BackThe Hubble Space Telescope has an aperture of 2.4 m and focuses visible light (380 - 750 nm). The Arecibo radio telescope in Puerto Rico is 305 m (1000 ft) in diameter (it is built in a mountain valley) and focuses radio waves of wavelength 75 cm. Under optimal viewing conditions, what is the smallest crater that each of these telescopes could resolve on our moon?
A wildlife photographer uses a moderate telephoto lens of focal length 135 mm and maximum aperture f/4.00 to photograph a bear that is 11.5 m away. Assume the wavelength is 550 nm. (a) What is the width of the smallest feature on the bear that this lens can resolve if it is opened to its maximum aperture? (b) If, to gain depth of field, the photographer stops the lens down to f/22.0, what would be the width of the smallest resolvable feature on the bear?
(III) The yellow sodium D lines have wavelengths of 589.0 and 589.6 nm. When they are used to illuminate a Michelson interferometer, it is noted that the interference fringes disappear and reappear periodically as the mirror M₁ is moved. Why does this happen? How far must the mirror move between one disappearance and the next?
Spy planes fly at extremely high altitudes (25 km) to avoid interception. If their cameras are to discern features as small as 5 cm, what is the minimum aperture of the camera lens to afford this resolution? (Use λ = 580nm.)
"(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 diffraction grating has 6.5 x 10⁵ slits/m. Find the angular spread in the second-order spectrum between red light of wavelength 7.0 x 10⁻⁷ m and blue light of wavelength 4.5 x 10⁻⁷ m.
A 3800-slit/cm grating produces a third-order fringe at a 35.0° angle. What wavelength of light is being used?
The Earth and Moon are separated by about 400 x 106 m. When Mars is 8 x 1010 m from Earth, could a person standing on Mars resolve the Earth and its Moon as two separate objects without a telescope? Assume a pupil diameter of 5 mm and λ = 550 nm.
At what angle will 480-nm light produce a second-order maximum when falling on a grating whose slits are 1.25 x 10-3 cm apart?
Unpolarized light falls on two polarizer sheets whose axes are at right angles. (a) What fraction of the incident light intensity is transmitted? (b) What fraction is transmitted if a third polarizer is placed between the first two so that its axis makes a 58° angle with the axis of the first polarizer? (c) What if the third polarizer is in front of the other two?
Show that the second- and third-order spectra of white light produced by a diffraction grating always overlap. What wavelengths overlap?
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.
Calculate the minimum thickness needed for an antireflective coating (n = 1.42) applied to a glass lens in order to eliminate (a) blue (450 nm), or (b) red (720 nm) reflections for light at normal incidence.
A micrometer is connected to the movable mirror of an interferometer. When the micrometer is tightened down on a thin metal foil, the net number of bright fringes that move, compared to the empty micrometer, is 272. What is the thickness of the foil? The wavelength of light used is 611 nm.
How far must the mirror M1 in a Michelson interferometer be moved if 730 fringes of 589-nm light are to pass by a reference line?