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college physics reasoning
College Physics Reasoning and Relationships 2nd edition Nicholas Giordano - Solutions
A converging lens has a focal length of f = 55 cm for blue light (n = 1.65). The index of refraction of this lens for red light is n = 1.55. What is the focal length for red light?
As we discussed in the chapter, the position of a star in the sky as viewed from the surface of the Earth is not where it actually is because the light from the star refracts as it enters the Earth’s atmosphere. Approximating the Earth’s atmosphere to be homogenous with a thickness of 100 km
Figure 24.49B shows a ray diagram for light from the Sun as it passes through a water droplet and produces a rainbow. Construct a careful ray diagram of this type for light rays of different colors (e.g., red and blue) and use it to explain the order (sequence) of colors in a rainbow.
A cell phone 7.0 cm tall is 40 cm in front of your eye (diameter 2.5 cm).(a) Find the size of the image of the cell phone on your retina.(b) The cell phone is now moved to a spot 60 cm from your eye. Is the image on the retina larger or smaller than the image in part (a)? By what factor?
Your eye (diameter 2.5 cm) is able to focus the image of a tree on your retina. The tree is 25 m tall and 75 m away. What is the size of the image of the tree on your retina?
A young child is just able to read a newspaper that is only 10 cm from her eyes. What is the focal length of the child’s eye? Assume her eye is 1.5 cm in diameter.
For a converging lens of focal length f, determine the minimum object-to-image distance so that the image is(a) real(b) virtual.
A converging lens has a focal length of 10 cm. How far from the lens should an object be placed to get(a) a real image with a magnification of 2.5(b) a virtual image with a magnification of 2.5?
A converging lens with a focal length of 25 cm is used to form an image on a screen that is 3.0 m from the lens. Where must the object be placed?
A converging glass lens (n = 1.50) is immersed in water. Does the focal length get longer or shorter and by what factor? Explain why. In the lens maker’s formula in Equation 24.32, the term n - 1 is actually the difference between the index of refraction of the lens and the surrounding air.
If the fly in Problem 68 moves farther from the lens, will the image become larger or smaller?
A fly appears to be upside down and twice its actual size when viewed through a converging lens with a focal length of 5.5 cm. How far is the fly from the lens?
A 5.0-cm-tall object is 25 cm in front of a converging lens with a focal length of 40 cm. Where is the image?
An object is a distance 2|f| in front of a diverging lens.(a) Following the steps outlined in the procedures for “Ray Tracing Applied to Lenses,” construct a ray diagram showing the location and orientation of the image.(b) Where is the image located?(c) Is it a real image or a virtual image?
An object is placed in front of a lens. The image is upright, 35 cm to the left of the lens, and is half as tall as the object. What is the focal length of the lens?
An object is 45 cm to the left of a lens, and the image is 25 cm to the left of the lens. What is the magnification?
An object is a distance 2f from a converging lens.(a) Following the steps outlined in the procedure for “Ray Tracing Applied to Lenses,” construct a ray diagram showing the location and orientation of the image.(b) Where is the image located?(c) Is it a real image or a virtual image?
An object 1.5 cm high is placed a distance of 10 cm in front of a converging lens with a focal length of 5.0 cm.(a) Follow the steps outlined in the procedure for “Ray Tracing Applied to Lenses” and make an accurate ray diagram to scale showing the location and size of the image.(b) Check your
A meter stick lies along the optical axis of a convex mirror of focal length -40 cm, with its nearest end 60 cm from the mirror. How long is the image of the meter stick?
An object is placed in front of a concave mirror with a focal length of 10 cm. What is the position of the resulting image if the image is upright and twice the size of the object?
An object 3.5 cm high is placed 20 cm in front of a convex mirror with a radius of 12 cm.(a) Make an accurate ray diagram showing the location and size of the image. Construct your ray diagram following the steps outlined in the procedures for “Ray Tracing Applied to Spherical Mirrors.”(b)
Suppose the rearview mirror on a car is convex with a radius of curvature of 25 m.(a) If a motorcycle is 40 m behind the car, what is the magnification of the motorcycle?(b) How does your answer change when the motorcycle is 15 m behind the car?
Suppose an object is somehow located a distance 35 cm behind a concave mirror with a radius of curvature of 1.50 m. Such a “virtual object” can be produced by a lens.(a) Use the mirror equation to find the location of the image.(b) Is the image real or virtual?(c) What is magnification of the
A convex mirror has a radius of curvature of 85 cm. An image is produced 30 cm in front of the mirror. Where is the object?
