3 Resolution of Single-Slit and Circular Apertures

Section 38.3 Resolution of Single-Slit and Circular Apertures

11. The pupil of a cat’s eye narrows to a vertical slit of width 0.500 mm in daylight. What is the angular resolution for horizontally separated mice? Assume that the average wavelength of the light is 500 nm.

12. Find the radius a star image forms on the retina of the eye if the aperture diameter (the pupil) at night is 0.700 cm and the length of the eye is 3.00 cm. Assume the represen- tative wavelength of starlight in the eye is 500 nm.

13. SuperStock A helium–neon laser emits light that has a wavelength of 632.8 nm. The circular aperture through which the

Figure P38.17 Sunday Afternoon on the Island of La Grande Jatte, by beam emerges has a diameter of 0.500 cm. Estimate the

Georges Seurat.

diameter of the beam 10.0 km from the laser. You are vacationing in a Wonderland populated by friendly

18. A binary star system in the constellation Orion has an angu-

lar interstellar separation of 1.00 & 10 ' 5 rad. If % " 500 nm, elves and a cannibalistic Cyclops that devours physics what is the smallest diameter the telescope can have to just students. The elves and the Cyclops look precisely alike

resolve the two stars?

(everyone wears loose jeans and sweatshirts) except that each elf has two eyes, about 10.0 cm apart, and the

19. A spy satellite can consist essentially of a large-diameter Cyclops—you guessed it—has only one eye of about the

concave mirror forming an image on a digital-camera same size as an elf’s. The elves and the Cyclops are con-

detector and sending the picture to a ground receiver by stantly at war with each other, so they rarely sleep and all

radio waves. In effect, it is an astronomical telescope in have red eyes, predominantly reflecting light with a

orbit, looking down instead of up. Can a spy satellite read wavelength of 660 nm. From what maximum distance can

a license plate? Can it read the date on a dime? Argue for you distinguish between a friendly elf and the predatory

your answers by making an order-of-magnitude calcula- Cyclops? The air in Wonderland is always clear. Dilated

tion, specifying the data you estimate. with fear, your pupils have a diameter of 7.00 mm.

20. A circular radar antenna on a Coast Guard ship has a

15. Narrow, parallel, glowing gas-filled tubes in a variety of colors diameter of 2.10 m and radiates at a frequency of 15.0 GHz. form block letters to spell out the name of a night club.

Two small boats are located 9.00 km away from the ship. Adjacent tubes are all 2.80 cm apart. The tubes forming

How close together could the boats be and still be detected one letter are filled with neon and radiate predominantly

as two objects?

red light with a wavelength of 640 nm. For another letter,

21. Grote Reber was a pioneer in radio astronomy. He con- the tubes emit predominantly violet light at 440 nm. The

structed a radio telescope with a 10.0-m-diameter receiving pupil of a dark-adapted viewer’s eye is 5.20 mm in diame-

dish. What was the telescope’s angular resolution for 2.00-m ter. If she is in a certain range of distances away, the viewer

radio waves?

can resolve the separate tubes of one color but not the

22. When Mars is nearest the Earth, the distance separating other. Which color is easier to resolve? The viewer’s distance

the two planets is 88.6 & 10 6 km. Mars is viewed through a must be in what range for her to resolve the tubes of

telescope whose mirror has a diameter of 30.0 cm. (a) If only one color?

the wavelength of the light is 590 nm, what is the angular

16. On the night of April 18, 1775, a signal was sent from the resolution of the telescope? (b) What is the smallest steeple of Old North Church in Boston to Paul Revere,

distance that can be resolved between two points on Mars?

CHAPTER 38• Diffraction Patterns and Polarization