CK-12 People's Physics Book Version 2
Page 19
b) For the beam of light to never leave the water, . For this to be true, . So, we will use following equation and then substitute for . This will allow us to solve for which will, in turn, allow for us to solve for James' distance from the edge of the pool.
Now we can use trigonometry to get our answer.
Light Problem Set
Which corresponds to light of longer wavelength, UV rays or IR rays?
Which corresponds to light of lower frequency, rays or millimeter-wavelength light?
Approximately how many blue wavelengths would fit end-to-end within a space of one millimeter?
Approximately how many short (“hard”) rays would fit end-to-end within the space of a single red wavelength?
Calculate the frequency in of a typical green photon emitted by the Sun. What is the physical interpretation of this (very high) frequency? (That is, what is oscillating?)
FM radio stations list the frequency of the light they are emitting in MHz, or millions of cycles per second. For instance, would operate at a frequency of . What is the wavelength of the radio-frequency light emitted by this radio station? Compare this length to the size of your car’s antenna, and make an argument as to why the length of a car’s antenna should be about the wavelength of the light you are receiving.
Consult the color table for human perception under the ‘Key Concepts’ section and answer the questions which follow. Your coat looks magenta in white light. What color does it appear in blue light? In green light?
Which secondary color would look black under a blue light bulb?
You look at a cyan-colored ribbon under white light. Which of the three primary colors is your eye not detecting?
Consider the following table, which states the indices of refraction for a number of materials.
Material
vacuum
air
water
typical glass
cooking oil
heavy flint glass
sapphire
diamond
For which of these materials is the speed of light slowest?
Which two materials have the most similar indices of refraction?
What is the speed of light in cooking oil?
A certain light wave has a frequency of . What is the wavelength of this wave in empty space? In water?
A light ray bounces off a fish in your aquarium. It travels through the water, into the glass side of the aquarium, and then into air. Draw a sketch of the situation, being careful to indicate how the light will change directions when it refracts at each interface. Include a brief discussion of why this occurs.
Why is the sky blue? Find a family member who doesn’t know why the sky is blue and explain it to them. Ask them to write a short paragraph explaining the situation and include a sketch.
Describe the function of the dye in blue jeans. What does the dye do to each of the various colors of visible light?
A light ray goes from the air into the water. If the angle of incidence is , what is the angle of refraction?
In the “disappearing test tube” demo, a test tube filled with vegetable oil vanishes when placed in a beaker full of the same oil. How is this possible? Would a diamond tube filled with water and placed in water have the same effect?
Imagine a thread of diamond wire immersed in water. Can such an object demonstrate total internal reflection? If so, what is the critical angle? Draw a picture along with your calculations.
A light source sits in a tank of water, as shown. If one of the light rays coming from inside the tank of water hits the surface at , as measured from the normal to the surface, at what angle will it enter the air?
Now suppose the incident angle in the water is as measured from the normal. What is the refracted angle? What problem arises?
Find the critical angle for the water-air interface. This is the incident angle that corresponds to the largest possible refracted angle, .
Nisha stands at the edge of an aquarium deep. She shines a laser at a height of that hits the water of the pool from the edge. Draw a diagram of this situation. Label all known lengths.
How far from the edge of the pool will the light hit bottom?
If her friend, James, were at the bottom and shined a light back, hitting the same spot as Nisha’s, how far from the edge would he have to be so that the light never leaves the water?
Here’s an example of the “flat mirror problem.” Marjan is looking at herself in the mirror. Assume that her eyes are 10 cm below the top of her head, and that she stands tall. Calculate the minimum length flat mirror that Marjan would need to see her body from eye level all the way down to her feet. Sketch at least ray traces from her eyes showing the topmost, bottommost, and middle rays. In the following five problems, you will do a careful ray tracing with a ruler (including the extrapolation of rays for virtual images). It is best if you can use different colors for the three different ray tracings. When sketching diverging rays, you should use dotted lines for the extrapolated lines behind a mirror or in front of a lens in order to produce the virtual image. When comparing measured distances and heights to calculated distances and heights, values within % are considered “good.” Use the following cheat sheet as your guide.
CONVERGING(CONCAVE)MIRRORS Ray #1: Leaves tip of candle, travels parallel to optic axis, reflects back through focus.
Ray #2: Leaves tip, travels through focus, reflects back parallel to optic axis.
