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Chapter 33: Q. 26 (page 956)
Infrared light of wavelength illuminates a diameter hole. What is the angle of the first dark fringe in radians? In degrees?
Angle of the first dark fringe in radians and in degree is
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a. Green light shines through a -diameter hole and is observed on a screen. If the hole diameter is increased by , does the circular spot of light on the screen decrease in diameter, increase in diameter, or stay the same? Explain.
b. Green light shines through a -diameter hole and is observed on a screen. If the hole diameter is increased by, does the circular spot of light on the screen decrease in diameter, increase in diameter, or stay the same? Explain.
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.
You've found an unlabeled diffraction grating. Before you can use it, you need to know how many lines per it has. To find out, you illuminate the grating with light of several different wavelengths and then measure the distance between the two first-order bright fringes on a viewing screen behind the grating. Your data are as follows:
Use the best-fit line of an appropriate graph to determine the number of lines per .
Two wide slits spaced apart are illuminated by blue laser light with a wavelength of . The interference pattern is observed on a screen behind the slits. How many bright fringes are seen in the central maximum that spans the distance between the first missing order on one side and the first missing order on the other side?
The intensity at the central maximum of a double-slit interference pattern is . The intensity at the first minimum is zero. At what fraction of the distance from the central maximum to the first minimum is the intensity ? Assume an ideal double slit.
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