34. Wave Optics

How far apart are the dark fringes in Example 34–6 if the glass plates are each 26.3 cm long?

Use your expression from part a to find an expression for the separation Δy on the screen of two fringes that differ in wavelength by Δλ.

FIGURE EX33.17 shows the interference pattern on a screen 1.0 m behind an 800 lines/mm diffraction grating. What is the wavelength (in nm) of the light?

If the planes of a crystal are 3.50 Å (1 Å = 10^-10 m = 1 Ångstrom unit) apart, what wavelength of electromagnetic waves is needed so that the first strong interference maximum in the Bragg reflection occurs when the waves strike the planes at an angle of 22.0°, and in what part of the electromagnetic spectrum do these waves lie?

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?

A Michelson interferometer uses red light with a wavelength of 656.45 nm from a hydrogen discharge lamp. How many bright-dark-bright fringe shifts are observed if mirror M₂ is moved exactly 1 cm?

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 670 nm, while a pinhole in a violet zone is going to be illuminated with a violet laser beam of wavelength 410 nm. 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’s diameter to that of the violet pinhole?

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.

The entrance to a boy’s bedroom consists of two doorways, each 1.0 m wide, which are separated by a distance of 3.0 m. The boy’s mother yells at him through the two doors as shown in Fig. 35–42, telling him to clean up his room. Her voice has a frequency of 400 Hz. Later, when the mother discovers the room is still a mess, the boy says he never heard her telling him to clean his room. The velocity of sound is 340 m/s. (a) Find all of the angles θ (Fig. 35–42) at which no sound will be heard within the bedroom when the mother yells. Assume sound is fully absorbed when it strikes a bedroom wall. (b) If the boy was at the position shown when his mother yelled, does he have a good explanation for not having heard her? Explain.

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