GRE Subject Test: Physics - GRE Subject Test: Physics
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A beam of light travels through a medium with index of refraction 
until it reaches an interface with another material, with index of refraction 
. No light is transmitted into the second material. At what angle (measured from the plane of the interface between the two materials) does the beam hit the second material?
A beam of light travels through a medium with index of refraction
Total internal reflection occurs at the angle:
However, this angle is measured from a line normal to the plane of the interface; the angle we want, therefore, is 
, which is 
.
Total internal reflection occurs at the angle:
However, this angle is measured from a line normal to the plane of the interface; the angle we want, therefore, is
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What is the total resistance of a circuit consisting of three resistors in a parallel configuration? The resistors have the following resistance: 
What is the total resistance of a circuit consisting of three resistors in a parallel configuration? The resistors have the following resistance:
The total resistance of a circuit in parallel is given by the following equation:
Now, we just plug in the values, and solve for the total resistance by inverting!
The total resistance of a circuit in parallel is given by the following equation:
Now, we just plug in the values, and solve for the total resistance by inverting!
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What is the total resistance of a circuit containing four resistors (
) hooked up in series.
What is the total resistance of a circuit containing four resistors (
For a circuit in series, the total resistance is simply given by the sum of each individual resistor:
For a circuit in series, the total resistance is simply given by the sum of each individual resistor:
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At one point in time, two twins are 30 years old. At this time, one of them gets on a rocket and travels at 0.8 c, for what he experiences to be 12 years. How old is the twin that remained on Earth when the traveling twin returns home?
At one point in time, two twins are 30 years old. At this time, one of them gets on a rocket and travels at 0.8 c, for what he experiences to be 12 years. How old is the twin that remained on Earth when the traveling twin returns home?
The equation for time dilation is given by:
In this problem v=0.8c T=12. Using this equation, we get:
Adding 20 years to the age initial age of 30:
The Earth-twin is now 50.
The equation for time dilation is given by:
In this problem v=0.8c T=12. Using this equation, we get:
Adding 20 years to the age initial age of 30:
The Earth-twin is now 50.
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At one point in time, two twins are 30 years old. At this time, one of them gets on a rocket and travels at 0.8 c, for what he experiences to be 12 years. How old is the twin that remained on Earth when the traveling twin returns home?
At one point in time, two twins are 30 years old. At this time, one of them gets on a rocket and travels at 0.8 c, for what he experiences to be 12 years. How old is the twin that remained on Earth when the traveling twin returns home?
The equation for time dilation is given by:
In this problem v=0.8c T=12. Using this equation, we get:
Adding 20 years to the age initial age of 30:
The Earth-twin is now 50.
The equation for time dilation is given by:
In this problem v=0.8c T=12. Using this equation, we get:
Adding 20 years to the age initial age of 30:
The Earth-twin is now 50.
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If the temperature of a blackbody doubles, what occurs to the wavelength of maximum emission?
If the temperature of a blackbody doubles, what occurs to the wavelength of maximum emission?
This is an application of Wein's Law that states the following:
, where 
is the wavelength of maximum emission of the object (measured in 
), and 
is the temperature in 
. Since the wavelength and the temperature are inversely proportional, if we double the temperature, we must cut the wavelength by the same proportion. Therefore, the temperature must be halved.
This is an application of Wein's Law that states the following:
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By what factor will the energy emitted each second off the surface of a blackbody change if the the temperature of the object is tripled?
By what factor will the energy emitted each second off the surface of a blackbody change if the the temperature of the object is tripled?
Stefan-Boltzmann's equation for a blackbody states:
, where 
is the energy emitted each second, 
is the Stefan-Boltzmann constant, and 
is the temperature of the blackbody. Therefore, if we triple the temperature, the energy will increase by a factor of 
Stefan-Boltzmann's equation for a blackbody states:
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Using the kinetic theory of gas, what is the fundamental property of a planet that dictates if it is able to retain an atmosphere?
Using the kinetic theory of gas, what is the fundamental property of a planet that dictates if it is able to retain an atmosphere?
