Page 427 - Schaum's Outline of Theory and Problems of Applied Physics

412 PHYSICAL AND QUANTUM OPTICS [CHAP. 33

SOLVED PROBLEM 33.5
A pair of “7 × 50” binoculars has a magnification of 7 and objective lens diameters of 50 mm. Find the
size of the smallest detail that can possibly be resolved by such binoculars when something 1 km away is
examined. Consider the wavelength of the light to be 5 × 10 −7 m, which is near the middle of the visible
spectrum and corresponds to green.
3
Since D = 50 mm = 5 × 10 −2 m and L = 1km = 10 m,
−7 3
λL (1.22)(5 × 10 m)(10 m)
d 0 = (1.22) = = 1.22 × 10 −2 m = 1.22 cm
D 5 × 10 −2 m
SOLVED PROBLEM 33.6
A radar operating at a wavelength of 3 cm is to have a resolving power of 30 m at a range of 1 km. Find
the minimum width its antenna must have.
The width of a radar antenna corresponds to the diameter of the objective lens of an optical system. Here
L = 1km = 1000 m, d 0 = 30 m, and λ = 0.03 m, so

λL (1.22)(0.03 m)(1000 m)
D = (1.22) = = 1.22 m
d 0 30 m

POLARIZATION
A polarized beam of light is one in which the electric fields of the waves are all in the same direction. If the
electric fields are in random directions (though, of course, always in a plane perpendicular to the direction of
propagation), the beam is unpolarized. Figure 33-4(a) shows a polarized beam and (b) shows an unpolarized
beam. Various substances differently affect light with different directions of polarization, and these substances
can be used to prepare devices that permit only light polarized in a certain direction to pass through them.

Polarized beam

Direction
of waves
Plane of
polarization
Electric fields occur in only
one direction perpendicular
to direction of wave motion

(a)

Unpolarized beam

Electric fields occur in all
directions perpendicular to
direction of wave motion
(b)
Fig. 33-4. (From Modern Technical Physics, 6th Ed., Arthur Beiser, c 1992. Reprinted by permission of Pearson
Education, Inc.)