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Why is it that photons can move at the speed of light, but other particles cannot?
Photons can move at the speed of light because they have no mass. Anything with mass can not be accelerated to the speed of light—it takes an infinite amount of energy to do so. We can get very close, but never exactly there.
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A ray of light strikes the surface of a pond at an angle of to the vertical. If it is moving from air to water, what will be the angle of refraction?
For this problem, use Snell's law: .
In this equation, is the index of refraction and
is the angle of refraction to the vertical. Using the values given in the question, we can find the resultant angle of refraction.
Take the arcsin of both sides to find the value of .
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A new crystal is discovered with an index of refraction of . What is the speed of light in this crystal?
The relationship between speed of light and the index of refraction is:
In this formula, is the speed of light in a vacuum,
is the observed speed of light in the substance, and
is the index of refraction. We are given the speed of light in a vacuum and the index of refraction, allowing us ot solve for the speed of light in the crystal.
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A new crystal is discovered. The speed of light inside of this crystal is measured to be . What is the index of refraction of the crystal?
The relationship between speed of light and the index of refraction is:
In this formula, is the speed of light in a vacuum,
is the observed speed of light in the substance, and
is the index of refraction. We given the values for the speed of light in the crystal and the speed of light in a vacuum, allowing us to solve for the index of refraction.
Plug in our given values and solve.
Note that the index of refraction is a ratio of two velocities, and therefore has no units.
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A certain gas has an index of refraction of . What is the speed of light in the gas?
The index of refraction is defined as the relationship between the speed of light in a vacuum over the speed of light in the gas/liquid/solid.
We know the index of refraction of the gas, and the speed of light in a vacuum. Using these values, we can solve for the speed of light in the gas.
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A beam of light hits a crystal at an angle of to the normal. The light is refracted in the crystal and changes to an angle of
to the normal. What is the index of refraction of the crystal?
To solve this problem, use Snell's law:
Remember that air has an index of refraction of . Using this value and the given values for the angle of incidence and angle of refraction, we can find the index of refraction of the crystal.
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A beam of light hits a crystal at an angle of incidence of . If the index of refraction of the crystal is
, what is the angle of refraction inside of the crystal?
To solve this problem, use Snell's law:
Remember that air has an index of refraction of . We know the index of refraction for each material and the initial angle of incidence. Using these values, we can find the angle of refraction.
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Light strikes a crystal from the air at an angle of to the normal. Inside the crystal, the angle of light is
to the normal. What is the index of refraction in the crystal?
To solve this problem, use Snell's law:
We are given the angle of incidence and the angle of refraction. The index of refraction for air is . Using these values, we can find the index of refraction in the crystal.
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A microwave has a wavelength of . What is the speed of the wave?
Since a microwave is a part of the electromagnetic spectrum, its velocity will be equal to the speed of light:
Any wave on the electromagnetic spectrum will have the same velocity, though their wavelengths and frequencies will vary, defining their individual characteristics.
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A microwave has a frequency of . A gamma ray has a frequency of
. Which one has a greater speed?
Both of these waves are on the electromagnetic spectrum. Any wave on the spectrum will have the same speed, the speed of light.
Radio waves, microwaves, infrared waves, visible light, ultraviolet light, and gamma rays are all on the spectrum. They all have the same ultimate speed, but vary in their wavelengths, frequencies, and energy levels.
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The frequency of a particular photon of infrared light is . What is the wavelength of the photon?
The relationship between wavelength, frequency, and velocity is:
In this case, because infrared light is a part of the electromagnetic spectrum, we would use for
.
We are given the speed of light and the frequency of the photon. Using these values, we can solve for the wavelength.
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An electromagnetic wave travels with a frequency of . What is the wavelength of the wave?
The relationship between velocity, frequency, and wavelength of a waveform is given by the formula:
In this case, we are dealing with an electromagnetic wave. All electromagnetic waves travel at the same velocity: the speed of light.
Using this value and the given frequency of the wave, we can solve for the wavelength.
Wavelength is traditionally reported in nanometers, corresponding to .
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Radio waves and X-rays are both on the electromagnetic spectrum. Which of the following statements is true?
Any wave on the electromagnetic spectrum will travel at the same constant speed, the speed of light. Each type of wave is determined by changes in the frequency, wavelength, and energy, but these factors always reflect a constant velocity. The types of waves in the electromagnetic spectrum are radio waves, microwaves, infrared light, visible light, ultraviolet light, X-rays, and gamma rays. Radio waves will have the largest wavelength, smallest frequency, and lowest energy. Gamma rays will have the smallest wavelength, highest frequency, and greatest energy.
The inverse relationship between frequency and wavelength means that the velocity can remain constant.
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