You're Probably Wrong About Rainbows

Most people don't understand rainbows (0s)

• A question about why rainbows are curved led to the creation of a video with demonstrations and animations to explain the phenomenon (2s).
• Most explanations of rainbows are oversimplifications, and common questions about rainbows, such as why they are not visible when looking in the direction of the Sun, remain unanswered (23s).
• The typical explanation that raindrops spread white light into colors like a prism does not fully explain the occurrence of rainbows (32s).
• Several unexplained aspects of rainbows include why it is darker above a rainbow than under it, how a rainbow can disappear with sunglasses, and why some rainbows appear smaller than usual (40s).
• The full explanation of rainbows is more complex and satisfying than common explanations, and it involves the combination of three elements: raindrops, the Sun, and an observer (1m0s).
• The study of rainbows has led to significant scientific discoveries, including one that directly led to a Nobel Prize (54s).

Light refraction explained (1m8s)

• A glass sphere is used to represent a raindrop in an experiment, as raindrops are essentially spherical in shape (1m17s).
• When light from a laser, representing a ray from the sun, strikes the sphere, some of it reflects back off the front surface, and some is transmitted into the sphere (1m37s).
• At the back of the sphere, some of the light reflects off the back surface, and some is transmitted, with the amount of reflection and transmission depending on the angle of the light, its polarization, and the nature of the two media (2m2s).
• The experiment uses the reflections to ensure the laser is lined up properly, and as the laser is moved up the sphere, the reflection off the front surface goes up, while the reflection off the back surface goes down (2m20s).
• The beam inside the sphere bends down as it refracts, due to the light slowing down as it enters the dense medium of the glass sphere (3m23s).
• Light is an electromagnetic wave, created by accelerating charges, and when it encounters charges in a medium, it pushes them back and forth, causing them to vibrate and create their own electromagnetic waves (3m52s).
• The net electromagnetic field is the sum of the incident wave and the new wave, resulting in a phase kick that shifts the wave back slightly, and the net effect is a decrease in the wavelength of the radiation (4m54s).
• This explanation of how light is slowed down in a medium is based on the work of Grant from 3 Blue 1 Brown (4m16s).
• When light enters a new medium at an angle, the part of the wave crests that enter the new medium first slow down, changing the angle of all the wave crests and causing the light to bend due to refraction (5m40s).
• The refractive index of a medium, which is the speed of light in a vacuum divided by the speed of light in the medium, determines how much the light bends, with a higher refractive index resulting in more bending (5m28s).
• The relationship between the angles of incidence and refraction and the refractive indexes of the two media is described by Snell's law, a simple mathematical expression that was independently discovered by several people (6m14s).
• When a laser beam hits a sphere, the angle of incidence and refraction causes the light to bend, with some of the light being reflected and visible as a beam coming out the front of the sphere (6m36s).
• As the laser beam is moved up the sphere, the angle of the reflected ray increases until it reaches a maximum angle, beyond which it turns around and goes back the other way (7m45s).
• This maximum angle results in a concentration of light rays, known as a caustic, which is a characteristic of curved surfaces such as coffee mugs, glasses, and rippling water (8m18s).
• The concentration of light rays at a specific angle means that over a range of impact parameters, the reflected beam comes out at essentially the same angle (8m6s).

How does a rainbow form? (8m20s)

• Water droplets create the light patterns we see by concentrating light rays, with the maximum scattering angle occurring at 42° below the horizontal for red light through a sphere of water (8m27s).
• The maximum scattering angle is a result of geometry, where the angle of incidence becomes so steep that the refracted ray stops hitting the back of the sphere higher and starts hitting it lower (9m5s).
• The precise maximum scattering angle depends on the color of light, with higher frequency light like blue causing charges to wiggle with greater amplitude and producing higher amplitude electromagnetic radiation (9m33s).
• This results in higher frequency light traveling slower and bending more than lower frequency light, causing different colors to have different maximum scattering angles (10m28s).
• Experiments with green and blue light show that they refract more than red light, resulting in smaller maximum scattering angles (10m40s).
• The maximum scattering angles for different colors are: around 42° for red, around 41° for green, and around 40° for blue (11m4s).
• When a sphere is illuminated uniformly with light, more light hits the sphere at higher impact parameters, resulting in most of the light ending up at the maximum scattering angle (11m58s).
• The difference in maximum scattering angles for different colors is what gives us the rainbow, as the reflections of different colors overlap and mix to produce white light, except at the maximum scattering angles (13m1s).

