Frank D. Drake, an investigator in the SETI (Search for Extra-Terrestrial Intelligence) program, once said that the large radio telescope in Arecibo, Puerto Rico in figure "can detect a signal which lays down on the entire surface of the earth, a power of only one $\mathrm{pico}‐\mathrm{watt}$." $\left(a\right)$ What is the power that would be received by the Arecibo antenna for such a signal? The antenna diameter is $300 \mathrm{m}$. $\left(b\right)$ What would be the power of an isotropic source $9000 \mathrm{ly}$ away that could provide such a signal? A light-year $\left(\mathrm{ly}\right)$ is the distance light travels in one year.

From the figure, approximate the $\left(a\right)$ smaller and $\left(b\right)$ larger wavelength at which the eye of a standard observer has half the eye's maximum sensitivity. What are the $\left(c\right)$ wavelength, $\left(d\right)$ frequency and $\left(e\right)$ period of the light at which the eye is the most sensitive?

Sunlight just outside the Earth's atmosphere has an intensity of $1.40 \mathrm{kW} {\mathrm{m}}^{-2}.$ Calculate

$\left(a\right)$ $E_{\mathrm{m}}$
$\left(b\right)$ $B_{\mathrm{m}}$
$\left(c\right)$ $E_{\mathrm{rms}}$ and
$\left(d\right)$ ${\mathrm{B}}_{\text{rms }}$ for sunlight there, assuming it to be a plane wave.

In the ray diagram of the given figure, where the angles are not drawn to scale, the ray is incident at the critical angle on the interface between materials $2$ and $3 .$ Angle $\mathrm{\varphi }=71.0°$ and two of the indexes of refraction are $n_1=1.70$ and $n_2=1.60.$ Find $\left(a\right)$ index of refraction $n_3$ and $\left(b\right)$ angle $\mathrm{\theta }.$ $\left(c\right)$ If $\mathrm{\theta }$ is decreased, does light refract into material $3$?