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Chapter 33: Q. 50 (page 957)
FIGURE P33.49 shows the interference pattern on a screen behind a diffraction grating. The wavelength of the light is . How many lines per millimeter does the grating have?
The grating hasof lines per millimetre.
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A double-slit experiment is set up using a helium-neon laser . Then a very thin piece of glass is placed over one of the slits. Afterward, the central point on the screen is occupied by what had been the dark fringe. How thick is the glass?
In a single-slit experiment, the slit width is times the wavelength of the light. What is the width of the central maximum on a screen behind the slit
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 鈥渞eflection.鈥� 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.
Scientists use laser range-finding to measure the distance to the moon with great accuracy. A brief laser pulse is fired at the moon, then the time interval is measured until the "echo" is seen by a telescope. A laser beam spreads out as it travels because it diffracts through a circular exit as it leaves the laser. In order for the reflected light to be bright enough to detect, the laser spot on the moon must be no more than in diameter. Staying within this diameter is accomplished by using a special large diameter laser. If , what is the minimum diameter of the circular opening from which the laser beam emerges? The earth-moon distance is
A Michelson interferometer is set up to display constructive interference (a bright central spot in the fringe pattern of Figure) using light of wavelength l. If the wavelength is changed to , does the central spot remain bright, does the central spot become dark, or do the fringes disappear? Explain. Assume the fringes are viewed by a detector sensitive to both wavelengths.
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