of this grating?

3.332 × 10 −6 m or 300 lines per millimeter

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Take the same simulation we used for double-slit diffraction and try increasing the number of slits from N = 2 to N = 3 , 4 , 5.. . . The primary peaks become sharper, and the secondary peaks become less and less pronounced. By the time you reach the maximum number of N = 20 , the system is behaving much like a diffraction grating.

Summary

  • A diffraction grating consists of a large number of evenly spaced parallel slits that produce an interference pattern similar to but sharper than that of a double slit.
  • Constructive interference occurs when d sin θ = m λ for m = 0 , ± 1 , ± 2 , ... , where d is the distance between the slits, θ is the angle relative to the incident direction, and m is the order of the interference.

Problems

A diffraction grating has 2000 lines per centimeter. At what angle will the first-order maximum be for 520-nm-wavelength green light?

5.97 °

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Find the angle for the third-order maximum for 580-nm-wavelength yellow light falling on a difraction grating having 1500 lines per centimeter.

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How many lines per centimeter are there on a diffraction grating that gives a first-order maximum for 470-nm blue light at an angle of 25.0 ° ?

8.99 × 10 3

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What is the distance between lines on a diffraction grating that produces a second-order maximum for 760-nm red light at an angle of 60.0 ° ?

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Calculate the wavelength of light that has its second-order maximum at 45.0 ° when falling on a diffraction grating that has 5000 lines per centimeter.

707 nm

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An electric current through hydrogen gas produces several distinct wavelengths of visible light. What are the wavelengths of the hydrogen spectrum, if they form first-order maxima at angles 24.2 ° , 25.7 ° , 29.1 ° , and 41.0 ° when projected on a diffraction grating having 10,000 lines per centimeter?

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(a) What do the four angles in the preceding problem become if a 5000-line per centimeter diffraction grating is used? (b) Using this grating, what would the angles be for the second-order maxima? (c) Discuss the relationship between integral reductions in lines per centimeter and the new angles of various order maxima.

a. 11.8 ° , 12.5 ° , 14.1 ° , 19.2 ° ; b. 24.2 ° , 25.7 ° , 29.1 ° , 41.0 ° ; c. Decreasing the number of lines per centimeter by a factor of x means that the angle for the x -order maximum is the same as the original angle for the first-order maximum.

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What is the spacing between structures in a feather that acts as a reflection grating, giving that they produce a first-order maximum for 525-nm light at a 30.0 ° angle?

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An opal such as that shown in [link] acts like a reflection grating with rows separated by about 8 μm . If the opal is illuminated normally, (a) at what angle will red light be seen and (b) at what angle will blue light be seen?

a. using λ = 700 nm, θ = 5 .0 ° ; b. using λ = 460 nm, θ = 3 .3 °

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At what angle does a diffraction grating produce a second-order maximum for light having a first-order maximum at 20.0 ° ?

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(a) Find the maximum number of lines per centimeter a diffraction grating can have and produce a maximum for the smallest wavelength of visible light. (b) Would such a grating be useful for ultraviolet spectra? (c) For infrared spectra?

a. 26,300 lines/cm; b. yes; c. no

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(a) Show that a 30,000 line per centimeter grating will not produce a maximum for visible light. (b) What is the longest wavelength for which it does produce a first-order maximum? (c) What is the greatest number of line per centimeter a diffraction grating can have and produce a complete second-order spectrum for visible light?

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The analysis shown below also applies to diffraction gratings with lines separated by a distance d . What is the distance between fringes produced by a diffraction grating having 125 lines per centimeter for 600-nm light, if the screen is 1.50 m away? ( Hin t : The distance between adjacent fringes is Δ y = x λ / d , assuming the slit separation d is comparable to λ . )

Figure shows two vertical lines, grating on the left and screen on the right separated by a line of length x, perpendicular to them both. There are two slits in the grating, a distance d apart. A line at an angle theta to x meets the screen at point delta y equal to x lambda by d.

1.13 × 10 −2 m

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Questions & Answers

can someone explain normalization condition
Priyojit Reply
1 millimeter is How many metres
Darling Reply
1millimeter =0.001metre
Gitanjali
The photoelectric effect is the emission of electrons when light shines on a material. 
Chris Reply
What is photoelectric effect
Amit Reply
it gives practical evidence of particke nature of light.
Omsai
particle nature
Omsai
photoelectric effect is the phenomenon of emission of electrons from a material(i.e Metal) when it is exposed to sunlight. Emitted electrons are called as photo electrons.
Anil
what are the applications of quantum mechanics to medicine?
Neptune
application of quantum mechanics in medicine: 1) improved disease screening and treatment ; using a relatively new method known as BIO- BARCODE ASSAY we can detect disease-specific clues in our blood using gold nanoparticles. 2) in Genomic medicine 3) in protein folding 4) in radio theraphy(MRI)
Anil
Quantam physics ki basic concepts?
Laxmikanta Reply
why does not electron exits in nucleaus
Kabbo Reply
electrons have negative
YASH
Proton and meltdown has greater mass than electron. So it naturally electron will move around nucleus such as gases surrounded earth
Amalesh
.......proton and neutron....
Amalesh
excuse me yash what negative
Rika
coz, electron contained minus ion
Manish
negative sign rika shrestha ji
YASH
electron is the smallest negetive charge...An anaion i.e., negetive ion contains extra electrons. How ever an atom is neutral so it must contains proton and electron
Amalesh
yes yash ji
Rika
yes friends
Prema
koantam theory
Laxmikanta
yes prema
Rika
quantum theory tells us that both light and matter consists of tiny particles which have wave like propertise associated with them.
Prema
proton and nutron nuclear power is best than proton and electron kulamb force
Laxmikanta
what is de-broglie wave length?
Ramsuphal
plot a graph of MP against tan ( Angle/2) and determine the slope of the graph and find the error in it.
Ime Reply
expression for photon as wave
BARISUA Reply
Are beta particle and eletron are same?
Amalesh Reply
yes
mari
how can you confirm?
Amalesh
sry
Saiaung
If they are same then why they named differently?
Amalesh
because beta particles give the information that the electron is ejected from the nucleus with very high energy
Absar
what is meant by Z in nuclear physic
Shubhu Reply
atomic n.o
Gyanendra
no of atoms present in nucleus
Sanjana
Note on spherical mirrors
Shamanth Reply
what is Draic equation? with explanation
M.D Reply
what is CHEMISTRY
trpathy Reply
it's a subject
Akhter
it's a branch in science which deals with the properties,uses and composition of matter
Eniabire
what is a Higgs Boson please?
FRANKLINE Reply
god particles is know as higgs boson, when two proton are reacted than a particles came out which is used to make a bond between than materials
M.D
bro little abit getting confuse if i am wrong than please clarify me
M.D
the law of refraction of direct current lines at the boundary between two conducting media of
BATTULA Reply
Practice Key Terms 1

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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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