91Ó°ÊÓ

In astronomy it is common to expose a photographic plate to a particular portion of the night sky for quite some time in order to gather plenty of light. Before leaving a plate exposed to the night sky, Matt decides to test his technique by exposing two photographic plates in his lab to light coming through several pinholes. The source of light is \(1.8 \mathrm{m}\) from one photographic plate and the exposure time is \(1.0 \mathrm{h}\). For how long should Matt expose a second plate located \(4.7 \mathrm{m}\) from the source if the second plate is to have equal exposure (that is, the same energy collected)?

A \(1.0-\mathrm{m}^{2}\) solar panel on a satellite that keeps the panel oriented perpendicular to radiation arriving from the Sun absorbs $1.4 \mathrm{kJ}\( of energy every second. The satellite is located at \)1.00 \mathrm{AU}\( from the Sun. (The Earth Sun distance is defined to be \)1.00 \mathrm{AU} .$. How long would it take an identical panel that is also oriented perpendicular to the incoming radiation to absorb the same amount of energy, if it were on an interplanetary exploration vehicle 1.55 AU from the Sun? ( W) tutorial: sunlight on Io).

The intensity of the sunlight that reaches Earth's upper atmosphere is approximately \(1400 \mathrm{W} / \mathrm{m}^{2} .\) (a) What is the total average power output of the Sun, assuming it to be an isotropic source? (b) What is the intensity of sunlight incident on Mercury, which is $5.8 \times 10^{10} \mathrm{m}$ from the Sun?

Prove that, in an EM wave traveling in vacuum, the electric and magnetic energy densities are equal; that is, prove that,$$\frac{1}{2} \epsilon_{0} E^{2}=\frac{1}{2 \mu_{0}} B^{2}$$ at any point and at any instant of time.,

Verify that the equation \(I=\langle u\rangle c\) is dimensionally consistent (i.e., check the units).

The solar panels on the roof of a house measure \(4.0 \mathrm{m}\) by $6.0 \mathrm{m} .\( Assume they convert \)12 \%$ of the incident EM wave's energy to electric energy. (a) What average power do the panels supply when the incident intensity is \(1.0 \mathrm{kW} / \mathrm{m}^{2}\) and the panels are perpendicular to the incident light? (b) What average power do the panels supply when the incident intensity is \(0.80 \mathrm{kW} / \mathrm{m}^{2}\) and the light is incident at an angle of \(60.0^{\circ}\) from the normal? (W) tutorial: solar collector) (c) Take the average daytime power requirement of a house to be about 2 kW. How do your answers to (a) and (b) compare? What are the implications for the use of solar panels?

The radio telescope in Arecibo, Puerto Rico, has a diameter of $305 \mathrm{m}$. It can detect radio waves from space with intensities as small as \(10^{-26} \mathrm{W} / \mathrm{m}^{2} .\) (a) What is the average power incident on the telescope due to a wave at normal incidence with intensity \(1.0 \times 10^{-26} \mathrm{W} / \mathrm{m}^{2} ?\) (b) What is the average power incident on Earth's surface? (c) What are the rms electric and magnetic fields?

Unpolarized light passes through two polarizers in turn with polarization axes at \(45^{\circ}\) to one another.What is the fraction of the incident light intensity that is transmitted?