Chapter 32

Answer as true or false with an explanation for the following: The wavelength of He-Ne laser light in water is less than its wavelength in the air. (The refractive index of water is \(1.33 .\)

Among the instruments Apollo astronauts left on the Moon were reflectors used to bounce laser beams back to Earth. These made it possible to measure the distance from the Earth to the Moon with unprecedented precision (uncertainties of a few centimeters out of \(384,000 \mathrm{~km}\) ), for the study both of celestial mechanics and of plate tectonics on Earth. The reflectors consisted not of ordinary mirrors, but of arrays of corner cubes, each consisting of three square plane mirrors fixed perpendicular to each other, as adjacent faces of a cube. Why? Explain the function and advantages of this design.

A \(45^{\circ}-45^{\circ}-90^{\circ}\) triangular prism can be used to reverse a light beam: The light enters perpendicular to the hypotenuse of the prism, reflects off each leg, and emerges perpendicular to the hypotenuse again. The surfaces of the prism are not silvered. If the prism is made of glass with in dex of refraction \(n_{\text {glass }}=1.520\) and the prism is surrounded by air, the light beam will be reflected with a minimum loss of intensity (there are reflection losses as the light enters and leaves the prism). a) Will this work if the prism is under water, which has index of refraction \(n_{\mathrm{H}_{2} \mathrm{O}}=1.333 ?\) b) Such prisms are used, in preference to mirrors, to bend the optical path in quality binoculars. Why?

You are under water in a pond and look up at the smooth surface of the water, noticing the sun in the sky. Is the sun in fact higher in the sky than it appears to you while under water, or is it lower?

A solar furnace uses a large parabolic mirror (mirrors several stories high have been constructed) to focus the light of the Sun to heat a target. A large solar furnace can melt metals. Is it possible to attain temperatures exceeding \(6000 \mathrm{~K}\) (the temperature of the photo sphere of the Sun) in a solar furnace? How, or why not?

A person sits \(1.0 \mathrm{~m}\) in front of a plane mirror. What is the location of the image?

Even the best mirrors absorb or transmit some of the light incident on them. The highest-quality mirrors might reflect \(99.997 \%\) of incident light intensity. Suppose a cubical "room, \(3.00 \mathrm{~m}\) on an edge, were constructed with such mirrors for the walls, floor, and ceiling. How slowly would such a room get dark? Estimate the time required for the intensity of light in such a room to fall to \(1.00 \%\) of its initial value after the only light source in the room is switched off.

The radius of curvature of a convex mirror is \(-25 \mathrm{~cm} .\) What is its focal length?

Convex mirrors are often used in side view mirrors on cars. Many such mirrors display the warning "Objects in mirror are closer than they appear." Assume a convex mirror has a radius of curvature of \(14.0 \mathrm{~m}\) and that there is a car that is \(11.0 \mathrm{~m}\) behind the mirror. For a flat mirror, the image distance would be \(11.0 \mathrm{~m}\) and the magnification would be 1\. Find the image distance and magnification for this mirror.

A \(5.00-\mathrm{cm}\) object is placed \(30.0 \mathrm{~cm}\) away from a convex mirror with a focal length of \(-10.0 \mathrm{~cm}\). Determine the size, orientation, and position of the image.