Irodov – Problems in General Physics

lel to its surface and perpendicular to the direction of the incident

beam. In this case the directions to the maxima of second and third

order from the system of planes parallel to the surface of the single

crystal form an angle a = 60° between them. Find the corresponding

interplanar distance.

5.156. On transmitting a beam of X-rays with wavelength X

17.8 pm through a polycrystalline specimen a system of diffrac-

tion rings is produced on a screen located at a distance 1= 15 cm

from the specimen. Determine the radius of the bright ring corres-

ponding to second order of reflection from the system of planes with

interplanar distance d = 155 pm.

5.4. Polarization of Light

• Degree of polarization of light:

P = I

max— I mi n

Imax+ I min •

I = I0 cost cp.

• Brewster's law:
  tan 0 13 = no/ni. (5.4c)


• Fresnel equations for intensity of light reflected at the boundary be-
  tween two dielectrics:
  sin 2 (0 1 -00 tan 2 (0 1 —0 2 )
  I1^

(5.4d)

sine (0 1 + 0 2 ) ' " tan 2 (0 1 + 0 2 ) '

where I and III are the intensities of incident light whose electric vector oscil-

lations are respectively perpendicular and parallel to the plane of incidence.

• A crystalline plate between two polarizers P and P'. If the angle between
  the plane of polarizer P and the optical axis 00' of the plate is equal to 45°,
  the intensity I' of light which passes through the polarizer P' turns out to be
  either maximum or minimum under the following conditions:

Polarizers

P and P' 2nk = (2k + 1) n

parallel I ' = max I' =min 3 (5 .4e)

crossed / ' =-- min I' = max

Here 6 = 2n (no — ne)da is the phase difference between the ordinary and

extraordinary rays, k = 0, 1, 2,...

• Natural and magnetic rotation of the plane of polarization:

Tnat =a1, Tmagn=1^7 111,^ (5.4f)

where a is the rotation constant, V is Verdet's constant.

5.157. A plane monochromatic wave of natural light with inten-
sity Io falls normally on a screen composed of two touching Polaroid
half-planes. The principal direction of one Polaroid is parallel,

• Malus's law:

(5.4a)

(5.4b)

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