Consider a common mirage formed by superheated air immediately above a roadway. A truck driver whose eyes are 2.00 m above the road, where n = 1.000293, looks forward. She perceives the illusion of a patch of water ahead on the road. The road appears wet only beyond a point on the road at which her line of sight makes an angle of $1.20^{\circ}$ below the horizontal. Find the index of refraction of the air immediately above the road surface.

Consider a light ray traveling between air and a diamond cut in the shape we discussed earlier.
(a) Find the critical angle for the total internal reflection of light in the diamond incident on the interface between the diamond and the outside air.
(b) Consider the light ray incident normally on the top surface of the diamond as we discussed earlier. Show that the light traveling toward point $P$ in the diamond is totally reflected. What If? Suppose the diamond is immersed in water.
(c) What is the critical angle at the diamond-water interface?
(d) When the diamond is immersed in water, does the light ray enter the top surface as we discussed earlier undergo total internal reflection at $P$? Explain.
(e) If the light ray entering the diamond remains vertical as we discussed earlier, which way should the diamond in the water be rotated about an axis perpendicular to the page through $O$ so that light will exit the diamond at $P$ ?
(f) At what angle of rotation in part
(e) will light the first exit of the diamond at point $P$?

Determine the maximum angle $\theta$ for which the light rays incident on the end of the pipe in the figure are subject to total internal reflection along the walls of the pipe. Assume that the pipe has an index of refraction of 1.36 and the outside medium is air.

Repeat Problem when the materials are surrounded by water.

Two light sources are used in a photoelectric experiment to determine the work function for a particular metal surface. When green light from a mercury lamp ($\lambda = 546.1$ nm) is used, a stopping potential of 0.376 V reduces the photocurrent to zero. What stopping potential would be observed when using the yellow light from a helium discharge tube ($\lambda = 587.5$ nm)?

The work function for zinc is 4.31 eV. If photons of energy 5.50 eV are incident on zinc, what is the maximum kinetic energy of the ejected photoelectrons?

Review. This problem is about how strongly matter is coupled to radiation, the subject with which quantum mechanics began. For a simple model, consider a solid iron sphere 2.00 cm in radius. Assume its temperature is always uniform throughout its volume. (a) Find the mass of the sphere. (b) Assume the sphere is at 20.0$^ { \circ } \mathrm { C }$ and has emissivity 0.860. Find the power with which it radiates electromagnetic waves. (c) If it were alone in the Universe, at what rate would the sphere’s temperature be changing? (d) Assume Wien’s law describes the sphere. Find the wavelength λmax of electromagnetic radiation it emits most strongly. Although it emits a spectrum of waves having all different wavelengths, assume its power output is carried by photons of wavelength λmax. Find (e) the energy of one photon and (f) the number of photons it emits each second.

This problem is about how strongly matter is coupled to radiation, the subject with which quantum mechanics began. For a simple model, consider a solid iron sphere 2.00 cm in radius. Assume its temperature is always uniform throughout its volume. Find the mass of the sphere.

A triangular glass prism with apex angle $\Phi=60.0^{\circ}$ has an index of refraction n = 1.50. What is the smallest angle of incidence $\theta_{1}$ for which a light ray can emerge from the other side?

For 589-nm light, calculate the critical angle for the following materials surrounded by air: ice.

For 589-nm light, calculate the critical angle for the following materials surrounded by air: flint glass.

A glass optical fiber (n = 1.50) is submerged in water (n = 1.33). What is the critical angle for light to stay inside the fiber?

A triangular glass prism with apex angle $\Phi$ has an index of refraction n. What is the smallest angle of incidence $\theta_{1}$ for which a light ray can emerge from the other side?

A beam of light traveling in an unknown material encounters a boundary with flint glass (n = 1.66). If the critical angle for total internal reflection is $32^{\circ}$, what is the index of refraction of the unknown material?