An object is 35 cm in front of a concave mirror and produces an upright image that is 2.5 times larger than the object. What is the focal length of the mirror?
When an object is placed 12 cm in front of a mirror, an image is formed 25 cm behind the mirror. Is the mirror concave or convex? What is the mirror’s focal length?
A pencil is placed 45 cm in front of a convex mirror. Is the image in front of or behind the mirror?
A convex mirror has a focal length of -20 cm. Where is the image if it is upright and one-fourth the size of the object?
An object 5.0 cm tall is 25 cm in front of a convex mirror with a radius of curvature of 25 cm. Construct a ray diagram to scale following the steps outlined in the procedures for “Ray Tracing Applied to Spherical Mirrors.” (a) Indicate the parallel, focal, and central rays in your diagram. (b)
An object 22 mm tall is located 1.5 m in front of a convex mirror. If the image is 1.2 m behind the mirror, what is the height of the image?
An object is placed 75 cm in front of a concave mirror. If the magnification is -0.75, what is the focal length of the mirror?
A ball whose diameter is 0.25 cm is placed 50 cm in front of a convex spherical mirror. If the focal length of the mirror is -40 cm, what is the diameter of the ball as viewed in the mirror?
A concave mirror has a focal length of 10 cm. What is the magnification of an object placed 100 cm in front of this mirror?
Where should the cat in Problem 41 sit so as to appear as large as possible (i.e., to be as scary as possible) to a dog?
If the cat in Problem 40 moves away from the mirror, does the cat’s image get larger or smaller in magnitude?
A cat is located 4.5 m in front of a concave mirror. The mirror has a radius of 1.5 m. Construct a ray diagram to scale following the steps outlined in the procedure for “Ray Tracing Applied to Spherical Mirrors.”(a) Where is the image of the cat?(b) Is this image real or virtual?(c) If the
An object 5.0 cm tall is 45 cm in front of a concave mirror with a radius of curvature of 15 cm. Construct a ray diagram to scale following the steps outlined in the procedure for “Ray Tracing Applied to Spherical Mirrors.”(a) Indicate the parallel, focal, and central rays in your diagram.(b)
Figure P24.38 shows light incident at an angle u on a prism with an index of refraction n = 1.55. It is found that light reflects from the upper right face of the prism and travels back along the path followed by the incident ray. Find θ.
A light ray is incident on a plate of plastic (n = 1.50) that is d = 2.5 cm thick (Fig. P24.27).(a) Show that the outgoing ray is parallel to the incident ray.(b) If the angle of incidence is 40°, what is the displacement h of the outgoing ray relative to the incident ray?
What is the critical angle for total internal reflection for light traveling between glass (n = 1.65) and water (n = 1.33)? Must the light start in the glass or the water?
For Problem 22, if the angle of refraction for green light is 14°, what is the refractive index for this wavelength (i.e., color)?
A light beam containing several different colors is incident on a flat piece of glass with θi= 25°. Which of the following statements is correct?(a) The angle of refraction will be greater for red light than for blue light.(b) The angle of refraction will be smaller for red light than for blue
A ray of light is incident upon a still water surface from above. What is the maximum possible angle of refraction?
What is the critical angle for light to stay inside a thin glass rod (n = 1.40) surrounded by air? What if the rod is surrounded by water?
Light is incident on a plane mirror with an angle of incidence θi = 65°. If this experiment takes place underwater (n =1.33), what is the angle of reflection?
Light from a helium-neon laser has a wavelength of 630 nm in a vacuum. What is its wavelength in water (n = 1.33)?
A particular type of glass has an index of refraction of 1.45. What is the frequency of light with a wavelength of 450 nm inside this glass? Recall from Chapter 12 that the speed of a wave is equal to the product fλ.
Suppose light with a wavelength of 560 nm in a vacuum is incident upon fused quartz, which has an index of refraction of 1.46. What will the wavelength of this light be inside the quartz?
Light is refracted through diamond from the air. If the angle of incidence is 30° and the angle of refraction is 12°, what is the speed of light in diamond?
The index of refraction of beer is about 1.35. What is the speed of light in beer?
A light ray is an incident from air onto the surface of a very quiet lake. If the angle of incidence is 35° and the angle of refraction is 25°, what is the index of refraction of the water?
