Electromagnetics, Waves, and Optics - Physics
Card 1 of 148
For most people, the nearest distance that objects can be located away from the eye and still seen clearly is 
. This is referred to as the near point; if the object comes any closer, the object cannot be seen clearly. Suppose that a person who needs glasses cannot see objects clearly if they are closer than 
from the eye; that is to say, their near point is 
. A lens with what refractive power is needed in order to correct this person's vision to bring their near point to 
?
For most people, the nearest distance that objects can be located away from the eye and still seen clearly is
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For this question, we're given the definition of near point. We're told what the near point is in the average person, and also the near point for a certain person who can't see well and needs glasses. We're asked to find the refractive power of a lens that will bring this individual's near point to the average, healthy value.
As was stated in the question stem, the near point is the closest distance of an object from the eye where that object can still be seen clearly. In the question, we're told that the normal value for this is 
. Moreover, a person with a near point of 
means that the object will need to be twice as far away, and no closer, to be seen clearly. Thus, in order to correct for this, a lens will be needed.
The idea is to be able to make the individual see things clearly when objects are located 
away. To accomplish this, a lens will need to diffract the light coming from an object 
away. This diffracted light will then need to form an image 
away, which is where this particular individual's near point is.
With this information in hand, we can use the lens-makers equation to solve for the refractive power of the lens.
We know that the object will be located a distance of 
away. Moreover, the image will need to form at a distance of 
away. However, since the image is forming on the same side of the lens that the object is located, the image will be virtual. Thus, the value used in the equation will be 
.
Also, remember that to find refractive power, we'll need to have our units be in meters.
Furthermore, recall that refractive power is equal to the inverse of focal length.
Hence, the power of the refractive lens will need to be 
diopters to correct this person's near point.
For this question, we're given the definition of near point. We're told what the near point is in the average person, and also the near point for a certain person who can't see well and needs glasses. We're asked to find the refractive power of a lens that will bring this individual's near point to the average, healthy value.
As was stated in the question stem, the near point is the closest distance of an object from the eye where that object can still be seen clearly. In the question, we're told that the normal value for this is
The idea is to be able to make the individual see things clearly when objects are located
With this information in hand, we can use the lens-makers equation to solve for the refractive power of the lens.
We know that the object will be located a distance of
Also, remember that to find refractive power, we'll need to have our units be in meters.
Furthermore, recall that refractive power is equal to the inverse of focal length.
Hence, the power of the refractive lens will need to be
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Suppose that car A and car B are both traveling in the same direction. Car A is going 
and is sounding a horn with a frequency of 
. If car B is traveling at a speed of 
in front of car A, what frequency of sound does car B hear?
Note: The speed of sound in air is 
.
Suppose that car A and car B are both traveling in the same direction. Car A is going
Note: The speed of sound in air is
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The important concept being tested in this question is the Doppler effect. When a source of sound waves (or any other wave) is emitted from a source and is moving relative to some observer, the actual frequency of the wave will be different for the observer.
For starters, we'll need to use the Doppler equation.
The trickiest part about this question is to decide whether to add or subtract in both the numerator and denominator. To find the right sign orientation, it's helpful to do a quick thought experiment. Imagine that only one of them is moving and the other is stationary. Decide how that will affect the observed frequency; will it increase it or decrease it? Then repeat for the other one.
First, let's consider the detector (aka observer). We're told that car B, the detector, is traveling ahead of car A and also in the same direction. This means that car B is driving away from car A. So in this situation, is the frequency that car B hears expected to increase or decrease? The answer is that it will decrease. Since car B is traveling away from car A, each successive wave will take longer to reach car B. Hence, we will use subtraction in the numerator because that will make the observed frequency smaller.
Now let's apply this same logic to the denominator, which deals with the source of the sound waves. We know that car A is traveling in the same direction as car B and is behind. This means that car A is traveling toward car B. So from this perspective, each successive wave is expected to get closer together, thus making the time between each wave smaller and the frequency bigger. In the denominator, will adding or subtracting make the observed frequency bigger? The answer is subtraction. By making a smaller number in the denominator, the entire fraction becomes larger.
