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Sunlight, or "white" light, is actually made up of continuous bands of different colored light--red, orange, yellow, green, blue, indigo and violet. Each color has a different wavelength, or frequency, which refracts slightly differently when it passes from one medium to another. As a result, white light can be broken up into its component colors by being passed through certain medium.

For example, a prism can also create rainbows because the glass, like the raindrop, bends the different colors of light at slightly different angles. Longer wavelengths are bent at larger angles, so longer wavelengths are bent less than shorter wavelengths. When sunlight hits a raindrop, the red light waves are bent at an angle of 42 degrees from their original direction from the sun. Shorter violet light waves are only bent at an angle of 40 degrees.

The other colored light frequencies are bent at angles in between these two. Reborn comments that it has been a long time since that happened and asks Tsuna if he thinks that Reborn, as his home tutor, will allow his skipping of school. Hearing this, Tsuna shouts at Reborn agitatedly, wondering how Reborn could say that. Tsuna recalls the day when he first met Reborn and how Reborn showed up out of nowhere, claiming to be a tutor for training Tsuna to be a Mafia boss.

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Tsuna says that he felt like the days after had been a mess and rattles off things that Reborn had forced him to do that turned his school life into a disaster in the process. However, even after going through all of that, Tsuna says that in the end, he had fun and that he even felt happy to have Reborn as a tutor.

Tsuna says that he was outraged when Reborn said that he never expected to die a decent death and angrily questions if Reborn is always thinking sad thoughts whenever he is by the former's side, even when he was having fun. Tsuna exclaims that Reborn is a failure as a home tutor if he has been behaving this way the whole time. Tsuna informs Reborn that this time, it is his turn to teach Reborn. Getting emotional, Tsuna is unable to complete his sentence and slumps onto the ground. After a few moments, Tsuna tells Reborn with conviction that he is not going to let Reborn die.

Tsuna finally gets his feelings off his chest, only to find out that Reborn is sleeping beside him. Tsuna feels incredulous that Reborn fell asleep while he was addressing such important concerns. Tsuna tries to rouse Reborn but stops himself in time after he thinks of the consequences. Tsuna wonders how much had Reborn heard before he slept.

As Tsuna heads home, it is revealed that Reborn is actually pretending to be asleep. Reborn, with a satisfied grin on his face, saying that Tsuna does as he pleases, but then said that impossible things is still impossible. Tsuna visits Yamamoto and Gokudera at the hospital and notifies them of the same matter that he had already told Mukuro, Byakuran, Enma and Xanxus.

Gokudera is upset that he did not get to know first and Tsuna explains that it is because Tsuna is so dependent on his guardian and sees them as his family that he just natrually assumes that they will help him out. Tsuna apologies but Gokudera brushes it off, exclaiming proudly that they are a family. After hearing Tsuna out, Yamamoto and Gokudera tells him that they will support him and to leave the matter to them. As Tsuna goes off to inform Dino, Yamamoto comments that it is the first time he has seen Tsuna being calm although he is about to be facing a decisive battle and somehow, that calmness is infectious.

Tsuna finds Dino and Hibari in a forest and is shocked to find that they have been battling since the battle against Team Mammon. Dino reassures Tsuna that he will be taking part in tomorrow's Representative Battle but is refuted by Hibari, who says harshly that it is impossible as Dino is going to be bitten to death by him. Tsuna says he has something important to tell them and his serious demeanor made them listen. Dino is shocked at the power of Team Bermuda after hearing the events that happened to Reborn.

Kyoko, Haru, Chrome and I-Pin have finished making the good luck charms and are on their way to Tsuna's house. Bianchi is waiting for them outside and brings them in. There is a huge crowd and Haru identifies some of the men as Dino's subordinates. Bianchi explains that there are many more others and that they were all summoned here. Haru questions the motive for gathering them and Bianchi comments that these are pretty scary people and summoning them is not a feat that just anyone could manage. This made them wondering who was the one who summoned them. Inside the house, Tsuna is speaking with the fighting forces that he approached, pleading for them to fight together.

He explained everything that Talbot had told him and his experience from his previous fight with Jager and the necessity for them to work together to defeat the Vindice, declaring that this time they should be the ones to make the first move. At the afternoon, Reborn approaches Tsuna, telling him to return the Boss watch since he decided to pull out from the battle and said it's impossible for Tsuna to defeat the Vindice even with all the team join forces together.

This enraged Tsuna and challenged Reborn to take the Boss fight by force if he wants to, entering Hyper Dying Will Mode and unleashed great amount of his flames, which impressed Reborn but saying that it's still not enough to defeat Bermuda or Jager. Reborn continues to say that his mission is to make him a splendid Tenth Vongola Boss and it would be pointless if he dies.