Two plane mirrors are each L = 3.5 m long. They are parallel and are placed 0.25 m apart. If a light ray enters from one end as shown in Figure P24.9, how many reflections occur before it leaves the region between mirrors?
Explain how you could use Snell’s law to measure the speed of light in a piece of plastic.
Explain why dispersion is essential for producing a rainbow.
Explain how you could measure the index of refraction of a liquid.
Explain how a person swimming under water could observe total internal reflection and how she would know when she saw it.
When you observe a fish in a spherical fishbowl, the fish appears larger than it actually is. Why?
In many convenience stores, a mirror is placed in a top corner of the store to allow the clerk to have a full view of the store. Is this mirror spherical concave or convex? Explain your answer.
Underwater, the human eye cannot focus. Why?
When you look at yourself at the center of two plane mirrors forming a 90° corner, your image is not reversed from right to left. In other words, you see yourself like others see you. Using a ray diagram, explain this observation.
Light travels from air into plastic. Which two of the following statements are correct? The results from Question 11 will be useful here.(a) The frequency of the light is greater in air than in plastic.(b) The frequency of the light is smaller in air than in plastic.(c) The frequency of the light
Explain how a refraction experiment could be used to measure the index of refraction of a material as a function of the frequency of the light.
Consider a diverging lens with an object in front of the lens. Prove that the image is always virtual.
When finding the image produced by a lens via ray tracing, it was suggested that you should always draw a ray that goes through the focal point (the focal ray). (In some cases, an extrapolation of the focal ray passes through the focal point.) Which of the following statements gives the most
Explain why reflection from a window consisting of a single pane of glass produces two images.
What is the focal length of a plane mirror? Explain. Consider how to apply the mirror equation to a plane mirror.
Does a plane mirror produce a real image or a virtual image? Explain.
Where is the image formed for an object in front of a plane mirror?
The efficiency of a reversible heat pump is given by Equation 16.28. Real heat pumps, however, may achieve an efficiency of only about 20% of this ideal limit. A heat pump with this reduced efficiency is used to heat a house for which TH = 300 K. What is the lowest value of the temperature of the
A particular engine runs for a period of time during which it is found that W = 2,000 J, QH = 12,000 J, TC = 450 K, and TH = 600 K. (a) Is this engine (i) A reversible heat engine, (ii) An irreversible heat engine, or (iii) Not possible according to the laws of thermodynamics? (b) If your
A cylinder and piston arrangement is made of an excellent conductor in contact with a thermal reservoir at 38°C and is filled with an ideal gas. The gas is slowly compressed in an isothermal process in which 80 J of work are done on the gas. (a) What is the change in entropy of the gas? (b) What
One engine versus two. A Carnot engine produces 1000 J of work when running between reservoirs of 470°C and 100°C. (a) How much heat flows from the hot reservoir? Consider the efficiency. (b) Find the heat flow to the cold reservoir. (c) Consider a second engine that uses the heat flow out of
(a) Calculate the efficiency of a Carnot engine running between a low temperature of 27.0°C and a high temperature of 387°C. Determine the change in efficiency if you were to (b) raise the high temperature by 10.0°C or (c) lower the low temperature by 10.0°C. Which improves the efficiency
Consider the following systems and how closely each approximates a reversible process. Rank them from approximately reversible to irreversible with greatest change in entropy. Consider a video of each in reverse.(a) A child swinging on a swing(b) Mars orbiting the Sun(c) Making a milkshake in a
The Sun emits heat via radiation. Estimate ΔS for the Sun during one day. The surface of the Sun is approximately 6000 K.
A 1.0-kg block of ice is initially at 0°C. Heat is added to this system, and the entropy is increased by 300 J/K. How much of the ice melts?
Sometimes even engineers make mistakes. In 1870, the Eads Bridge was opened for traffic; it was the first bridge to span the Mississippi River at St. Louis and was one of the first larges cale applications of steel. The bridge, which is still in use, has three arches, each about 500 ft (about 150
Mechanical equivalent of heat. When you catch a fast-moving object such as a baseball with bare hands, your hands will feel warm immediately after the catch. Suppose a baseball (m = 0.22 kg) moving at 30 m/s (about 60 mi/h) is caught in one hand. How much will the temperature of the surface of your
A general rule of thumb is that a person should drink about 1 L of fluid for every hour of moderate exercise. If this much fluid is lost as perspiration, what is the approximate amount of heat energy that is lost each hour?
