A ray of yellow light crosses the boundary between glass and air, going from the glass into air. If the angle of incidence is $20^{\circ}$, what is the angle of refraction?

A light ray in air enters a block of clear plastic. Which of the numbered paths represents the correct one for the ray in the plastic? Justify your choice by appealing to the appropriate law(s) of optics.

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.

A piece of glass is immersed in water. If a light ray enters the glass from the water with an angle of incidence greater than zero, in which direction is the ray bent?

Every transparent material can be characterized by what is called its index of refraction, $n$, given by the equation

$$n=\frac{c}{v}$$

Here $c$ is the speed of light in a vacuum and $v$ is the speed of light in the transparent material. Although normal air is not quite a vacuum, its density is small enough that $v_{\text {arr }}$ is approximately equal to $c$, so that we may take $n_{\text {air }}=1.00$ without too much error. The precise mathematical relationship between the angles of incidence and refraction is given by what is known as Snell's law,

$$n_1 \sin A_1-n_2 \sin A_2$$

where $n_1$ and $A_1$ are the index of refraction and the angle between the light ray and the normal, respectively, in medium 1 , and $n_2$ and $A_2$ are the corresponding quantities for medium 2. (a) Using the information in Table 9.1, compute the index of refraction for water and for fused silica (glass). (b) Verify the result in Example $9.2$ using Snell's law explicitly. Show, using the same relationship, that the values for the angles of refraction in air (medium 2) in panels (b), (c), (d), and (e) of Figure $9.36$ are correct for the given angles of incidence in glass (medium 1).

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?

The speed of light in a certain kind of glass is exactly the same as the speed of light in benzene-a liquid. Describe what happens when light passes from benzene into this glass, and vice versa.

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

What do you see if you hold out your right hand in front of an aeroplane mirror? (Be cautious now. Describe the image carefully.) If you’re having trouble, place a tube of toothpaste or other object with writing on it in front of the mirror. Now what can you say? (The process you’re witnessing is called inversion and is one of the common characteristics of plane mirrors.)

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.

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.

On a summer day in Houston, the temperature is $35^{\circ} \mathrm{C}$ and the relative humidity is 77 percent. (a) What is the humidity? (b) To what temperature could the air be cooled before condensation would start to take place? (That is, what is the dew point?)

What is the frequency of the EM wave emitted most strongly by a glowing element on a stove with temperature $1,500 \mathrm{~K}$ ?

A 12 V DC power supply is connected to the primary coil of a transformer. The primary coil has 100 turns and the secondary coil has 200. What is the rms voltage across the secondary?