BackA He–Ne gas laser which produces monochromatic light of wavelength λ = 6.328 x 10-7 m is used to calibrate a reflection grating in a spectroscope. The first-order diffraction line is found at an angle of 18.5° to the incident beam. How many lines per meter are imprinted on this reflecting diffraction grating?
(II) Suppose a thin piece of glass is placed in front of the lower slit in Fig. 34–7 so that the two waves enter the slits 180° out of phase (Fig. 34–44). Describe in detail the interference pattern on the screen.
In the atom interferometer experiment of Figure 38.13, laser-cooling techniques were used to cool a dilute vapor of sodium atoms to a temperature of 0.0010 K=1.0 mK. The ultracold atoms passed through a series of collimating apertures to form the atomic beam you see entering the figure from the left. The standing light waves were created from a laser beam with a wavelength of 590 nm. Because interference is observed between the two paths, each individual atom is apparently present at both point B and point C. Describe, in your own words, what this experiment tells you about the nature of matter.
A beam of 125-eV electrons is scattered from a crystal, as in X-ray diffraction, and a first-order peak is observed at θ = 43°. What is the spacing between planes in the diffracting crystal? (See Section 35–11.)
If a diffraction grating produces its third-order bright band at an angle of 78.4° for light of wavelength 681 nm, find (a) the number of slits per centimeter for the grating and (b) the angular location of the first-order and second-order bright bands. (c) Will there be a fourth-order bright band? Explain.
How far apart are the dark fringes in Example 34–6 if the glass plates are each 26.3 cm long?
What is the f-number of a relaxed eye with the pupil fully dilated to 8.0 mm? Model the eye as a single lens 2.4 cm in front of the retina.
Show that the radius r of the mᵗʰ dark Newton’s ring, as viewed from directly above (Fig. 34–18), is given by r = √mλR where R is the radius of curvature of the curved glass surface and λ is the wavelength of light used. Assume that the thickness of the air gap is much less than R at all points and that r ≪ R . [Hint: Use the binomial expansion.]
When driving at night, your eyes’ pupils have dilated to a 7.5-mm diameter. If your vision is diffraction limited, what would be the greatest distance at which you could resolve the two headlights of an oncoming car, which are spaced 1.5 m apart? Assume a wavelength of 550 nm for the light.
When yellow sodium light, λ = 589nm, falls on a diffraction grating, its first-order peak on a screen 62.0 cm away falls 3.32 cm from the central peak. Another source produces a line 3.71 cm from the central peak. What is its wavelength? How many slits/cm are on the grating?
Two satellites at an altitude of 1200 km are separated by 28 km. If they broadcast 3.6 cm microwaves, what minimum receiving-dish diameter is needed to resolve (by Rayleigh’s criterion) the two transmissions?
Red laser light from a He–Ne laser (λ = 632.8 nm) creates a second-order fringe at 53.2° after passing through a grating. What is the wavelength λ of light that creates a first-order fringe at 21.2°?
"(II) A fine metal foil separates one end of two pieces of optically flat glass, as in Fig. 34–20. When light of wavelength 670 nm is incident normally, 24 dark bands are observed (with one at each end). How thick is the foil?"
A thin film of soap (n = 1.34) coats a piece of flat glass (n = 1.52). What is the minimum film thickness if it reflects 643-nm red light most strongly when illuminated normally by white light?