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Chapter 33: Q. 57 (page 957)
FIGURE P33.56 shows the light intensity on a screen behind a single slit. The wavelength of the light is and the slit width is . What is the distance from the slit to the screen?
The distance from the slit to the screen
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FIGURE shows two nearly overlapped intensity peaks of the sort you might produce with a diffraction grating . As a practical matter, two peaks can just barely be resolved if their spacing equals the width w of each peak, where is measured at half of the peak’s height. Two peaks closer together than will merge into a single peak. We can use this idea to understand the resolution of a diffraction grating.
a. In the small-angle approximation, the position of the peak of a diffraction grating falls at the same location as the fringe of a double slit: . Suppose two wavelengths differing by pass through a grating at the same time. Find an expression for localid="1649086237242" , the separation of their first-order peaks.
b. We noted that the widths of the bright fringes are proportional to localid="1649086301255" , where localid="1649086311478" is the number of slits in the grating. Let’s hypothesize that the fringe width is localid="1649086321711" Show that this is true for the double-slit pattern. We’ll then assume it to be true as localid="1649086339026" increases.
c. Use your results from parts a and b together with the idea that localid="1649086329574" to find an expression for localid="1649086347645" , the minimum wavelength separation (in first order) for which the diffraction fringes can barely be resolved.
d. Ordinary hydrogen atoms emit red light with a wavelength of localid="1649086355936" In deuterium, which is a “heavy” isotope of hydrogen, the wavelength is localid="1649086363764" What is the minimum number of slits in a diffraction grating that can barely resolve these two wavelengths in the first-order diffraction pattern?
The wings of some beetles have closely spaced parallel lines of melanin, causing the wing to act as a reflection grating. Suppose sunlight shines straight onto a beetle wing. If the melanin lines on the wing are spaced apart, what is the first-order diffraction angle for green light ?
A diffraction grating having diffracts visible light at .What is the light's wavelength?
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?
If sunlight shines straight onto a peacock feather, the feather appears bright blue when viewed fromon either side of the incident beam of light. The blue color is due to diffraction from parallel rods of melanin in the feather barbules, as was shown in the photograph on page . Other wavelengths in the incident light are diffracted at different angles, leaving only the blue light to be seen. The average wavelength of blue light is . Assuming this to be the first-order diffraction, what is the spacing of the melanin rods in the feather?
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