Circular rainbows (13m10s)

• When a sphere is uniformly illuminated with white light, a circle of white light appears from the reflections off the back of the sphere, surrounded by a ring of rainbow colors (13m14s).
• A single raindrop creates a cone of light, with the inside being all white and the ring around the outside being colored, representing the perspective of a rainbow from a single raindrop (13m39s).
• Different light rays coming in at different places reflect back off the front and back surfaces of the raindrop, with the reflection off the back surface reaching a maximum angle that varies for different colors, resulting in the red maximum angle being the furthest and appearing on the outside (13m56s).
• The cone of different colored light rays produces the ring of colors seen in a rainbow, and this color cone can be observed by positioning one's eye within it (14m22s).
• The color cone appears as a focused, intense beam of light on the back of the sphere, which can cause burns if touched (14m39s).
• A single raindrop's rainbow cone is just one of billions of raindrops projecting a rainbow cone back toward the Sun, which collectively create a single unified rainbow (15m1s).

Why are rainbows curved? (15m14s)

• To see a specific color of a rainbow, such as red, the light from that color must pass directly from a raindrop into the observer's eye, which only occurs at an angle of 42° from the Sun to the raindrop to the eye (15m33s).
• The angle of 42° explains why rainbows appear as an arch, and the violet light from the same raindrops passes above or beside the observer's eye, making it invisible (15m42s).
• However, there are raindrops below and inside the arc of the red-giving raindrops whose violet light intersects the observer's eye, forming a shallower angle of 40° between the Sun and the eye (15m57s).
• Raindrops at intermediate angles send all the other colors of the rainbow to the observer's eye, making a rainbow an optical illusion from billions of droplets each projecting a rainbow cone (16m11s).
• The droplets sending colors to the observer's eye are constantly changing, and a single drop might send different colors as it falls, such as red, orange, yellow, green, blue, indigo, and violet (16m26s).
• The center of the rainbow's arch must be on a line that passes from the Sun through the back of the observer's head, making the observer's shadow the center of their rainbow (16m41s).
• This means that no two people can see the exact same rainbow, and even the observer's left and right eyes don't see the same rainbow, making it an optical illusion unique to each perspective (16m57s).
• The reason rainbows are usually only visible in the early morning or late afternoon is that the higher the Sun is, the lower the top of the rainbow is, and when the Sun is more than 42° above the horizon, no rainbow is visible from the ground (17m22s).

Why can’t you see a rainbow with sunglasses? (17m30s)

• Polarized sunglasses can make rainbows invisible because rainbows are created by polarized light, which is oriented in a specific direction (17m31s).
• Light from the sun is unpolarized, meaning its electric fields are randomly oriented and oscillate equally in all directions (17m38s).
• When light in a rainbow ray reflects off the back of a droplet, it does so at an angle close to Brewster's angle, causing light with its electric field oriented parallel to the plane of reflection to be transmitted (17m52s).
• The light that is reflected and creates the rainbow has its electric field perpendicular to the plane of reflection, making rainbow light polarized (18m10s).
• The polarization of rainbow light is along the direction of the rainbow, which is horizontal at the top and closer to vertical on the sides (18m23s).
• A polarizing filter can be used to make a rainbow disappear or brighter by orienting it to allow the polarized light to pass through (18m35s).