Ray #3: Leaves tip, reflects off center of mirror with an angle of reflection equal to the angle of incidence.
DIVERGING (CONVEX) MIRRORS Ray #1: Leaves tip, travels parallel to optic axis, reflects OUTWARD by lining up with focus on the OPPOSITE side as the candle.
Ray #2: Leaves tip, heads toward the focus on the OPPOSITE side, and emerges parallel to the optic axis.
Ray #3: Leaves tip, heads straight for the mirror center, and reflects at an equal angle.
CONVERGING (CONVEX) LENSES Ray #1: Leaves tip, travels parallel to optic axis, refracts and travels through to the focus.
Ray #2: Leaves tip, travels through focus on same side, travels through lens, and exits lens parallel to optic axis on opposite side.
Ray #3: Leaves tip, passes straight through center of lens and exits without bending.
DIVERGING (CONCAVE) LENSES Ray #1: Leaves tip, travels parallel to optic axis, refracts OUTWARD by lining up with focus on the SAME side as the candle.
Ray #2: Leaves tip, heads toward the focus on the OPPOSITE side, and emerges parallel from the lens.
Ray #3: Leaves tip, passes straight through the center of lens and exits without bending.
Consider a concave mirror with a focal length equal to two units, as shown below. Carefully trace three rays coming off the top of the object in order to form the image.
Measure and .
Use the mirror/lens equation to calculate .
Find the percent difference between your measured and your calculated .
Measure the magnification and compare it to the calculated magnification.
Consider a concave mirror with unknown focal length that produces a virtual image six units behind the mirror. Calculate the focal length of the mirror and draw an at the position of the focus.
Carefully trace three rays coming off the top of the object and show how they converge to form the image.
Does your image appear bigger or smaller than the object? Calculate the expected magnification and compare it to your sketch.
Consider a convex mirror with a focal length equal to two units. Carefully trace three rays coming off the top of the object and form the image.
Measure and .
Use the mirror/lens equation to calculate .
Find the percent difference between your measured and your calculated .
Measure the magnification and compare it to the calculated magnification.
Consider a converging lens with a focal length equal to three units. Carefully trace three rays coming off the top of
the object and form the image.
Measure and .
Use the mirror/lens equation to calculate .
Find the percent difference between your measured and your calculated .
Measure the magnification and compare it to the calculated magnification.
Consider a diverging lens with a focal length equal to four units. Carefully trace three rays coming off the top of the object and show where they converge to form the image.
Measure and .
Use the mirror/lens equation to calculate .
Find the percent difference between your measured and your calculated .
f. Measure the magnification and compare it to the calculated magnification.
A piece of transparent goo falls on your paper. You notice that the letters on your page appear smaller than they really are. Is the goo acting as a converging lens or a diverging lens? Explain. Is the image you see real or virtual? Explain.
An object is placed in front of a lens. An image of the object is located behind the lens. Is the lens converging or diverging? Explain your reasoning.
What is the focal length of the lens?
Little Red Riding Hood (aka Hood) gets to her grandmother’s house only to find the Big Bad Wolf (aka BBW) in her place. Hood notices that BBW is wearing her grandmother’s glasses and it makes the wolf’s eyes look magnified (bigger). Are these glasses for near-sighted or far-sighted people? For full credit, explain your answer thoroughly. You may need to consult some resources online.
Create a diagram of how these glasses correct a person’s vision.
To the right is a diagram showing how to make a “ghost light bulb.” The real light bulb is below the box and it forms an image of the exact same size right above it. The image looks very real until you try to touch it. What is the focal length of the concave mirror?
In your laboratory, light from a laser shines on two thin slits. The slits are separated by . A flat screen is located behind the slits. Find the angle made by rays traveling to the third maximum off the optic axis.
How far from the center of the screen is the third maximum located?
How would your answers change if the experiment was conducted underwater?
Again, in your laboratory, light falls on a pinhole in diameter. Diffraction maxima are observed on a screen away. Calculate the distance from the central maximum to the first interference maximum.
Qualitatively explain how your answer to (a) would change if you …
i. …move the screen closer to the pinhole. ii. …increase the wavelength of light. iii. …reduce the diameter of the pinhole.
You are to design an experiment to determine the index of refraction of an unknown liquid. You have a small square container of the liquid, the sides of which are made of transparent thin plastic. In addition you have a screen, laser, ruler and protractors. Design the experiment. Give a detailed procedure; include a diagram of the experiment. Tell which equations you would use and give some sample calculations. Finally, tell in detail what level of accuracy you can expect and explain the causes of lab error in order of importance.