Keeping this information in mind, we'll need to use subtraction in both the numerator and denominator. Once we plug in the values given in the question stem, we have everything we need to solve for the answer.
The important concept being tested in this question is the Doppler effect. When a source of sound waves (or any other wave) is emitted from a source and is moving relative to some observer, the actual frequency of the wave will be different for the observer.
For starters, we'll need to use the Doppler equation.
The trickiest part about this question is to decide whether to add or subtract in both the numerator and denominator. To find the right sign orientation, it's helpful to do a quick thought experiment. Imagine that only one of them is moving and the other is stationary. Decide how that will affect the observed frequency; will it increase it or decrease it? Then repeat for the other one.
First, let's consider the detector (aka observer). We're told that car B, the detector, is traveling ahead of car A and also in the same direction. This means that car B is driving away from car A. So in this situation, is the frequency that car B hears expected to increase or decrease? The answer is that it will decrease. Since car B is traveling away from car A, each successive wave will take longer to reach car B. Hence, we will use subtraction in the numerator because that will make the observed frequency smaller.
Now let's apply this same logic to the denominator, which deals with the source of the sound waves. We know that car A is traveling in the same direction as car B and is behind. This means that car A is traveling toward car B. So from this perspective, each successive wave is expected to get closer together, thus making the time between each wave smaller and the frequency bigger. In the denominator, will adding or subtracting make the observed frequency bigger? The answer is subtraction. By making a smaller number in the denominator, the entire fraction becomes larger.
Keeping this information in mind, we'll need to use subtraction in both the numerator and denominator. Once we plug in the values given in the question stem, we have everything we need to solve for the answer.
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On planet Borg, a male insect is flying toward his mate at 
while buzzing at 
. The female insect is stationary and is buzzing at 
. What is the speed of the sound on planet Borg?
On planet Borg, a male insect is flying toward his mate at
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To begin, we'll start with the Doppler Effect equation:
Rearrange the equation by solving for 
to get:
Finally we plug in our known values and solve for 
:
To begin, we'll start with the Doppler Effect equation:
Rearrange the equation by solving for
Finally we plug in our known values and solve for
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When a ray of light is reflected off of the surface of another medium, some of the energy from the light is transferred into this medium. As a result, which of the following is true about the reflected light ray?
When a ray of light is reflected off of the surface of another medium, some of the energy from the light is transferred into this medium. As a result, which of the following is true about the reflected light ray?
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For this question, we're told that light is reflected off of the surface of another medium. As a result, the light loses some of its energy, which is transferred into the medium where it reflected.
Because the light has lost some of its energy, we need to determine how the wavelength and frequency of the wave will be affected. To do this, we can recall the equation for the energy of a wave.
Where 
is Planck's constant and 
represents the frequency. We can see that when energy is decreased, the frequency also decreases. Thus, we can eliminate two of the answer choices.
To see how the wavelength changes, it's important to recall the relationship that wavelength and frequency have with each other.
Where 
is the speed of light and 
is the wavelength. Since the light is still traveling in the same medium, its speed will not change. Thus, as the frequency of the wave decreases, the wavelength has to increase. We can alternatively show how all of these variables are related as follows.
So, in summary, when the energy of light decreases, the frequency will decrease and the wavelength will increase.
For this question, we're told that light is reflected off of the surface of another medium. As a result, the light loses some of its energy, which is transferred into the medium where it reflected.
Because the light has lost some of its energy, we need to determine how the wavelength and frequency of the wave will be affected. To do this, we can recall the equation for the energy of a wave.
Where
To see how the wavelength changes, it's important to recall the relationship that wavelength and frequency have with each other.
Where
So, in summary, when the energy of light decreases, the frequency will decrease and the wavelength will increase.
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A 
string under tension is oscillated at the 5th harmonic. What is the wavelength of this oscillation?
A
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Each harmonic has a wavelength that behaves according to the equation
, where 
is the wavelength and 
is the harmonic.
Since this is the 5th harmonic, 
and 
. Solving for wavelength gives 
.