Why is it brighter underneath a rainbow? (18m43s)

• Raindrops beneath a rainbow reflect all colors of light off their back surfaces, creating a brighter appearance, whereas raindrops above the rainbow do not reflect any light to the observer off their back surfaces (18m49s).
• The raindrops above the top of the rainbow do not reflect light to the observer because their eye is outside the maximum deflection angle of all the colors (19m2s).
• Looking up further, a second, fainter rainbow with its colors inverted, known as a double rainbow, can sometimes be seen, which is caused by an additional reflection inside the raindrops (19m14s).
• This additional reflection creates colored caustics, but they are much fainter because light is lost with each reflection (19m29s).
• The light from the second reflection starts going out the back of the raindrop at an angle of 180°, but as it hits further out from the center, the angle of reflection decreases until it reaches a minimum of around 50° for red light (19m41s).
• Between 42 and 50°, it is dark because no light reflected once or twice inside a raindrop comes out at this angle, known as Alexander's dark band (19m59s).
• Photographic evidence exists of third and fourth order rainbows formed after three or four internal reflections, but these are only visible when looking in the direction of the Sun and are extremely faint (20m17s).
• Higher-order rainbows, up to 200th order, have been detected under lab conditions, but these are not related to the phenomenon being described, which is known as a supernumerary rainbow, characterized by multiple rainbow-like bands (20m42s).

Different types of rainbow (20m44s)

• Supernumerary rainbows occur when the raindrops are small, just tths of a millimeter in diameter, and the light rays that pass just above and below the primary rainbow travel slightly different distances, producing a series of light and dark bands inside the main rainbow (20m50s).
• The colors in supernumerary rainbows overlap more than in the main rainbow, producing strange colors like magenta, a combination of blue and red (21m16s).
• Supernumeraries offer a clue to how small rainbows work, and they require tiny water droplets, just tth of a millimeter in diameter (21m28s).
• Glories or Brocken bows are small rainbows that are only around 2 to 4° wide, and they are due to interference, requiring tiny water droplets (21m42s).
• Glories are formed when light strikes the edge of a tiny water droplet and goes around the back, coming straight back at the source, creating a ring source of light (22m11s).
• The distance from one point to all edges of a tiny water droplet can vary on the order of a wavelength, causing the light to interfere constructively and destructively, producing a bright spot and a dark spot (22m34s).
• When the light from a tiny water droplet is rotated around 360° and extended out in all directions, it creates a fuzzy Bullseye pattern, with different colors of light having different wavelengths and producing rings of color (23m11s).
• The pattern from a single droplet is just the beginning, as millions or billions of droplets contribute to produce the same pattern, with the observer's shadow at the center (23m36s).

Invention of the cloud chamber (23m46s)

• CTR Wilson, a scientist, visited an observatory in the Scottish Hills in September 1894, where he observed colored rings surrounding the shadow cast on mist or cloud, which greatly excited his interest and inspired him to imitate the phenomenon in the laboratory (23m49s).
• Wilson invented the Cloud chamber for the explicit purpose of observing glories, but later discovered that it made the tracks of energetic particles visible, leading to a Nobel Prize-winning discovery (24m11s).
• The Cloud chamber was initially intended to study the mystery of rings of color in the fog, but it ultimately led to a greater understanding of energetic particles (24m30s).
• The study of rainbows has been a challenge to humans for millennia, but it is satisfying to have figured out the underlying physics, including why rainbows are curved and polarized (25m3s).
• Learning about rainbows is an example of how learning should be about mastering a subject, not just memorizing facts, and that true understanding comes from interactive and hands-on learning (25m38s).
• Brilliant is a platform that offers interactive lessons on various subjects, including math, science, and data analysis, and is effective in building intuition and real understanding through hands-on problem-solving (25m44s).
• Brilliant's lessons are bite-sized, allowing users to learn and build skills in short periods, and their course on scientific thinking is a great resource for those interested in learning about the physics of rainbows (26m12s).
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