Snell's Law and Conservation of Energy ```Name: Leo Status: other Age: N/A Location: N/A Country: N/A Date: N/A ``` Question: Assume the follow condition: A Prism in a vacuum Now shoot a ray of light through the prism. We know through observation that the light will slow relative to the refractive index. However, when the ray of light leaves the prism it speed back up to 3.0x 10^8 m/s when no additional energy is added to the system. How can this be? I know that the conservation of energy must be true, so what am I missing? Replies: The energy of the photon of light does not depend on its velocity. It does depend on its frequency (red, blue etc). So the next question you would ask is why is this? But remember a photon has no "rest" mass, no mass at all if it were not moving, and it has to be moving. Steve Ross Leo, When we consider light traveling through a prism at the level of individual atoms, the contradiction goes away. A beam of light is made of a great many little bundles of light energy called photons. More photons means brighter light. Higher energy photons means higher frequency light (i.e. a different color). When these millions, or perhaps billions, of photons travel through a prism, photons of light will definitely crash into prism atoms. A photon that hits an atom is absorbed. If it is a frequency (i.e. color) that the atom can hold, the light energy stays in the atom, making the atom bounce around. This is how light heats things up. In most cases, however, the photon does not stay inside the atom. It is quickly released. The photon travels on until it hits another atom. All these small delays within the atoms are what slows down the photons. Consider two cars being driven at 45 miles per hour through town. The first car hits all green lights; there are no delays. The second car hits many red lights; there are many delays. Both cars move at the same speed (45mph), but the delayed car travels more slowly. Dr. Ken Mellendorf Physics Instructor Illinois Central College If photons were massive, we would indeed have a big problem here! However, they are massless and the energy of a single photon is related only to its frequency. The frequency is unchanged during all the transitions. Energy = (Plancks constant) * (frequency) It is also possible to re-write the energy (or frequency) in terms of the velocity and wavelength of the light. The velocity changes during the transitions, going from fast to slow and back to fast as the photons leave the substance. However, the wavelength of the light also changes by the same factor during the transitions going from long to short and back to long. E = (Planck's constant) * (Velocity) / (wavelength) = (Planck's Constant) * (Velocity/Index of Refraction) / (Wavelength/Index of Refraction) The Index of Refraction cancels itself out and you are left with the same before and after any transition. All in all, the energy remains constant. Michael S. Pierce Materials Science Division Argonne National Laboratory Click here to return to the Physics Archives

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