Each harmonic has a wavelength that behaves according to the equation
Since this is the 5th harmonic,
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Suppose that the fifth harmonic of a standing wave contained within a pipe closed at both ends has a wavelength of 
. What is the length of the pipe?
Suppose that the fifth harmonic of a standing wave contained within a pipe closed at both ends has a wavelength of
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For this question, we're told that a standing wave is contained within a pipe closed at both ends. We're also given the wavelength for the fifth harmonic, and are asked to find the length of the pipe.
The first step to solve this problem is to use the equation for a pipe closed at both ends.
Since we're told which harmonic the wave is on, as well as its wavelength, we have everything we need to solve for the length of the pipe.
For this question, we're told that a standing wave is contained within a pipe closed at both ends. We're also given the wavelength for the fifth harmonic, and are asked to find the length of the pipe.
The first step to solve this problem is to use the equation for a pipe closed at both ends.
Since we're told which harmonic the wave is on, as well as its wavelength, we have everything we need to solve for the length of the pipe.
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A pipe has a length of 
. If the pipe is open at both ends, what is the frequency of the third harmonic assuming that the velocity in which sound moves through the air is 
.
A pipe has a length of
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Since the pipe is open at both ends, we can use the equation 
where f is the frequency we are solving for, 
is the number of the harmonic, 
is the velocity at which sound moves through air, and L is the length of the pipe.
We know from the question that:
When we plug in these values into the frequency equation, we get 
as the answer.
Since the pipe is open at both ends, we can use the equation
We know from the question that:
When we plug in these values into the frequency equation, we get
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A convex lens connected to a projector projects an image onto a board of an object that is 
away from the lens. If the object is 
tall and the inverted image is 
tall, what is the focal length of the projector lens?
A convex lens connected to a projector projects an image onto a board of an object that is
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To solve this one will require two equations. First, to find focal length, you will need the lens equation.
But we are only given the object distance, not the image distance. So to find that we need to know the relationship between magnification and object and image distances.
Plug in the quantities we know.
(remember it was inverted)
. Then solve for 
which is 
. So the projector would sit that far from the board.
Now finally we can find the focal length of this lens.
Plugging in:
Solving for 
gives a focal length of 
or 
To solve this one will require two equations. First, to find focal length, you will need the lens equation.
But we are only given the object distance, not the image distance. So to find that we need to know the relationship between magnification and object and image distances.
Plug in the quantities we know.
Now finally we can find the focal length of this lens.
Plugging in:
Solving for
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An object located 
away from a convex lens whose focal point is 
produces an image located at what distance away from the lens?
An object located
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For this question, we'll need to use the thin lens equation in order to determine the image distance from the lens.
Because this is a convex lens, the refracted light will form an image on the side of the lens where light is expected to go (real image). Thus, we know that the focal length should be a positive value. Moreover, the object distance is also positive.
Rearranging the above equation, we can isolate the term for image distance.
Then we can plug in the values given to us in the question stem.
And finally we take the inverse of this value to arrive at the correct answer.
For this question, we'll need to use the thin lens equation in order to determine the image distance from the lens.
Because this is a convex lens, the refracted light will form an image on the side of the lens where light is expected to go (real image). Thus, we know that the focal length should be a positive value. Moreover, the object distance is also positive.
Rearranging the above equation, we can isolate the term for image distance.
Then we can plug in the values given to us in the question stem.
And finally we take the inverse of this value to arrive at the correct answer.
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A light ray is traveling through air hits a transparent material at an angle of 
from the normal. It is then refracted at 
. What is the speed of light in the material?
A light ray is traveling through air hits a transparent material at an angle of
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This problem requires Snell's Law and the corresponding equation:
We know that the index of refraction of air is:
We also know that:
and 
Now we can plug in these values into the Snell's Law equation to find the index of refraction for the transparent material.
Finally, we need to calculate the speed of light moving through this transparent material now that we know the index of refraction for it. To do that, we need to use this equation:
Where 
is the speed of light and 
is the index of refraction. We plug in our known values and get:
This problem requires Snell's Law and the corresponding equation:
We know that the index of refraction of air is:
We also know that:
Now we can plug in these values into the Snell's Law equation to find the index of refraction for the transparent material.
