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Rainbows

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Rainbows are produced by electromagnetic radiation – visible light – reflecting in marvelous ways from the dispersion of light.

Let’s start with the basics:

A prism separates white light into many colors

How? Each wavelength of light refracts by a different amount

The result is dispersion – each wavelength is bent by a different amount

prism-refraction-dispersion-of-visible-light-into-spectrum

The physics of rainbow formation

Rainbows: At Atmospheric optics

http://hyperphysics.phy-astr.gsu.edu/hbase/atmos/rbowpri.html

http://www.atmo.arizona.edu/students/courselinks/spring13/atmo170a1s1/1S1P_stuff/atmos_optical_phenomena/optical_phenomena.html

Rebecca McDowell  How rainbows form

 

The shape of a rainbow

A discussion of this comic is here Explain XKCD. 1944: The End of the Rainbow

If one considers the path that light takes to form a rainbow, then it forms a two-cone structure, where the Sun (the vertex of the outer cone) emits light rays that move towards the Earth (forming the faces of the outer cone),

Then the rays reflect off water droplets located at just the right angle (the circular base) to reach our eyes (the vertex of the inner cone).

Thus, such a rainbow structure can be said to have “ends”, represented by the vertices of the two cones: one at the eye of the viewer, and another at the light source (usually the sun).

XKCD End of the rainbow 1944

from the webcomic XKCD.

Do rainbows have reflections?

It certainly seems like rainbows can have reflections. Consider this great photo by Terje O. Nordvik, September ’04 near Sandessjøen, Norway.
http://www.atoptics.co.uk/rainbows/bowim6.htm

But rainbows aren’t real objects – and so they literally can’t have reflections!
So what are we seeing here? See Rainbow reflections: Rainbows are not Vampires

terje-nordvik-rainbow-in-norway

Learning Standards

2016 Massachusetts Science and Technology/Engineering Curriculum Framework

HS-PS4-3. Evaluate the claims, evidence, and reasoning behind the idea that electromagnetic radiation can be described by either a wave model or a particle model, and that for some situations involving resonance, interference, diffraction, refraction, or the photoelectric effect, one model is more useful than the other.

SAT subject test in Physics: Waves and optics

• General wave properties, such as wave speed, frequency, wavelength, superposition, standing wave diffraction, and Doppler effect
• Reflection and refraction, such as Snell’s law and changes in wavelength and speed
• Ray optics, such as image formation using pinholes, mirrors, and lenses
• Physical optics, such as single-slit diffraction, double-slit interference, polarization, and color.

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