91Ó°ÊÓ

The intensity Iof light from an isotropic point source is determined as a function of distance r from the source. The Figure gives intensity I versus the inverse square of that square r^-2. The vertical axis scale is set by I_s=200 w/m², and the horizontal axis scale is set by r_s^-2 = 8.0 m^-2. What is the power of the source?

Figure:

High-power lasers are used to compress a plasma (a gas of charged particles) by radiation pressure. A laser generating radiation pulses with peak power $\mathbf{1}\mathbf{.5}\mathbf{×}{\mathbf{10}}^{\mathbf{3}}\mathbf{\text{MW}}$is focused onto 1.00 mm² of high-electron-density plasma. Find the pressure exerted on the plasma if the plasma reflects all the light beams directly back along their paths.

Someone plans to float a small, totally absorbing sphere 0.500m above an isotropic point source of light so that the upward radiation force from the light matches the downward gravitational force on the sphere. The sphere’s density is 19.0 g/cm³, and its radius is 2.00mm. (a) What power would be required of the light source? (b) Even if such a source were made, why would the support of the sphere be unstable?

In Fig.33-38, a laser beam of power 4.60W and diameter d=2.60mm is directed upward at one circular face (of diameter d<2.60mm) of a perfectly reflecting cylinder. The cylinder is levitated because the upward radiation force matches the downward gravitational force. If the cylinder’s density is 1.20 g/cm³, what is its height H?

Question: The average intensity of the solar radiation that strikes normally on a surface just outside Earth’s atmosphere is 1.4kw/m².(a) What radiation pressure P_r is exerted on this surface, assuming complete absorption?(b) For comparison, find the ratio of P_r to Earth’s sea-level atmospheric pressure, which is$\mathbf{\text{1.0}}\mathbf{×}{\mathbf{\text{10}}}^{\mathbf{\text{5}}}\mathbf{\text{ P²¹}}$

A small spaceship with a mass of only${\mathbf{\text{1.5×10}}}^{\mathbf{\text{3}}}\mathbf{\text{kg}}$ (including an astronaut) is drifting in outer space with negligible gravitational forces acting on it. If the astronaut turns on a 10kw laser beam, what speed will the ship attain in 1.0 day because of the momentum carried away by the beam.

In Fig. 33-76, unpolarized light is sent into a system of three polarizing sheets with polarizing directions at angles, ${\mathit{θ}}_{\mathbf{1}}\mathbf{=}\mathbf{20}\mathbf{°}$, ${\mathit{θ}}_{\mathbf{2}}\mathbf{=}\mathbf{60}\mathbf{°}$and${\mathit{θ}}_{\mathbf{3}}\mathbf{=}\mathbf{40}\mathbf{°}$.What fraction of the initial light intensity emerges from the system?

In Fig. 33-77, an albatross glides at aconstant $\mathbf{15}\mathbf{}\mathbf{\text{ }}\mathit{m}\mathbf{/}\mathit{s}$horizontallyabove level ground, moving in a vertical plane that contains the Sun. It glides toward a wallof height$\mathit{h}\mathbf{=}\mathbf{2}\mathbf{.}\mathbf{0}\mathbf{\text{ }}\mathit{m}$, which it will just barely clear. At that time of day, the angle of the Sun relative to the groundis$\mathit{θ}\mathbf{=}\mathbf{30}\mathbf{°}$.At what speed does the shadow of the albatross move (a) across the level ground and then (b) up the wall? Suppose that later a hawk happens to glide along the same path, alsoat$\mathbf{15}\mathbf{\text{ }}\mathit{m}\mathbf{/}\mathit{s}$.You see that when its shadow reaches the wall, the speed of the shadow noticeably increases. (c) Is the Sun now higher or lower in the sky than when the albatross flew by earlier? (d) If the speed of the hawk’s shadow on the wallis$\mathbf{45}\mathbf{\text{ }}\mathit{m}\mathbf{/}\mathit{s}$,what is the angle u of the Sun just then?

The magnetic component of a polarized wave of light is given by.${\mathit{B}}_{\mathbf{x}}\mathbf{=}\mathbf{\left(}\mathbf{4}\mathbf{μ}\mathbf{T}\mathbf{\right)}\mathit{s}\mathit{i}\mathit{n}\mathbf{[}\mathit{k}\mathit{y}\mathbf{+}\mathbf{(}\mathbf{2}\mathbf{×}{\mathbf{10}}^{\mathbf{15}}{\mathbf{s}}^{\mathbf{-}\mathbf{1}}\mathbf{)}\mathit{t}$ (a) In which direction does the wave travel, (b) parallel to which axis is it polarized, and (c) what is its intensity? (d) Write an expression for the electric field of the wave, including a value for the angular wave number. (e) What is the wavelength? (f) In which region of the electromagnetic spectrum is this electromagnetic wave?

In Fig. 33-78, where ${\mathit{n}}_{\mathbf{1}}\mathbf{=}\mathbf{1}\mathbf{.70}$, ${\mathit{n}}_{\mathbf{2}}\mathbf{=}\mathbf{1}\mathbf{.50}$,and${\mathit{n}}_{\mathbf{3}}\mathbf{=}\mathbf{1}\mathbf{.30}$,light refracts from material 1 into material 2. If it is incident at point A at the critical angle for the interface between materials 2 and 3, what are (a) the angle of refraction at pointBand (b) the initialangle$\mathit{θ}$?If, instead, light is incident atBat the critical angle for the interface between materials 2 and 3, what are (c) the angle of refraction at pointAand (d) the initial angle$\mathit{θ}$? If, instead of all that, light is incident at point Aat Brewster’s angle for the interface between materials 2 and 3, what are (e) the angle of refraction at point B and (f) the initialangle$\mathit{θ}$?