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Chapter 33: Q.28 (page 956)

Your artist friend is designing an exhibit inspired by circular-aperture diffraction. A pinhole in a red zone is going to be illuminated with a red laser beam of wavelength 670nm, while a pinhole in a violet zone is going to be illuminated with a violet laser beam of wavelength 410nm. She wants all the diffraction patterns seen on a distant screen to have the same size. For this to work, what must be the ratio of the red pinhole鈥檚 diameter to that of the violet pinhole?

Short Answer

Expert verified

Ratio of red pinhole diameter to violet pinhole ,DredDviolet=1.63

Step by step solution

01

Laser Beam

A laser beam is a single-wavelength stream of concentrated, coherent light.

02

Find ratio

In order for the diffraction patterns from the two pinholes to have the same size, the angle of the first minimum in the two patterns must be the same, where this angle is given by the following relation

胃1=1.22位D

When you multiply 胃1by the number of pinholes, you get

1.22位redDred=1.22位violetDviolet

rearranging the equations,

DredDviolet=位red位violet=670nm410nm=1.63

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Most popular questions from this chapter

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 10kHzsound waves pass through such a grating, listeners 10mfrom the grating report "loud spots" 1.4mon both sides of center. What is the spacing between the slits? Use 340msfor the speed of sound.

3. FIGURE Q33.3 shows the viewing screen in a double-slit experiment. FringeCis the central maximum. What will happen to the fringe spacing if

a. The wavelength of the light is decreased?

b. The spacing between the slits is decreased?

c. The distance to the screen is decreased?

d. Suppose the wavelength of the light islocalid="1649170567955" 500nm. How much farther is it from the dot on the screen in the center of fringe E to the left slit than it is from the dot to the right slit?

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 (位=1.000渭m)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 is1.522.

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 1.522that changes the optical switch to the state opposite the state you found in part a?

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Light from a helium-neon laser (位=633nm)passes through a circular aperture and is observed on a screen 4.0mbehind the aperture. The width of the central maximum is2.5cm. What is the diameter (in mm) of the hole?
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