However, Tsuna corrected him that Vongola Primo would surely say that someone that abandoned their friends cannot be entrsuted with the fate of Vongola, telling him that someone unwilling to risk death for the sake of their friends is not qualify to become Vongola Decimo, surprising Reborn. Seeing Tsuna's determination, Reborn admitted that he wants to live longer and wants to die without any regret as he has gained desire to see Tsuna to grow more, requesting him to keep him alive, finally agree with Tsuna's plan, much to the latter's relief.

The other Arcobaleno revealed themselves, also agreeing with Tsuna's plan to defeat Bermuda and his team. The watch announced that the battle would be held with 90 minutes time limit. Bermuda sensed that the three teams each are in separate locations, so he ordered them to split into three groups. He and Jager appeared in front of Reborn's team, asking for Reborn's answer of his invitation.

Reborn refused once again, saying that he cannot accept Bermuda's way. With his invitation rejected, Bermuda ordered Jager to finish them off, bidding them good bye. However, it turns out that the team members are only Decoy Puppet. Reborn explained that they have predicted Bermuda able to sense their flames and precense, so they have Irie, Spanner, and Verde to create decoy puppets that able to emit flames and heartbeat to fool them.

After defeating Alejandro, the three moves to their next targets. Receiving report that Alejandro was defeated and unable to sense their flames afterwards, Bermuda guessing that they're using some sort of barrier cover that make protecting their flames from being detected by him.

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Also, the members of Team Verde that defeated by Big Pino and Small Gia were also puppets but then someone's illusions appears to fight them, realizing that it is meant to hold them until Tsuna, Enma, and Basil arrives to defeat them. Knowing this, Jager suggested that they should go to help Big Pino and Small Gia , but before they can do so, Dino, Mukuro, Squalo, Xanxus, and Byakuran reveal themselves, preparing to fight them. Back at the park, Jager immediately defeated the majority of the elite team until Mukuro and Hibari were the only ones who are still standing and work together.

Tsuna, and the rest of the team members arrived just in time to assist both of them. With the team's teamwork, they able to heavily injured Jager, leaving him unable to fight. However, before Tsuna could destroy his boss watch, Bermuda finally interferes and released his curse, officially entering the battle. Checker Face revealed himself directly, much to the shock of everybody present.

Realizing that they have known the truth behind the Representative battle of the Rainbow as well as the secret behind Arcobaleno Pacifiers, Checker Face confirmed that it was true. When they questioned his presence, Checker Face revealed that he merely hiding his presence with Segno Ring as he opened his mask, revealing himself as Kawahira, surprising them.

Kawahira then unleashed his flames, showing that they are on entirely different level to defeat him as they are just normal humans. He revealed that he belong to a special species who had lived on Earth before human ever born whose duty is to protect the planet Earth. However, over the only ones of these species who are still alive on present day are only him and Yuni.

He explained that the Tri-ni-set originally were not set of 21 rings they all know but a seven stones. When his species were still about ten people alive, they gave their flames to the seven stones. However, as their members died one by one until only five of them remains, the decided to borrow the humans' powers and thus, splitting th stones into Arcobaleno Pacifiers.

When there's only him and Yuni's ancestor, Sepira the only ones who were alive, they were unable to provide the stones with their own powers and thus, furthering split up the stones into set of Vongola Rings and set of Mare Rings. Hearing this, Yuni says that she never heard the story from her ancestor and Kawahira revealed that he and Sepira partways after their opinions differs with each other; while Sepira wanted to coexist with humans, he didn't. Ending the talk, Kawahira demanded for them to return the Pacifiers.

Tsuna shouted that there must be another way to maintain the Tri-ni-set without sacrificing the Arcobaleno's lives. Kawahira, however, replied that there's no other option left and warned Tsuna that he is the first one on the list to become the next Arcobaleno, something that Tsuna already prepared for. At this time, Talbot arrived, carrying seven jars and told Kawahira that by using the jars, Arcobaleno Pacifiers are no longer needed.

By using the flame of Night within the jars, the flame is configered in loop and by repeatedly passing through the warp holes, the seven flames of the sky would continuously accelerated, which replenishes their flames for basically half of an eternity. This method, however, requiring Bermuda to keep continuously using his Flames.

Everybody become skeptical as Bermuda only lives to get his revenge on Kawahira and they doubt he would accept the role to protect the Tri-ni-set that Kawahira cares for so much.

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Surprisingly, however, Bermuda accepted the role as he thinks that they would have control over the Tri-ni-set away from Kawahira. Hearing this, Kawahira about to refuse, but Yuni convinced to accept as he won't live forever. Convinced that Yuni has saw the peaceful existence of Tri-ni-set, Kawahira agreed to the term as he actually believes that if there's another method without sacrficing anyone, he would entrust the Tri-ni-set to the future generations.

