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Chapter 33: Q. 51 (page 957)
Light from a sodium lamp illuminates a narrow slit and is observed on a screen behind the slit. The distance between the first and third dark fringes is . What is the width (in ) of the slit?
The slit's width of is
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Optical computers require microscopic optical switches to turn signals on and off. One device for doing so, which can be implemented in an integrated circuit, is the Mach-Zender interferometer seen in FIGURE. Light from an on-chip infrared laser is split into two waves that travel equal distances around the arms of the interferometer. One arm passes through an electro-optic crystal, a transparent material that can change its index of refraction in response to an applied voltage. Suppose both arms are exactly the same length and the crystal鈥檚 index of refraction with no applied voltage is.
a. With no voltage applied, is the output bright (switch closed, optical signal passing through) or dark (switch open, no signal)? Explain.
b. What is the first index of refraction of the electro-optic crystal larger than that changes the optical switch to the state opposite the state you found in part a?
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.
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
Light ofwavelength illuminates a single slit of width . FIGURE shows the intensity pattern seen on a screen behind the slit. What is the distance to the screen
A 4.0-cm-wide diffraction grating has 2000 slits. It is illuminated by light of wavelength . What are the angles (in degrees) of the first two diffraction orders?
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