<< Chapter < Page Chapter >> Page >

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

Got questions? Get instant answers now!

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 °

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

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 ° ?

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

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?

Got questions? Get instant answers now!

(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.

Got questions? Get instant answers now!

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?

Got questions? Get instant answers now!

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 °

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

(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

Got questions? Get instant answers now!

(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?

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

Questions & Answers

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
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
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
what is the effect of heat on refractive index
Nepal Reply
As refractive index depend on other factors also but if we supply heat on any system or media its refractive index decrease. i.e. it is inversely proportional to the heat.
ganesh
you are correct
Priyojit
law of multiple
Wahid
if we heated the ice then the refractive index be change from natural water
Nepal
can someone explain normalization condition
Priyojit Reply
please tell
Swati
yes
Chemist
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
Practice Key Terms 1

Get the best University physics vol... course in your pocket!





Source:  OpenStax, University physics volume 3. OpenStax CNX. Nov 04, 2016 Download for free at http://cnx.org/content/col12067/1.4
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'University physics volume 3' conversation and receive update notifications?

Ask