we described how the speed of light varies with wavelength (or frequency) for transparent solids. But the speed of light in matter is also a function of temperature and pressure. This dependence is most marked for gases and is instrumental in producing such things as mirages and atmospheric refraction, the latter phenomenon being the displacement of an astronomical object (like the Sun or another star) from its true position because of the passage of its light through the atmosphere. Because Earth's atmosphere is a gaseous mixture and easily compressed, its density is highest near Earth's surface and gradually declines with altitude. Thus, the speed of light in the atmosphere is lowest near the surface and gradually gets higher, approaching $c$ as one goes farther and farther into space. Using this fact and the law of refraction, sketch the path a light ray from the Sun would follow upon entering Earth's atmosphere, and predict the apparent position of the Sun relative to its true position. What does this tell you about the actual location of the Sun's disk relative to your local horizon when you see it apparently setting brilliantly in the west in the evening?

A camera is equipped with a telephoto lens that has a focal length of $200 \mathrm{~mm}$. Repeat part (c) of Challenge 8 for this situation.

How would figure mentioned $\mathrm{a}$ be different if the glass were replaced by water or by diamond?

Describe how the path of a ray is deviated as it passes (at an angle) from one medium into a second medium in which the speed of light is lower. Contrast this with the case when the speed of light in the second medium is higher.

What kind of mirror (concave, convex, or plane) do you think dental care workers use to examine patients' teeth and gums for disease? Explain your choice.

What is the ideal shape of concave mirrors used in telescopes?

What is different about an image formed with a convex mirror compared to an image formed with a concave mirror? What are the advantages of each type of mirror?

Two plane mirrors are hinged along one edge and set at right angles to one another as shown in Figure mentioned. A light ray enters the system, striking mirror 1 with an angle of incidence of $45^{\circ}$. Draw a diagram showing the direction in which the ray will exit the system. This device is called a corner reflector and is the basis for the design of bicycle reflectors and some highway signs.

Distinguish between specular reflection and diffuse reflection.

As the footnote on above page indicates, the separation, $\Delta x$, between two adjacent bright areas or fringes in the double slit interference pattern is determined by the distance, $a$, between the slits, the distance, $S$, between the plane of the slits and the screen on which the pattern is projected, and the wavelength, $\lambda$, of light used in the experiment. Specifically, the relationship among these variables is given by:

$$\Delta x=\left(\frac{S}{a}\right) \lambda .$$

Based on this equation, for a given slit spacing and screen distance, for which color of light, red or blue, will the fringe spacing be greater? For a given slit spacing and wavelength, if the screen distance, $S$, is increased, what happens to the fringe spacing? If the separation between the slits is decreased, for a given value of $\lambda$ and $S$, how will $\Delta x$ change? Suppose that a beam of red light from a He-Ne laser $(\lambda=633 \mathrm{~nm})$ strikes a screen containing two narrow slits separated by $0.200 \mathrm{~mm}$. The fringe pattern is projected on a white screen located $1.00 \mathrm{~m}$ away. Find the distance in millimeters between adjacent bright areas near the center of the interference pattern that develops. As mentioned in the text, the relationship given above could be used to calculate the wavelength of light in an experiment in which the other three quantities are measured.

Consider Figure mentioned below. At which of the lettered positions would an observer be able to see the image of the dot in the mirror?

If the wavelength of light is doubled, by what fraction does the amount of the light scattered by Earth's atmosphere change? Is the amount of light scattered at the new wavelength larger or smaller than the amount of light scattered at the old wavelength?

Light traveling along direction $\mathrm{SO}$ strikes the surface of a plane mirror. Which of the paths $O P, O Q, O R$, or $U I$ best describes the path of the light reflected from the mirror? Defend your choice by appealing to the appropriate law(s) of optics.

Compute the approximate ratio of the amount of blue light in scattered sky light to the amount of orange.