Finally, we need to calculate the speed of light moving through this transparent material now that we know the index of refraction for it. To do that, we need to use this equation:
Where
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A single string of wire has a resistance of 
. If the wire is connected to a 
power source, what is the strength of the magnetic field 
away from the wire?
A single string of wire has a resistance of
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So this is all about the magnetic field strength around a current carrying wire.
The equation for this is:
But you must use Ohm's Law 
in order to find the current in the wire.
Since the wire has 
of resistance and the voltage through the wire is 
, that means the current in the wire is 
.
Being sure to change 
into 
, plug everything in and get the answer, which is
So this is all about the magnetic field strength around a current carrying wire.
The equation for this is:
But you must use Ohm's Law
Since the wire has
Being sure to change
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Suppose that a magnetic field is oriented such that it is pointing directly to the left, as in the picture shown below. If a positively charged particle were to begin traveling through this magnetic field to the right, in which direction would the particle's trajectory begin to curve?
Suppose that a magnetic field is oriented such that it is pointing directly to the left, as in the picture shown below. If a positively charged particle were to begin traveling through this magnetic field to the right, in which direction would the particle's trajectory begin to curve?
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In order to answer this question, it's important to understand the factors that determine the magnetic force experienced by a charge. We can begin by writing out the equation for magnetic force.
As shown in the above equation, the magnetic force is directly proportional to the particle's charge, its velocity, and the strength of the magnetic field itself. But, for the purposes of the this question, the most important factor is the angle of the particle's velocity with respect to the magnetic field.
Notice that if theta is equal to zero, then the sine of theta will be equal to zero as well. This, in turn, will cause the magnetic force to also be zero. This is also true if we were to define theta as 
.
Since the particle is moving in a direction that is parallel to the magnetic field lines but in the opposite direction, we have a situation in which theta is equal to 
. This means that the magnetic force on the particle is zero. As a result, the particle will continue to move through the magnetic field without changing its direction.
In order to answer this question, it's important to understand the factors that determine the magnetic force experienced by a charge. We can begin by writing out the equation for magnetic force.
As shown in the above equation, the magnetic force is directly proportional to the particle's charge, its velocity, and the strength of the magnetic field itself. But, for the purposes of the this question, the most important factor is the angle of the particle's velocity with respect to the magnetic field.
Notice that if theta is equal to zero, then the sine of theta will be equal to zero as well. This, in turn, will cause the magnetic force to also be zero. This is also true if we were to define theta as
Since the particle is moving in a direction that is parallel to the magnetic field lines but in the opposite direction, we have a situation in which theta is equal to
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What is the main difference between electrical and gravitational forces?
What is the main difference between electrical and gravitational forces?
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Electric forces can be attractive or repulsive because charges may be positive or negative. In the case for gravitational forces, there are only attractive forces because mass is always positive.
Electric forces can be attractive or repulsive because charges may be positive or negative. In the case for gravitational forces, there are only attractive forces because mass is always positive.
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An x-ray machine emits electromagnetic photons carrying a frequency of 
. What is the approximate energy carried by each photon?
An x-ray machine emits electromagnetic photons carrying a frequency of
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The energy of a photon of a given frequency is determined by the equation
, where 
is Plank's constant 
So plug in Plank's constant and the frequency of the x-ray photons to get an energy of very near 
The energy of a photon of a given frequency is determined by the equation
So plug in Plank's constant and the frequency of the x-ray photons to get an energy of very near
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A parallel plate capacitor with no dielectric has capacitance 
. The distance between the capacitor plates is halved. What is the new capacitance?
A parallel plate capacitor with no dielectric has capacitance
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The capacitance of a parallel plate capacitor is proportional to the inverse of the distance between the plates. If the distance is halved, the capacitance is doubled.
The capacitance of a parallel plate capacitor is proportional to the inverse of the distance between the plates. If the distance is halved, the capacitance is doubled.
