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- 1. What is Speed of Light? Speed OF Light Chapters
- 2. 1. Reminders: light 2. speed of light in a vacuum 3. A brief historical reminder of the speed of light 4. Invariance of the speed of light in a vacuum 5. Influence of the propagation medium 6. Speed or celerity? 7. Speed, distance traveled, and duration 8. Relations including the speed of light 9. Faster than light? 10. Speed of light: did you know? Reminders: light Light is an electromagnetic wave, consisting of a magnetic field and an electric field oscillating perpendicular to each other in a plane perpendicular to the direction of propagation of the light wave. In a vacuum, light travels in a straight line at the speed of light noted c. speed of light in a vacuum Exact value The exact value of the speed of light was fixed in 1983 by the Bureau of Weights and Measures at: c = 299 792 458 m/s or c = 2.99792458 x 10 8 m/s, using the units of the international system. It can also be expressed in kilometers per hour by multiplying the value in m/s by 3.6: c = 1,079,252,848.8 km/h or c = 1.0792528488 x 10 9 km/h. This value, which represents a fundamental constant of physics, can be used for calculations requiring great precision. It is also used to define the meter in the international system of units: one meter corresponds to the length traveled in a vacuum by light for a duration of 1/299,792,458 seconds. A brief historical reminder of the speed of light The first conception concerning light suppose that it can be either present in a space, or absent: the light would therefore be instantaneous.
- 3. Galileo not only ruled on the shape of planet Earth! The notion of propagation in space, and therefore of speed, is then not present. The Arab scholar Alhazen (965-1039) was interested in optics and wrote reference treatises. He is the first to have the intuition that the appearance of light is not instantaneous, that it has a speed of propagation, but he cannot prove it. Galileo (1564-1039) tries to measure the propagation time of light between two hills using two people a few kilometers apart and equipped with clocks. He fails to measure the speed of light (which, in the context of this experiment, takes 10 -5 seconds to travel the previously defined
- 4. distance, not measurable for the time) and deduces from the failure of this experiment that the speed of propagation of light is very high. Cassini (1625-1712) speculated that the irregularity in the movement of Io, a satellite of Jupiter, could come from a delay in the arrival of light from the satellite, "such that it takes 10 or 11 minutes for it travels a distance equal to the radius of the Earth's orbit". Römer (1644-1710) explains the discrepancy between the eclipses of Io (a satellite of Jupiter) and Cassini's predictions by assuming that light has a speed of propagation. It is the first to give an order of magnitude of the speed of light. Bradley (1693-1762) confirms Römer's hypothesis and proposes a first estimate of the speed of light at approximately 10188 times that of the rotation of the Earth around the Sun, the latter being however poorly known. His discovery is linked to the aberration of light, an optical phenomenon that results in the fact that the apparent direction of a light source depends on the speed of the person observing it. Fizeau (1819-1896) developed a device that allowed him to assess the speed of light. It sends a beam of light between the town of Suresnes (Hauts-de-Seine, 92) and Montmartre (Paris). The light passes through a toothed wheel, is reflected by a mirror, goes back through the wheel, and finally arrives on a screen. Depending on the speed of the wheel, the light may or may not be obscured. This last parameter is known, as well as the interval between two teeth and the exact distance traveled by light, Fizeau manages to estimate the speed of light at 3.15 x 10 5 km/s. Cornu (1841-1902): he perfected Fizeau's device and found a value of 3.004 X 10 5 km/s The measurements were carried out later (by Michelson, Newcomb, and Perrotint) made it possible to obtain increasingly precise values, in order to arrive at the one used today. ● Telescope history ● Telegraph Machine history Invariance of the speed of light in a vacuum In classical mechanics, any speed depends on the chosen frame of reference. However, this is not the case for light (and electromagnetic radiation in general): its speed is invariant. This means that light
- 5. propagates at the same speed (c in vacuum) for a stationary observer relative to its source or for a moving observer. On the contrary, the speed of a sound wave measured by an observer depends on the speed at which the latter moves relative to the source of the sound. A modern test of the invariance of the speed of light was carried out in 1964 by the team of Alväger, a Swedish physicist, within the Proton Synchrotron of CERN (European Organization for Nuclear Research). This test, based on the time-of-flight technique, consisted in measuring the speed of γ rays coming from the disintegration of particles called neutral pions π 0, which produce photons while degrading. The invariance of the speed of light constitutes the basic postulate of special relativity established by Albert Einstein at the beginning of the 20th century. The speed of propagation of light in a vacuum is invariable whatever the frequency of the light wave and whatever the Galilean frame of reference considered. Influence of the propagation medium speed of light in the matter In most transparent material media, light propagates at a speed slower than that of a vacuum: its speed then depends on the chemical nature of the medium, its density, its concentration (for solutions), but also on certain quantities physical such as: ● temperature, ● pressure ● or the wavelength of the radiation under consideration. The different transparent media are characterized by their refractive index (noted n). This index without unit is always higher than 1, because it is considered that for the vacuum n=1, and makes it possible to find at which speed the light propagates in a given medium. Indeed, the refractive index (n) of a medium is defined as the ratio of the speed of propagation of light in vacuum (c) by the speed of propagation in this medium (v) i.e.: [n=frac{c}{v}] So [v=frac{C}{n}] Some examples :
