Digression:

Sorry I haven’t posted in a while. Since classes actually started this week (yesterday), I’ve had less time to devote to blogging, so I’ll probably post less frequently. Unless I feel like sacrificing my grades to the Altar of Tsunku … which is mighty tempting. I’m actually skipping a class right now to write this. Terrible, I know. But this is more interesting.

Ironically (since I’m a math and comp sci major), I’m taking no math classes and, if you count the classes I’m listening in on, twice as many humanities courses as science courses (if you consider linguistics a humanities subject), including one on Japanese popular culture. I wonder if H!P will be discussed. I might bring it up.

Anyway… I notice a new single from Buono!, a new album from Ongaku Gatas, and a new PV from C-ute have all been released in the last couple of days. I will probably not be reviewing them individually on this blog, as I’ve decided the focus of ★MINI MONI MANIA★ is mainly on particular aspects of Hello! Project that most fans probably haven’t noticed (usually the geeky aspects), and also more general critical assessments of H!P (like my top 100 PV countdown).

So… on to the actual post:

“Mikan” and the Physics of Rainbows

“Mikan” is coming up on the countdown, and I’ve already written up a discussion of its artistic merits. I do want to take the time aside, though, to discuss the depiction of rainbows in this PV, and I think it deserves its own post.

So here’s a summary of how rainbows work:

A rainbow forms when sunlight reflects off a sheet of water particles. If we assume the sun is infinitely far away, then the incident rays are parallel (the actual case is a good approximation). Then each particle interacts with the incoming rays in the same way. This is what happens for each particle (image from Wikipedia):

The incoming ray of white light is refracted as it enters the raindrop, with shorter wavelengths (the blue end of the spectrum) refracting at a larger angle. The light then reflects off the back of the drop, and exits the drop, refracting once again. The light that comes out is spread out across a frequency spectrum, due to the effect of refraction. So blue light exits with a more horizontal angle, while red light exits with a more vertical angle. Since this is uniform for all raindrops, you as the observer (when looking at the top part of the rainbow) see red light at a more vertical angle and blue light further down, coming from drops farther away. And since this happens independently of direction, you ultimately see a circle with red on the outside and blue on the inside.

A ray of light, however, can enter a drop at different points, so most of the refracted light blends in with other rays, resulting in the appearance of white light in the interior of the rainbow. It’s the rays that enter furthest away from the center that result in the color spectrum characterizing a rainbow:

So what does this have to do with “Mikan”?

Hmm…

Correct:

• The rainbow is a circle. Not everyone understands this (and the bow morpheme of the word is misleading). But this video correctly demonstrates that a rainbow is circular and not an open arc. (BTW, the statement There is a pot of gold at the end of every rainbow is logically correct, albeit vacuously so.)
• The colors form a continuous spectrum. This might be hard to tell from the low-res screenshot above, but the colors do form a gradient, unlike the (also low-res) ROYGBIV discretization common in rainbow representations.
• The colors are in the right order. You’d be amazed how often people mess this one up.
• The sun, or light source, is behind the viewer. I think.
• There is white light in the interior of the rainbow. Probably the most neglected visual aspect of a rainbow.

Dubious:

• There is white light on the outside of the rainbow. This should be relatively dark, compared to the interior. Looks like there’s an additional light source behind the rainbow.

Incorrect:

• The rainbow moves and is not circular with respect to the viewer. Rainbows being an optical phenomenon rather than a physical manifestation, their orientation is entirely dependent on the reference frame from which they are viewed, and they always appear circular, for the reasons given above. So this is obviously incorrect.

Overall, the only real technical flaw is in the non-fixed nature of the rainbow. However, I’ll grant that artistic license supersedes physical considerations on this one (it’d be kind of boring to have a static circular rainbow, not to mention difficult to surround MoMusu members with), and am impressed with the attention given to physical details.

EDIT: A clarification of what I mean by “move”: A rainbow can change its apparent location, but only if the viewer’s frame moves with respect to the light source, for example if you (or the sun) were rocking back and forth while you were looking at a rainbow. However, in this case, the line connecting your eye and the center of the rainbow is always perpendicular to the apparent plane of the rainbow (its axis), so it would appear circular if you were to look at it directly. The visuals of the PV, in contradiction, show the rainbow moving where the axis has a mean position approximately parallel, not perpendicular, to the viewer’s field of vision.

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