Irodov – Problems in General Physics

5.219. A point source of monochromatic light emitting a luminous
flux 1:1) is positioned at the centre of a spherical layer of substance.
The inside radius of the layer is a, the outside one is b. The coeffi-
cient of linear absorption of the substance is equal to x, the reflection
coefficient of the surfaces is equal to p. Neglecting the secondary
reflections, find the intensity of light that passes through that layer.
5.220. How many times will the intensity of a narrow X-ray
beam of wavelength 20 pm decrease after passing through a lead
plate of thickness d = 1.0 mm if the mass absorption coefficient
for the given radiation wavelength is equal to Rip = 3.6 cm 2 /g?
5.221. A. narrow beam of X-ray radiation of wavelength 62 pm
penetrates an aluminium screen 2.6 cm thick. How thick must
a lead screen be to attenuate the beam just as much? The mass
absorption coefficients of aluminium and lead for this radiation are
equal to 3.48 and 72.0 cm 2 /g respectively.
5.222. Find the thickness of aluminium layer which reduces by
half the intensity of a narrow monochromatic X-ray beam if the
corresponding mass absorption coefficient is p,/p = 0.32 cm^2 /g.
5.223. How many 50%-absorption layers are there in the plate
reducing the intensity of a narrow X-ray beam ri = 50 times?

5.6. Optics of Moving Sources

• Doppler effect for < c:

Ace v

=— cos e

where e is the velocity of a source, 0 is the angle between the source's motion

direction and the observation line.

• Doppler effect in the general case:

—13 2

0)0 1— cos 0'

where 5= v/c.

• If 0 = 0, the Doppler effect is called radial, and if 0 = n/2, transverse.


• Vavilov-Cherenkov effect-.

cos 0 —c

nu (5.6c)

where 0 is the angle between the radiation propagation direction and the velo-

city vector v of a particle.

5.224. In the Fizeau experiment on measurement of the velocity

of light the distance between the gear wheel and the mirror is 1

= 7.0 km, the number of teeth is z = 720. Two successive disappear-

ances of light are observed at the following rotation velocities of

the wheel: n 1 = 283 rps and n 2 = 313 rps. Find the velocity of

light.

(5.6a)

(5.6b)