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They all gathered around the jars and filled the jars with their flames at the fullest as Kawahira promised he would remove the curse. The Arcobaleno were all imagining themselves return to their real form, only to find Lal is the only one who returned. Verde concludes that the only part of their curse that been removed is the part where they will stay as infant and will never grow, which means it would take a long time for them until the return to their original form as they'll grow like normal human does.

They then went to the hospital to visit Dino and Basil. To avoid ruckus, Tsuna and Reborn went to their rooms first, However, much to their surprise, Leviathan came out from the room with syringues all over his face, which he explained that Xanxus ordered him to take it all in his place. Squalo the approached them with the rest of the Varia, reminding that he also survived thanks to Mammon's immediate action to make illusionary heart during the battle with Jager and would stay that way until they find suitable heart transplant. Byakuran, along with Bluebell destroyed the wall of the room, greeting Tsuna.

He explained that he also submitted into the hospital because Mammon created his illusionary organs for This angered Squalo and Xanxus who are annoyed by the interruption, making Xanxus, blast his gun, which they easily dodged, destroying the walls to the next rooms. Rainbows caused by sunlight always appear in the section of sky directly opposite the sun. Rainbows can be full circles. However, the observer normally sees only an arc formed by illuminated droplets above the ground, [1] and centered on a line from the sun to the observer's eye.

In a primary rainbow, the arc shows red on the outer part and violet on the inner side. This rainbow is caused by light being refracted when entering a droplet of water, then reflected inside on the back of the droplet and refracted again when leaving it. In a double rainbow, a second arc is seen outside the primary arc, and has the order of its colors reversed, with red on the inner side of the arc. This is caused by the light being reflected twice on the inside of the droplet before leaving it.

A rainbow is not located at a specific distance from the observer, but comes from an optical illusion caused by any water droplets viewed from a certain angle relative to a light source. Thus, a rainbow is not an object and cannot be physically approached. Indeed, it is impossible for an observer to see a rainbow from water droplets at any angle other than the customary one of 42 degrees from the direction opposite the light source.

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Even if an observer sees another observer who seems "under" or "at the end of" a rainbow, the second observer will see a different rainbow—farther off—at the same angle as seen by the first observer. Rainbows span a continuous spectrum of colours. Any distinct bands perceived are an artefact of human colour vision , and no banding of any type is seen in a black-and-white photo of a rainbow, only a smooth gradation of intensity to a maximum, then fading towards the other side.

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  • Rainbows can be caused by many forms of airborne water. These include not only rain, but also mist, spray, and airborne dew. Rainbows can be observed whenever there are water drops in the air and sunlight shining from behind the observer at a low altitude angle. Because of this, rainbows are usually seen in the western sky during the morning and in the eastern sky during the early evening.

    The most spectacular rainbow displays happen when half the sky is still dark with raining clouds and the observer is at a spot with clear sky in the direction of the sun. The result is a luminous rainbow that contrasts with the darkened background. During such good visibility conditions, the larger but fainter secondary rainbow is often visible. The rainbow effect is also commonly seen near waterfalls or fountains.

    In addition, the effect can be artificially created by dispersing water droplets into the air during a sunny day. Rarely, a moonbow , lunar rainbow or nighttime rainbow, can be seen on strongly moonlit nights. As human visual perception for colour is poor in low light, moonbows are often perceived to be white. Now that software for stitching several images into a panorama is available, images of the entire arc and even secondary arcs can be created fairly easily from a series of overlapping frames.

    From above the earth such as in an aeroplane, it is sometimes possible to see a rainbow as a full circle. The sky inside a primary rainbow is brighter than the sky outside of the bow. This is because each raindrop is a sphere and it scatters light over an entire circular disc in the sky. The radius of the disc depends on the wavelength of light, with red light being scattered over a larger angle than blue light. Over most of the disc, scattered light at all wavelengths overlaps, resulting in white light which brightens the sky.

    At the edge, the wavelength dependence of the scattering gives rise to the rainbow. A spectrum obtained using a glass prism and a point source is a continuum of wavelengths without bands. The number of colours that the human eye is able to distinguish in a spectrum is in the order of The apparent discreteness of main colours is an artefact of human perception and the exact number of main colours is a somewhat arbitrary choice.

    Newton, who admitted his eyes were not very critical in distinguishing colours, [8] originally divided the spectrum into five main colours: Later he included orange and indigo, giving seven main colours by analogy to the number of notes in a musical scale. According to Isaac Asimov , "It is customary to list indigo as a color lying between blue and violet, but it has never seemed to me that indigo is worth the dignity of being considered a separate color. To my eyes it seems merely deep blue.

    The colour pattern of a rainbow is different from a spectrum, and the colours are less saturated. There is spectral smearing in a rainbow owing to the fact that for any particular wavelength, there is a distribution of exit angles, rather than a single unvarying angle. The number of colour bands of a rainbow may therefore be different from the number of bands in a spectrum, especially if the droplets are particularly large or small. Therefore, the number of colours of a rainbow is variable. If, however, the word rainbow is used inaccurately to mean spectrum , it is the number of main colours in the spectrum.

