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Find the angle for the third-order maximum for 580-nm-wavelength yellow light falling on a difraction grating having 1500 lines per centimeter.

Calculate the wavelength of light that has its secondorder maximum at \(45.0^{\circ}\) when falling on a diffraction grating that has 5000 lines per centimeter.

(a) Find the maximum number of lines per centimeter a diffraction grating can have and produce a maximum for the smallest wavelength of visible light. (b) Would such a grating be useful for ultraviolet spectra? (c) For infrared spectra?

The analysis shown below also applies to diffraction gratings with lines separated by a distance \(d .\) What is the distance between fringes produced by a diffraction grating having 125 lines per centimeter for 600 -nm light, if the screen is \(1.50 \mathrm{m}\) away? (Hint: The distance between adjacent fringes is \(\Delta y=x \lambda / d, \quad\) assuming the slit separation \(d\) is comparable to \(\lambda_{-}\) )

The 305 -m-diameter Arecibo radio telescope pictured in Figure 4.20 detects radio waves with a 4.00 -cm average wavelength. (a) What is the angle between two justresolvable point sources for this telescope? (b) How close together could these point sources be at the 2 million lightyear distance of the Andromeda Galaxy?

(a) What is the minimum angular spread of a 633 -nm wavelength He-Ne laser beam that is originally \(1.00 \mathrm{mm}\) in diameter? (b) If this laser is aimed at a mountain cliff 15.0 km away, how big will the illuminated spot be? (c) How big a spot would be illuminated on the moon, neglecting atmospheric effects? (This might be done to hit a corner reflector to measure the round- trip time and, hence, distance.)

A telescope can be used to enlarge the diameter of a laser beam and limit diffraction spreading. The laser beam is sent through the telescope in opposite the normal direction and can then be projected onto a satellite or the moon. (a) If this is done with the Mount Wilson telescope, producing a 2.54 -m-diameter beam of 633 -nm light, what is the minimum angular spread of the beam? (b) Neglecting atmospheric effects, what is the size of the spot this beam would make on the moon, assuming a lunar distance of \(3.84 \times 10^{8} \mathrm{m} ?\)

The limit to the eye's acuity is actually related to diffraction by the pupil. (a) What is the angle between two just-resolvable points of light for a 3.00 -mm-diameter pupil, assuming an average wavelength of \(550 \mathrm{nm}\) ? (b) Take your result to be the practical limit for the eye. What is the greatest possible distance a car can be from you if you can resolve its two headlights, given they are \(1.30 \mathrm{m}\) apart? (c) What is the distance between two just-resolvable points held at an arm's length (0.800 m) from your eye? (d) How does your answer to (c) compare to details you normally observe in everyday circumstances?

Can an astronaut orbiting Earth in a satellite at a distance of \(180 \mathrm{km}\) from the surface distinguish two skyscrapers that are \(20 \mathrm{m}\) apart? Assume that the pupils of the astronaut's eyes have a diameter of \(5.0 \mathrm{mm}\) and that most of the light is centered around \(500 \mathrm{nm}\).

Calcite crystals contain scattering planes separated by \(0.30 \mathrm{nm} .\) What is the angular separation between first and second-order diffraction maxima when X-rays of \(0.130 \mathrm{nm}\) wavelength are used?