The kinetic theory of gas states:
. Whenever the velocity of the individual gas particles is larger than the escape speed of the planet,
, the gas particles will leak into space and deplete the atmosphere. The physical property that determines this is the mass of the planet.
The kinetic theory of gas states:
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If the temperature of a blackbody doubles, what occurs to the wavelength of maximum emission?
If the temperature of a blackbody doubles, what occurs to the wavelength of maximum emission?
This is an application of Wein's Law that states the following:
, where is the wavelength of maximum emission of the object (measured in ), and is the temperature in . Since the wavelength and the temperature are inversely proportional, if we double the temperature, we must cut the wavelength by the same proportion. Therefore, the temperature must be halved.
This is an application of Wein's Law that states the following:
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By what factor will the energy emitted each second off the surface of a blackbody change if the the temperature of the object is tripled?
By what factor will the energy emitted each second off the surface of a blackbody change if the the temperature of the object is tripled?
Stefan-Boltzmann's equation for a blackbody states:
, where is the energy emitted each second, is the Stefan-Boltzmann constant, and is the temperature of the blackbody. Therefore, if we triple the temperature, the energy will increase by a factor of
Stefan-Boltzmann's equation for a blackbody states:
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Using the kinetic theory of gas, what is the fundamental property of a planet that dictates if it is able to retain an atmosphere?
Using the kinetic theory of gas, what is the fundamental property of a planet that dictates if it is able to retain an atmosphere?
The kinetic theory of gas states:
. Whenever the velocity of the individual gas particles is larger than the escape speed of the planet,
, the gas particles will leak into space and deplete the atmosphere. The physical property that determines this is the mass of the planet.
The kinetic theory of gas states:
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A beam of light travels through a medium with index of refraction until it reaches an interface with another material, with index of refraction . No light is transmitted into the second material. At what angle (measured from the plane of the interface between the two materials) does the beam hit the second material?
A beam of light travels through a medium with index of refraction
Total internal reflection occurs at the angle:
However, this angle is measured from a line normal to the plane of the interface; the angle we want, therefore, is , which is .
Total internal reflection occurs at the angle:
However, this angle is measured from a line normal to the plane of the interface; the angle we want, therefore, is
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The focal length of a thin convex lens is 
. A candle is placed 
to the left of the lens. Approximately where is the image of the candle?
The focal length of a thin convex lens is
Because the object is beyond 2 focal lengths of the lens, the image must be between 1 and 2 focal lengths on the opposite side. Therefore, the image must be between 
on the right side of the lens.
Alternatively, one can apply the thin lens equation:
Where 
is the object distance 
and 
is the focal length 
. Plug in these values and solve.
Because the object is beyond 2 focal lengths of the lens, the image must be between 1 and 2 focal lengths on the opposite side. Therefore, the image must be between
Alternatively, one can apply the thin lens equation:
Where
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A candle 
tall is placed 
to the left of a thin convex lens with focal length 
. What is the height and orientation of the image created?
A candle
First, find the image distance 
from the thin lens equation:
Magnification of a lens is given by:
Where 
and 
are the image height and object height, respectively. The given object height is 
, which we can use to solve for the image height:
Because the sign is negative, the image is inverted.
First, find the image distance
Magnification of a lens is given by:
Where
Because the sign is negative, the image is inverted.
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Sirius is a binary star system, consisting of two white dwarfs with an angular separation of 3 arcseconds. What is the approximate minimum diameter lens needed to resolve the two stars in Sirius for an observation at 
?
Sirius is a binary star system, consisting of two white dwarfs with an angular separation of 3 arcseconds. What is the approximate minimum diameter lens needed to resolve the two stars in Sirius for an observation at
The Rayleigh Criterion gives the diffraction limit on resolution of a particular lens at a particular wavelength:
Where theta is the angular resolution in radians, 
is the wavelength of light, and 
is the diameter the lens in question. Solving for 
and converting 3 arcseconds into radians, one can approximate the diameter to be about 
:
The Rayleigh Criterion gives the diffraction limit on resolution of a particular lens at a particular wavelength:
Where theta is the angular resolution in radians,
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A black hole is an object whose gravitational field is so strong that even light cannot escape. Assuming no change in radius, approximately how much mass would our Sun have to have in order to become a black hole?
