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Chapter 33: Q.61 (page 958)
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)?
The aperture's diameter
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FIGURE shows the light intensity on a viewing screen behind a circular aperture. What happens to the width of the central maximum if
a. The wavelength of the light is increased?
b. The diameter of the aperture is increased?
c. How will the screen appear if the aperture diameter is less than the light wavelength?
The pinhole camera of FIGURE images distant objects by allowing only a narrow bundle of light rays to pass through the hole and strike the film. If light consisted of particles, you could make the image sharper and sharper (at the expense of getting dimmer and dimmer) by making the aperture smaller and smaller. In practice, diffraction of light by the circular aperture limits the maximum sharpness that can be obtained. Consider two distant points of light, such as two distant streetlights. Each will produce a circular diffraction pattern on the film. The two images can just barely be resolved if the central maximum of one image falls on the first dark fringe of the other image. (This is called Rayleigh鈥檚 criterion, and we will explore its implication for optical instruments in Chapter .)
a. Optimum sharpness of one image occurs when the diameter of the central maximum equals the diameter of the pinhole. What is the optimum hole size for a pinhole camera in which the film is behind the hole? Assume localid="1649089848422" an average value for visible light.
b. For this hole size, what is the angle a (in degrees) between two distant sources that can barely be resolved?
c. What is the distance between two street lights localid="1649089839579" away that can barely be resolved?
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.
A double-slit experiment is set up using a helium-neon laser . Then a very thin piece of glass is placed over one of the slits. Afterward, the central point on the screen is occupied by what had been the dark fringe. How thick is the glass?
Scientists shine a laser beam on a -wide slit and produce a diffraction pattern on a screen behind the slit. Careful measurements show that the intensity first falls to of maximum at a distance of from the center of the diffraction pattern. What is the wavelength of the laser light?
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