Light - Momentum and Energy
Someone asked this question on my last/first sciencey post. I decided that it was too long an answer to just leave in the comments, so here it is, question and answer:
Question: What happens to light (a photon) as it passes through a transparent medium? We know that photons do not have a mass, however they do have energy and momentum. If we consider the equation: E = m c^2 / sqrt(1 - v^2/c^2), a massless particle, must always move at the speed of light (in a vacuum), c [E = 0/0]. But what happens when light passes from a vacuum into air, or from air into glass? Does the photon slow down, causing the bending of light? And if so, what happens to its energy (as E would equal zero if the velocity were anything but c)?
Answer:
This is one of those wave/particle we'll use the model that arbitrarily suites us best questions. Basically, light behaves as a particle in some instances and as a wave in others or, sometimes, as both at the same time. Apart from refraction (bending), though, the answer involves mostly particle light.
The momentum of a single photon is given by Plank's constant divided by it's wavelength, which can be re-written as Plank's constant multiplied by it's frequency (the number of oscillations per second) divided by it's speed.
Experimentally, it has been observed that when light passes between mediums, it's velocity changes and it's wavelength changes. Frequency stays the same. Because momentum depends on wavelength or velocity, then the momentum must also change when light enters a different medium. So where does the 'lost' momentum go when light enters glass from air (for example)? Well, quite simply, it's transferred TO the glass. Now, obviously we don't see bits of glass flying around when light hits them, and that's because the momentum of light is very small (plank's constant is very small, think zero point thirty-three zeros followed by six, six, two, six), but this is a very real phenomena and They (NASA, ESA, miscellaneous researchers) are trying to figure out a way to harness the pushing power of light to propel a spaceship. The current plans include very large solar sails.
As for energy - well the energy of a single photon is given by Plank's constant multiplied by it's frequency. Because frequency doesn't depend on the medium, the energy of the photon doesn't change when it enters a different medium.
Finally, light 'bending' when it enters a different medium is due to it behaving like a wave. Here is a picture which I think illustrates refraction quite well. The lines are the crests of waves (think of waves in water) also called wavefronts. Jumping back to thinking about light, medium A could be air and medium B could be water and the direction of travel of the wave is perpendicular (at right angles) to the wavefronts and could be going either from A to B or from B to A (the result would look the same at any snapshop point in time). In medium B, the wave travels at a slower speed and the wave fronts are closer together, giving a shorter wavelength. The image makes this clearer.
Hopefully that answers the questions.
Question: What happens to light (a photon) as it passes through a transparent medium? We know that photons do not have a mass, however they do have energy and momentum. If we consider the equation: E = m c^2 / sqrt(1 - v^2/c^2), a massless particle, must always move at the speed of light (in a vacuum), c [E = 0/0]. But what happens when light passes from a vacuum into air, or from air into glass? Does the photon slow down, causing the bending of light? And if so, what happens to its energy (as E would equal zero if the velocity were anything but c)?
Answer:
This is one of those wave/particle we'll use the model that arbitrarily suites us best questions. Basically, light behaves as a particle in some instances and as a wave in others or, sometimes, as both at the same time. Apart from refraction (bending), though, the answer involves mostly particle light.
The momentum of a single photon is given by Plank's constant divided by it's wavelength, which can be re-written as Plank's constant multiplied by it's frequency (the number of oscillations per second) divided by it's speed.
Experimentally, it has been observed that when light passes between mediums, it's velocity changes and it's wavelength changes. Frequency stays the same. Because momentum depends on wavelength or velocity, then the momentum must also change when light enters a different medium. So where does the 'lost' momentum go when light enters glass from air (for example)? Well, quite simply, it's transferred TO the glass. Now, obviously we don't see bits of glass flying around when light hits them, and that's because the momentum of light is very small (plank's constant is very small, think zero point thirty-three zeros followed by six, six, two, six), but this is a very real phenomena and They (NASA, ESA, miscellaneous researchers) are trying to figure out a way to harness the pushing power of light to propel a spaceship. The current plans include very large solar sails.
As for energy - well the energy of a single photon is given by Plank's constant multiplied by it's frequency. Because frequency doesn't depend on the medium, the energy of the photon doesn't change when it enters a different medium.
Finally, light 'bending' when it enters a different medium is due to it behaving like a wave. Here is a picture which I think illustrates refraction quite well. The lines are the crests of waves (think of waves in water) also called wavefronts. Jumping back to thinking about light, medium A could be air and medium B could be water and the direction of travel of the wave is perpendicular (at right angles) to the wavefronts and could be going either from A to B or from B to A (the result would look the same at any snapshop point in time). In medium B, the wave travels at a slower speed and the wave fronts are closer together, giving a shorter wavelength. The image makes this clearer.
Hopefully that answers the questions.