Fig. 5.32.(b) the degree of polarization of the transmitted light if the
light falling on the plate is natural.
5.172. A narrow beam of natural light falls on a set of N thick
plane-parallel glass plates at the Brewster angle. Find:
(a) the degree P of polarization of the transmitted beam;
(b) what P is equal to when N = 1, 2, 5, and 10.
5.173. Using the Fresnel equations, find:
(a) the reflection coefficient of natural light falling normally
on the surface of glass;
(b) the relative loss of luminous flux due to reflections of a paraxial
ray of natural light passing through an aligned optical system compris-
ing five glass lenses (secondary reflections of light are to be neglected).
5.174. A light wave falls normally on the surface of glass coated
with a layer of transparent substance. Neglecting secondary reflec-
tions, demonstrate that the amplitudes of light waves reflected
from the two surfaces of such a laver will be equal under the condi-
tion n' = irn—, where n' and n are the refractive indices of the layer
and the glass respectively.
5.175. A beam of natural light falls on the surface of glass at an
angle of 45°. Using the Fresnel equations, find the degree of polari-
zation of
(a) reflected light;
(b) refracted light.
5.176. Using Huygens's principle, construct the wavefronts and
the propagation directions of the ordinary and extraordinary rays
in a positive uniaxial crystal whose
optical axis
(a) is perpendicular to the inci-
dence plane and parallel to the
surface of the crystal;
(b) lies in the incidence plane
and is parallel to the surface of
the crystal;
(c) lies in the incidence plane at
an angle of 45° to the surface of
the crystal, and light falls at right
angles to the optical axis.
5.177. A narrow beam of na-
tural light with wavelength X =
589 nm falls normally on the surface of a Wollaston polarizing
prism made of Iceland spar as shown in Fig. 5.32. The optical axes
of the two parts of the prism are mutually perpendicular. Find the
angle 8 between the directions of the beams behind the prism if the
angle 0 is equal to 30°.
5.178. What kind of polarization has a plane electromagnetic
wave if the projections of the vector E on the x and y axes are per-
pendicular to the propagation direction and are defined by the
following equations: