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Why the formation of rainbows require a total internal reflection on the part of light. I mean can't the rainbows be formed without it , simply through refraction by the water droplet at a suitable angle?

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    $\begingroup$ Rainbows are seen away from the Sun, so clearly there was reflection involved. Descartes gave the detailed explanation. Other bows may be on the same side as the Sun. $\endgroup$ – Pieter Feb 18 '18 at 14:30
  • $\begingroup$ Have u seen them? $\endgroup$ – Arunabh Feb 18 '18 at 15:05
  • $\begingroup$ Yes. Halos are on the same side of the Sun. It is common to see them around the moon, but that is probably because we look at the moon more often. Parhelia are often seen left and right when the Sun is low. $\endgroup$ – Pieter Feb 18 '18 at 15:14
  • $\begingroup$ Let me tell you a real story: when I studied EM waves at the univ. we had some lessons (lectures)on "the Rainbow". I was excited than then I knew a lot of it, and I was looking forward to spread it and amaze friends and children. Then the proffesor said: congrats, this is the 1st part of one of the many books exclusively dedicated to the rainbow formation. This is just to tell you that a full answer can take a whole book haha. $\endgroup$ – FGSUZ Jan 22 at 21:22
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Rainbow formation does not involve Total Internal Reflection in any way. In fact, TIR is impossible in spherical raindrops. Light cannot enter them at an angle (relative to the surface normal) that is greater than the critical angle, and the angle a ray makes when it encounters the surface from the inside is the same angle it had when it entered.

A rainbow is an example of a caustic, which is when reflection and/or refraction causes a wave front to fold back upon itself. The light becomes extremely bright at the point where it reverses. Other examples include star-like patterns when light shines through a goblet of water, and the bright lines on the bottom of a swimming pool in sunlight.

A reflection is required, tho. The folding doesn't happen without it.

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