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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

what is light
Ayebanifesunday Reply
What is photoelectric
Hsssan Reply
light energy (photons) through semiconduction of N-P junction into electrical via excitation of silicon purified and cristalized into wafers with partially contaminated silicon to allow this N-P function to operate.
Michael
i.e. Solar pannel.
Michael
If you lie on a beach looking at the water with your head tipped slightly sideways, your polarized sunglasses do not work very well.Why not?
Rakhi Reply
it has everything to do with the angle the UV sunlight strikes your sunglasses.
Jallal
this is known as optical physics. it describes how visible light, ultraviolet light and infrared light interact when they come into contact with physical matter. usually the photons or light upon interaction result in either reflection refraction diffraction or interference of the light.
Jallal
I hope I'm clear if I'm not please tell me to clarify further or rephrase
Jallal
what is bohrs model for hydrogen atom
Swagatika Reply
hi
Tr
Hello
Youte
Hi
Nwangwu-ike
hi
Siddiquee
hi
Omar
helo
Mcjoi
what is the value of speed of light
Propessor Reply
1.79×10_¹⁹ km per hour
Swagatika
what r dwarf planet
Sivalakshmi Reply
what is energy
Isiguzo Reply
কাজের একক কী
Jasim
কাজের একক কী
Jasim
friction ka direction Kaise pata karte hai
Rahul Reply
friction is always in the opposite of the direction of moving object
Punia
A twin paradox in the special theory of relativity arises due to.....? a) asymmetric of time only b) symmetric of time only c) only time
Varia Reply
b) symmetric of time only
Swagatika
fundamental note of a vibrating string
fasoyin Reply
every matter made up of particles and particles are also subdivided which are themselves subdivided and so on ,and the basic and smallest smallest smallest division is energy which vibrates to become particles and thats why particles have wave nature
Alvin
what are matter waves? Give some examples
mallam Reply
according to de Broglie any matter particles by attaining the higher velocity as compared to light'ill show the wave nature and equation of wave will applicable on it but in practical life people see it is impossible however it is practicaly true and possible while looking at the earth matter at far
Manikant
a centeral part of theory of quantum mechanics example:just like a beam of light or a water wave
Swagatika
Mathematical expression of principle of relativity
Nasir Reply
given that the velocity v of wave depends on the tension f in the spring, it's length 'I' and it's mass 'm'. derive using dimension the equation of the wave
obia Reply
What is the importance of de-broglie's wavelength?
Mukulika Reply
he related wave to matter
Zahid
at subatomic level wave and matter are associated. this refering to mass energy equivalence
Zahid
it is key of quantum
Manikant
how those weight effect a stable motion at equilibrium
Nonso 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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