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Chapter 33: Q. 16 (page 955)
A helium-neon laser illuminates a single slit and is observed on a screenbehind the slit. The distance between the first and second minima in the diffraction pattern is . What is the width of the slit
Width of the slit is.
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FIGURE Q33.5 shows the light intensity on a viewing screen behind a single slit of width a The light's wavelength is. Is, or is it not possible to tell? Explain
A diffraction grating is illuminated simultaneously with red light of wavelengthand light of an unknown wavelength. The fifth-order maximum of the unknown wavelength exactly overlaps the third-order maximum of the red light. What is the unknown wavelength
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.
Because sound is a wave, it's possible to make a diffraction grating for sound from a large board of sound-absorbing material with several parallel slits cut for sound to go through. When sound waves pass through such a grating, listeners from the grating report "loud spots" on both sides of center. What is the spacing between the slits? Use for the speed of sound.
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