FIGURE shows the light intensity on a viewing screen behind a single slit of width . The light’s wavelength is . Is , , , or is it not possible to tell? Explain.
Behind a single slit, the light intensity on a viewing screen is
When it comes to waves like acoustic waves (sound) or electromagnetic waves like light or radio waves, intensity refers to the average power transfer across one period of the wave. Intensity can be used in a variety of situations where energy is delivered. For example, the intensity of the kinetic energy carried by drops of water from a garden sprinkler may be calculated.
As , the first minima from the central maximum need , which must be smaller than .
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’s 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 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 away that can barely be resolved?
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