The rims on a regulation basketball court are exactly 10 ft above ground level. Suppose a regulation court is designed to be used at 20°C and the rims are supported by steel posts. On a very hot day, it is found that the rims are 4.0 mm too high. (a) What is the temperature? (b) Do you think it
Apply the results of Example 14.14 to estimate the temperature of the dwarf planet Pluto. In your calculation, assume Pluto is at its mean distance from the Sun, 5.9 × 1012 m. Compare your answer with the measured temperature of Pluto, about 40 K. How do you think astronomers are able to measure
Winter survival. If you are stranded in a cold and snowy environment, it is never a good idea to eat snow for hydration. Estimate the heat energy needed to convert 0.50 kg of snow to water and then heat the water to body temperature. Assume the snow is at 0°C in the survival snow cave you built as
Measuring the temperature of very cold substances can be challenging. Here is one way to measure the temperature of liquid nitrogen. A 50-g flake of aluminum is submerged in liquid nitrogen and left immersed until it is in thermal equilibrium. The flake is then removed and placed in a
Dry ice. At standard atmospheric pressure, the solid form of carbon dioxide called “dry ice” undergoes a phase change not to a liquid, but straight to a gas. This process is called sublimation, and like other phase transitions, heat energy is required. In this case, it is the latent heat of
The Rankine scale. Named after William John Macquorn Rankine (a Scottish engineer and physicist who proposed it in 1859), the Rankine scale is similar to the Kelvin scale in that the zero point is placed at absolute zero, but the size of temperature differences are the same as that of the
An aluminum block slides along a horizontal surface. The block has an initial speed of 10 m/s and an initial temperature of 10°C. The block eventually slides to rest due to friction. Assuming all the initial kinetic energy is converted to heat energy and all this energy stays in the block, what is
A pot of very cold water (0°C) is placed on a stove with the burner adjusted for maximum heat. The water just begins to boil after 2.0 min. How much longer will it take the water to completely boil away?
An incandescent light bulb produces light using a thin tungsten filament (wire) heated to about 3000 K by an electric current that passes through it. A typical filament has a diameter of 10 µm and a length of 2.0 cm. (a) What is the rate at which heat energy is emitted by the filament? (b) When
An ice-cube tray containing 600 g of water at room temperature is placed into a freezer. It is found that all the water becomes solid after 60 min. What is the average rate at which heat energy flows out of the water into the freezer?
A typical coal-burning power plant produces energy at the rate of 1000 MW. How large in area must a solar power plant be to produce the same amount of energy during daylight hours?
(a) What is the approximate energy emitted as black body radiation by a human being each second? (b) What is the black body energy absorbed by a person in 1 s in a room? Why are the answers different?
Estimate the temperature of the Moon’s surface in two cases: (a) When it is facing toward the Sun and (b) When it is facing away from the Sun. Explain qualitatively why your answer in part (b) is probably lower than the actual temperature.
An incandescent light bulb emits 100 W of radiation. If the filament is at a temperature of 3000 K, what is the surface area of the filament?
Estimate the temperature of the surface of Mars. Assume Mars acts as a perfect black body and the only heat input comes from the Sun. How does your result compare with the Earth’s temperature?
In Problem 47, we noted that the intensity of sunlight reaching the Earth is about 1400 W/m2. (a) What is the intensity of sunlight at Mars?(b) The Martian “rovers” (small robots that move about on wheels) sent to explore the surface of Mars use solar panels to charge their batteries. If the
The intensity of sunlight at the top of the Earth’s atmosphere is about 1400 W/m2. (The intensity at the surface of the Earth is somewhat smaller due to absorption and reflection by the atmosphere.) What is the total power emitted by the Sun?
A snake is sunning itself on a rock. (a) If the snake is 0.3 m long, what is the approximate amount of radiation it absorbs from the Sun in 10 min? (b) If no heat flows out of the snake via conduction or by evaporative cooling, how much does its temperature increase during 10 min? Assume all the
A typical incandescent light bulb has a filament temperature of approximately 3000 K. At what wavelength is the intensity of the emitted light highest?
A jogger generates heat energy at a rate of 800 W. If all this energy is removed by sweating, how much water must evaporate from the jogger’s skin each hour?
A winter hiker’s body generates heat at a rate up to a maximum value of 120 W. She is hiking on a brisk day in which the outdoor temperature is -10°C, while wearing a jacket with goose down insulation. How thick must the jacket be so that she can maintain a normal body temperature? Assume her
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