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An RC circuit is connected to a 
power supply. If the resistance of the resistor is 
and the capacitance is 
, how long will it take for this capacitor to become fully charged?
An RC circuit is connected to a
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The formula for finding the voltage of a simple RC circuit is
, where 
is the capacitor voltage, 
is the source voltage, 
is the resistance, and 
is the capacitance.
We want to know when the capacitor will reach the voltage of the power source 
so
and thus 
Using the properties of natural logs yields
Solving for 
yields 
The formula for finding the voltage of a simple RC circuit is
We want to know when the capacitor will reach the voltage of the power source
Using the properties of natural logs yields
Solving for
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Which of the following expressions gives the capacitance for a capacitor in a circuit in which the only factors known are a) the current through the circuit, b) the resistance of the circuit, and c) the charge that has accumulated on the capacitor?
Which of the following expressions gives the capacitance for a capacitor in a circuit in which the only factors known are a) the current through the circuit, b) the resistance of the circuit, and c) the charge that has accumulated on the capacitor?
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In this question, we're given a number of parameters of a circuit and are asked to find how we can use these various parameters to show the capacitance of the circuit's capacitor.
First, recall what a capacitor is; something that stores charge for a given voltage difference. In other words, when there is a voltage difference between the two plates of a capacitor, a certain amount of charge can be stored on these plates. The more charge that can be stored for a given voltage difference, the greater that capacitor's capacitance. This can be shown by the following equation.
From the above expression, 
is the capacitance which we are trying to find a proper expression for. 
is the charge accumulated on the plates, which is one parameter we're given. Voltage, 
, on the other hand, is not provided.
To put the voltage into different terms, we'll need to use Ohm's law, which states the following.
In other words, the voltage is proportional to both the current and the resistance of the circuit.
Since we are given both current and resistance as known parameters in the question stem, we can use these for our final answer. By substituting the 
in the capacitance expression with 
, we obtain the following answer.
In this question, we're given a number of parameters of a circuit and are asked to find how we can use these various parameters to show the capacitance of the circuit's capacitor.
First, recall what a capacitor is; something that stores charge for a given voltage difference. In other words, when there is a voltage difference between the two plates of a capacitor, a certain amount of charge can be stored on these plates. The more charge that can be stored for a given voltage difference, the greater that capacitor's capacitance. This can be shown by the following equation.
From the above expression,
To put the voltage into different terms, we'll need to use Ohm's law, which states the following.
In other words, the voltage is proportional to both the current and the resistance of the circuit.
Since we are given both current and resistance as known parameters in the question stem, we can use these for our final answer. By substituting the
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What size resistor should be connected across the terminals of a 
battery to produce a current of 
?
What size resistor should be connected across the terminals of a
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Ohm's law is 
.
In this case, 
and 
.
Solving for the resistance, 
, we get:
Substitute known values and solve for the unknown resistance:
Ohm's law is
In this case,
Solving for the resistance,
Substitute known values and solve for the unknown resistance:
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A 
battery is connected to a small heater with constant resistance 
. How much current flows through the heater?
A
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Ohm's law relates voltage to current and resistance, 
. To find the current, we simply divide the voltage by the resistance and get 
Ohm's law relates voltage to current and resistance,
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The picture below shows the electron energy levels of a hydrogen atom.
If an electron is excited to the 5th energy level, how many different transitions can it make to return to ground state?
The picture below shows the electron energy levels of a hydrogen atom.
If an electron is excited to the 5th energy level, how many different transitions can it make to return to ground state?
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Electrons don't always drop from the top to the bottom, sometimes they can make 2 or more transitions during the journey. For example, it could drop to the n=4 then to the n=1 levels. Or n=4 to n=2 then n=1. So when you count up all the possible transitions that can be made between n=5 and n=1, you get 10.
Electrons don't always drop from the top to the bottom, sometimes they can make 2 or more transitions during the journey. For example, it could drop to the n=4 then to the n=1 levels. Or n=4 to n=2 then n=1. So when you count up all the possible transitions that can be made between n=5 and n=1, you get 10.
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