- 6. Environment Air Water Glass Diamond Refractive index (n) 1.00 1.33 1.50 2.42 Speed (c) 3.00 x 10^8 m/s 2.25 x 10^8 m/s 2.00 x 10^8 m/s 1.24 x 10^8 m/s This passage of light from one medium to another is at the origin of the notions of refraction and reflection of light. Speed or celerity? The letter “c” used to express the speed of light derives from the term “celerity”. This term generally refers to the propagation speed of waves and can be used for light since it is an electromagnetic wave. It involves the transmission of a variation in a physical parameter (such as electromagnetic fields, pressure, elongation, etc.), whereas "speed" rather designates a movement of matter. It is, therefore, more accurate to use the term “celerity” than that of “speed”, unless it is specified that it is a “speed of propagation”. The term "speed" nevertheless remains in more common use. Speed, distance traveled, and duration Like all speeds, the speed of light (c) is defined as the ratio of the distance traveled noted d (the distance over which there was propagation) by the duration of propagation noted Δt which can be translated by the relationship : [c=frac{d}{triangle t}] The speed of light is already known, but this relation does not present any real practical utility. However, it is possible to use this relationship to express either distance or duration. ● Distance traveled by light: [d=ctimestriangle t]
- 7. ● Spread time: [triangle t=frac{c}{d}] Relations including the speed of light The speed of light in vacuum (c) is involved in many relationships: ● Einstein's mass-energy equivalence: [E=mc^{2}] ● Relationship between frequency (ν) and wavelength (λ) of an electromagnetic wave: [lambda=frac{c}{nu}] ● Relationship between a measured duration (ΔT m ) and a proper duration (ΔT 0 ): [triangle T_{m}=frac{triangle T_{0}}{sqrt{1-frac{c^{2}}{v^{2}}}}] Note: the speed of light is involved in most of the physical quantities expressed in the context of relativistic physics. Faster than light? Einstein's theory of relativity assumes that no object can reach a speed greater than c in a vacuum. However, it is possible for an object or particle to exceed the speed of light in a medium other than a vacuum. In this case, the particle produces an intense blue light when it moves at the speed of light, then forms the tip of a "cone" of blue light when this speed is exceeded: this is called l Cherenkov effect, named after the researcher who discovered it, which won him a Nobel Prize in 1958. It is this effect that produces the characteristic blue color of the cooling pools of nuclear power plants.
- 8. The blue light from nuclear power plants is caused by the Cherenkov effect (because no, water is not naturally blue!)Although this phenomenon is for the moment limited to particles, it is not impossible that humans can one day also move at the speed of light, like the Enterprise from Star Trek! Speed of light: did you know? A little sound delay... You can see lightning before you hear it! This is explained by the difference between the speed of light and the speed of sound: the latter has an approximate value of 340 m/s, against 3 x 10 8 m/s for light. Since sound is therefore much slower than light, it is common to observe the lightning
- 9. before hearing the thunder: the moment when the lightning is visible is therefore really the moment when the lightning crosses the sky, but the moment where thunder is heard may have a lag. The further the lightning strike point is from the observation point, the greater this offset will be. It is also possible to estimate the distance separating us from this flash, by counting the difference between light and sound:3 seconds of offset is approximately equivalent to 1 km distance. It is, therefore, necessary to divide by 3 the offset counted in order to obtain an estimate in km. Attention, it is important to remember that sound does not propagate in a vacuum, because it is a mechanical wave, and not electromagnetic like light. It, therefore, needs a medium to propagate. All the sounds produced in space that can therefore be observed in films are false! Information at the speed of light! Many internet service providers offer fiber-optic offers. Unlike satellite, based on a wireless network, or ADSL, based on a network of copper wires, optical fiber is a method of transmitting information based on the refraction and reflection of light within a glass or plastic thread. The core of the fiber has a higher refractive index than the sheath that surrounds it, the light signal is trapped and will be reflected multiple times all along with the fiber thanks to the phenomenon of total internal reflection. The signal, emitted by an LED or lasers, translates the information by modulating its intensity and will be transmitted without loss to the end of the fiber by taking a zigzag path. Currently, the speed of information transmission through fiber optics (not to be confused with throughput) currently reaches 70% to 75% of the speed of light. However, there are experimental fibers whose speed can reach 99%. Light and health Electromagnetic waves are widely used in medical imaging because visible and infrared radiation is less dangerous than X-rays from radios or MRIs. They carry less energy. Optical fibers are notably used in medical imaging. We can take the example of the fiberscope, a type of endoscope allowing for visualize previously inaccessible areas of the human body.