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Chapter 33: Q. 7 (page 955)
On a screen behind such a diffracting grating, narrow, bright fringes can be seen. After that, the entire research is submerged in water. Do the screen's fringes get closer together, farther apart, stay the same, or simply disappear? Explain
The fringes move away from each other.
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FIGURE shows the light intensity on a screen behind an aperture. The aperture is illuminated with light of wavelength .
a. Is the aperture a single slit or a double slit? Explain.
b. If the aperture is a single slit, what is its width? If it is a double slit, what is the spacing between the slits?
A Michelson interferometer operating at a wavelength has a -long glass cell in one arm. To begin, the air is pumped out of the cell and mirror is adjusted to produce a bright spot at the center of the interference pattern. Then a valve is opened and air is slowly admitted into the cell. The index of refraction of air at pressure is . How many brightdark-bright fringe shifts are observed as the cell fills with air?
Scientists shine a laser beam on a -wide slit and produce a diffraction pattern on a screen behind the slit. Careful measurements show that the intensity first falls to of maximum at a distance offrom the center of the diffraction pattern. What is the wavelength of the laser light?
Hint: Use the trial-and-error technique demonstrated in Example to solve the transcendental equation.
FIGURE shows light of wavelength incident at angle on a reflection grating of spacing . We want to find the angles um at which constructive interference occurs.
a. The figure shows paths and along which two waves travel and interfere. Find an expression for the path-length difference .3
b. Using your result from part a, find an equation (analogous to Equation localid="1650299740348" for the angles localid="1650299747450" at which diffraction occurs when the light is incident at angle localid="1650299754268" . Notice that m can be a negative integer in your expression, indicating that path localid="1650299766020" is shorter than path localid="1650299773517" .
c. Show that the zeroth-order diffraction is simply a “reflection.” That is, localid="1650299781268"
d. Light of wavelength 500 nm is incident at localid="1650299787850" on a reflection grating having localid="1650299794954" reflection lines/mm. Find all angles localid="1650299802944" at which light is diffracted. Negative values of localid="1650299812949"
are interpreted as an angle left of the vertical.
e. Draw a picture showing a single localid="1650299823499" light ray incident at localid="1650299833529" and showing all the diffracted waves at the correct angles.
A chemist identifies compounds by identifying bright lines in their spectra. She does so by heating the compounds until they glow, sending the light through a diffraction grating, and measuring the positions of first-order spectral lines on a detector behind the grating. Unfortunately, she has lost the card that gives the specifications of the grating. Fortunately, she has a known compound that she can use to calibrate the grating. She heats the known compound, which emits light at a wavelength of , and observes a spectral line from the center of the diffraction pattern. What are the wavelengths emitted by compounds and that have spectral lines detected at positions and , respectively?
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