Students are doing an experiment with a Helium-neon laser, which emits light. They use a diffraction grating with lines/cm. They place the laser from a screen and the diffraction grating, initially, from the screen. They observe the first and then the second order diffraction peaks. Afterwards, they move the diffraction grating closer to the screen. Fill in the table below with the expected data based on your understanding of physics. Hint: find the general solution through algebra before plugging in any numbers.
Distance of diffraction grating to screen Distance from central maximum to first order peak
Plot a graph of the first order distance as a function of the distance between the grating and the screen.
How would you need to manipulate this data in order to create a linear plot?
In a real experiment what could cause the data to deviate from the expected values? Explain.
What safety considerations are important for this experiment?
f. Explain how you could use a diffraction grating to calculate the unknown wavelength of another laser.
An abalone shell, when exposed to white light, produces an array of cyan, magenta and yellow. There is a thin film on the shell that both refracts and reflects the light. Explain clearly why these and only these colors are observed.
A crystal of silicon has atoms spaced apart. It is analyzed as if it were a diffraction grating using an ray of wavelength . Calculate the angular separation between the first and second order peaks from the central maximum.
Laser light shines on an oil film sitting on water. At a point where the film is thick, a order dark fringe is observed. What is the wavelength of the laser?
You want to design an experiment in which you use the properties of thin film interference to investigate the variations in thickness of a film of water on glass. List all the necessary lab equipment you will need.
Carefully explain the procedure of the experiment and draw a diagram.
List the equations you will use and do a sample calculation using realistic numbers.
Explain what would be the most significant errors in the experiment and what effect they would have on the data.
Answers to Selected Problems
.
.
blue wavelengths
rays
.
.
.
b. vacuum & air c.
.
.
Absorbs red and green.
.
a. b. No such angle
c.
b. c.
C. units e.
a. units b. bigger;
c. units d.
c. units e.
c. units
.
b.
.
a. b.
c.
a.
.
.
Chapter 19: Fluids Version 2
The Big Idea
In studying fluids we apply the concepts of force, momentum, and energy -- which we have learned previously -- to new phenomena. Since fluids are made from a large number of individual molecules, we have to look at their behavior as an ensemble and not individually. For this reason, we use the concept of conservation of energy density in place of conservation of energy. Energy density is energy divided by volume.
Key Concepts
The pressure of a fluid is a measure of the forces exerted by a large number of molecules when they collide and bounce off its boundary. The unit of pressure is the Pascal (Pa).
Mass density represents the amount of mass in a given volume. We also speak of fluids as having gravitational potential energy density, kinetic energy density, and momentum density. These represent the amount of energy or momentum possessed by a given volume of fluid. If we multiply these quantities by a volume, they will be completely identical to their versions from earlier chapters.
Pressure and energy density have the same units: . The pressure of a fluid can be thought of as an arbitrary level of energy density.
For static fluids and fluids flowing in a steady state all locations in the connected fluid system must have the same total energy density. This means that the algebraic sum of pressure, kinetic energy density and gravitational energy density equals zero. Changes in fluid pressure must be equal to changes in energy density (kinetic and/or gravitational).
Liquids obey a continuity equation which is based on the fact that liquids are very difficult to compress. This means that the total volume of a fluid will remain constant in most situations. Imagine trying to compress a filled water balloon!
The specific gravity of an object is the ratio of the density of that object to the density of water. Objects with specific gravities greater than (i.e., greater than water) will sink in water; otherwise, they will float. The density of fresh water is .
Key Equations and Definitions
Key Applications
> In a fluid at rest, pressure increases linearly with depth – this is due to the weight of the water above it.
Archimedes’ Principle states that the upward buoyant force on an object in the water is equal to the weight of the displaced volume of water. The reason for this upward force is that the bottom of the object is at lower depth, and therefore higher pressure, than the top. If an object has a higher density than the density of water, the weight of the displaced volume will be less than the object’s weight, and the object will sink. Otherwise, the object will float.
Pascal’s Principle reminds us that, for a fluid of uniform pressure, the force exerted on a small area in contact with the fluid will be smaller than the force exerted on a large area. Thus, a small force applied to a small area in a fluid can create a large force on a larger area. This is the principle behind hydraulic machinery.