    The question of whether everyone sees seven colours in a rainbow is related to the idea of Linguistic relativity. Suggestions have been made that there is universality in the way that a rainbow is perceived. When sunlight encounters a raindrop, part of the light is reflected and the rest enters the raindrop. The light is refracted at the surface of the raindrop. When this light hits the back of the raindrop, some of it is reflected off the back. When the internally reflected light reaches the surface again, once more some is internally reflected and some is refracted as it exits the drop.

    The light that reflects off the drop, exits from the back, or continues to bounce around inside the drop after the second encounter with the surface, is not relevant to the formation of the primary rainbow. Seawater has a higher refractive index than rain water, so the radius of a "rainbow" in sea spray is smaller than a true rainbow. This is visible to the naked eye by a misalignment of these bows. If the sun were a laser emitting parallel, monochromatic rays, then the luminance brightness of the bow would tend toward infinity at this angle ignoring interference effects.

    But since the sun's luminance is finite and its rays are not all parallel it covers about half a degree of the sky the luminance does not go to infinity. Furthermore, the amount by which light is refracted depends upon its wavelength , and hence its colour. This effect is called dispersion. Blue light shorter wavelength is refracted at a greater angle than red light, but due to the reflection of light rays from the back of the droplet, the blue light emerges from the droplet at a smaller angle to the original incident white light ray than the red light. Due to this angle, blue is seen on the inside of the arc of the primary rainbow, and red on the outside.

    The result of this is not only to give different colours to different parts of the rainbow, but also to diminish the brightness. A "rainbow" formed by droplets of a liquid with no dispersion would be white, but brighter than a normal rainbow. The light at the back of the raindrop does not undergo total internal reflection , and some light does emerge from the back. However, light coming out the back of the raindrop does not create a rainbow between the observer and the sun because spectra emitted from the back of the raindrop do not have a maximum of intensity, as the other visible rainbows do, and thus the colours blend together rather than forming a rainbow.

    A rainbow does not exist at one particular location. Many rainbows exist; however, only one can be seen depending on the particular observer's viewpoint as droplets of light illuminated by the sun. All raindrops refract and reflect the sunlight in the same way, but only the light from some raindrops reaches the observer's eye.

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    This light is what constitutes the rainbow for that observer. The whole system composed by the sun's rays, the observer's head, and the spherical water drops has an axial symmetry around the axis through the observer's head and parallel to the sun's rays. The rainbow is curved because the set of all the raindrops that have the right angle between the observer, the drop, and the sun, lie on a cone pointing at the sun with the observer at the tip.

    We can determine the perceived angle which the rainbow subtends as follows. The term double rainbow is used when both the primary and secondary rainbows are visible. In theory, all rainbows are double rainbows, but since the secondary bow is always fainter than the primary, it may be too weak to spot in practice.

    Secondary rainbows are caused by a double reflection of sunlight inside the water droplets. As a result of the "inside" of the secondary bow being "up" to the observer, the colours appear reversed compared to those of the primary bow. The secondary rainbow is fainter than the primary because more light escapes from two reflections compared to one and because the rainbow itself is spread over a greater area of the sky. Each rainbow reflects white light inside its coloured bands, but that is "down" for the primary and "up" for the secondary. Unlike a double rainbow that consists of two separate and concentric rainbow arcs, the very rare twinned rainbow appears as two rainbow arcs that split from a single base.

    A "normal" secondary rainbow may be present as well. Twinned rainbows can look similar to, but should not be confused with supernumerary bands. The two phenomena may be told apart by their difference in colour profile: The cause of a twinned rainbow is the combination of different sizes of water drops falling from the sky. Due to air resistance, raindrops flatten as they fall, and flattening is more prominent in larger water drops.

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    When two rain showers with different-sized raindrops combine, they each produce slightly different rainbows which may combine and form a twinned rainbow. That small difference in droplet size resulted in a small difference in flattening of the droplet shape, and a large difference in flattening of the rainbow top. Meanwhile, the even rarer case of a rainbow split into three branches was observed and photographed in nature. In theory, every rainbow is a circle, but from the ground, only its upper half can be seen.

    Viewing the rainbow's lower half requires the presence of water droplets below the observer's horizon, as well as sunlight that is able to reach them. These requirements are not usually met when the viewer is at ground level, either because droplets are absent in the required position, or because the sunlight is obstructed by the landscape behind the observer. From a high viewpoint such as a high building or an aircraft, however, the requirements can be met and the full-circle rainbow can be seen.

    A circular rainbow should not be confused with the glory , which is much smaller in diameter and is created by different optical processes. In the right circumstances, a glory and a circular rainbow or fog bow can occur together.