Sun's radius: 
A black hole is an object whose gravitational field is so strong that even light cannot escape. Assuming no change in radius, approximately how much mass would our Sun have to have in order to become a black hole?
Sun's radius:
To derive the Schwarzschild radius of a black hole, set gravitational potential energy equal to kinetic energy at escape velocity:
Solving for mass of the black hole:
To derive the Schwarzschild radius of a black hole, set gravitational potential energy equal to kinetic energy at escape velocity:
Solving for mass of the black hole:
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The difference in age for the twins in the Twin Paradox occurs during which key moment in the trip?
The difference in age for the twins in the Twin Paradox occurs during which key moment in the trip?
While moving clocks do in fact record time moving at different rates, the time dilation works both ways. This means that a stationary person will view a moving clock ticking slower, but at the same time, a person moving alongside the moving clock will see the stationary clock ticking slower. However, clocks experiencing great accelerations will be permanently changed, "losing" time relative to a clock not being accelerated. Thus, the age difference occurs during the portion of the journey when the traveler accelerates at a great rate in order to return to Earth.
While moving clocks do in fact record time moving at different rates, the time dilation works both ways. This means that a stationary person will view a moving clock ticking slower, but at the same time, a person moving alongside the moving clock will see the stationary clock ticking slower. However, clocks experiencing great accelerations will be permanently changed, "losing" time relative to a clock not being accelerated. Thus, the age difference occurs during the portion of the journey when the traveler accelerates at a great rate in order to return to Earth.
Compare your answer with the correct one above
At one point in time, two twins are 30 years old. At this time, one of them gets on a rocket and travels at 0.8 c, for what he experiences to be 12 years. How old is the twin that remained on Earth when the traveling twin returns home?
At one point in time, two twins are 30 years old. At this time, one of them gets on a rocket and travels at 0.8 c, for what he experiences to be 12 years. How old is the twin that remained on Earth when the traveling twin returns home?
The equation for time dilation is given by:
In this problem v=0.8c T=12. Using this equation, we get:
Adding 20 years to the age initial age of 30:
The Earth-twin is now 50.
The equation for time dilation is given by:
In this problem v=0.8c T=12. Using this equation, we get:
Adding 20 years to the age initial age of 30:
The Earth-twin is now 50.
Compare your answer with the correct one above
A black hole is an object whose gravitational field is so strong that even light cannot escape. Assuming no change in radius, approximately how much mass would our Sun have to have in order to become a black hole?
Sun's radius:
A black hole is an object whose gravitational field is so strong that even light cannot escape. Assuming no change in radius, approximately how much mass would our Sun have to have in order to become a black hole?
Sun's radius:
To derive the Schwarzschild radius of a black hole, set gravitational potential energy equal to kinetic energy at escape velocity:
Solving for mass of the black hole:
To derive the Schwarzschild radius of a black hole, set gravitational potential energy equal to kinetic energy at escape velocity:
Solving for mass of the black hole:
Compare your answer with the correct one above
The difference in age for the twins in the Twin Paradox occurs during which key moment in the trip?
The difference in age for the twins in the Twin Paradox occurs during which key moment in the trip?
While moving clocks do in fact record time moving at different rates, the time dilation works both ways. This means that a stationary person will view a moving clock ticking slower, but at the same time, a person moving alongside the moving clock will see the stationary clock ticking slower. However, clocks experiencing great accelerations will be permanently changed, "losing" time relative to a clock not being accelerated. Thus, the age difference occurs during the portion of the journey when the traveler accelerates at a great rate in order to return to Earth.
While moving clocks do in fact record time moving at different rates, the time dilation works both ways. This means that a stationary person will view a moving clock ticking slower, but at the same time, a person moving alongside the moving clock will see the stationary clock ticking slower. However, clocks experiencing great accelerations will be permanently changed, "losing" time relative to a clock not being accelerated. Thus, the age difference occurs during the portion of the journey when the traveler accelerates at a great rate in order to return to Earth.
Compare your answer with the correct one above