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Chapter 33: Q. 39 (page 956)
A diffraction grating having diffracts visible light at .What is the light's wavelength?
The wavelength of sunshine is
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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?
Find an expression for the positions of the first-order fringes of a diffraction grating if the line spacing is large enough for the small-angle approximation to be valid. Your expression should be in terms of and.
. Use your expression from part a to find an expression for the separationon the screen of two fringes that differ in wavelength by.
Rather than a viewing screen, modern spectrometers use detectors-similar to the one in your digital camera-that are divided into pixels. Consider a spectrometer with a grating and a detector with located behind the grating. The resolution of a spectrometer is the smallest wavelength separation that can be measured reliably. What is the resolution of this spectrometer for wavelengths near localid="1649156925210" , in the center of the visible spectrum? You can assume that the fringe due to one specific wavelength is narrow enough to illuminate only one column of pixels.
A student performing a double-slit experiment is using a green laser with a wavelength of . She is confused when the maximum does not appear. She had predicted that this bright fringe would be from the central maximum on a screen behind the slits.
a. Explain what prevented the fifth maximum from being observed.
b. What is the width of her slits?
Light of wavelengthilluminates a diffraction grating. The second-order maximum is at angle . How many lines per millimeter does this grating have?
Light from a helium-neon laser illuminates a circular aperture. It is noted that the diameter of the central maximum on a screen behind the aperture matches the diameter of the geometric image. What is the aperture's diameter (in mm)?
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