Download The Theory of The Rainbows

The Theory of The Rainbows
Physic 464
Project
By: Thao Dang
What is a rainbow?
• Rainbow is an arc of colors appearing
opposite the sun as a result of the refraction
of sunlight in rain.
Presentation points
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How does a rainbow form?
What make colors in the rainbows?
Mathematical of Rainbows
Types of rainbows
Experiment
How does a rainbow form?
• Rainbows are created by sunlight shine and water
droplets.
• Rainbows are created by refraction and reflection
of sun’s rays in falling rain or mist.
• Sunlight strikes the front of raindrop and is
refracted and separated into it’s colors. Then the
light hit the back of the raindrop and is reflected,
and is refracted again as it leaves the raindrop.
Light travel through the raindrop to create
rainbow
What makes colors in the rainbow?
• The sunlight consists of all wavelengths of visible
light, which we simply see as white because they
are all combined together.
• When light is refracted, different wavelengths
refract at different angles, therefore the various
colors are separated.
• Rainbows have 7 colors; however, they actually
consist of every color. The color is constantly
changing from red to violet.
What makes the colors of rainbow?
• Each of the colors presents in white light are bent
a different amount in passing through the drop.
• 7 colors in a rainbow is formed follow the order:
Red, Orange, Yellow, Green, Blue, Indigo, and
Violet.
• The red bends the least and violet bends the most.
• The rest of the color lie in between the red and the
violet.
What makes colors in the rainbow?
What makes colors in the rainbow?
Mathematics of Rainbows
™The mathematics of rainbow relates to
¾Law of Refraction (Snell’s Law)
¾Law of Reflection
¾Law of Sines
¾Geometry
¾Derivative
Rainbow Angle
Calculation Rainbow Angle
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Using Snell’s law
n*sin(a) = n*sin(b)
The radius of the circle is r
We have: sin(a) = h/r = M
Rainbow angle
• The angle of incident equal the angle of
reflection
• The angle we want to find is the one
between the incoming ray and outgoing ray
which is named e
• The sum of the interior angles of a triangle
is 180 degree
Rainbow Angle
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Sum of all angle at the center of circles is 360 degree
360 = a + (180 – 2b) + (180 – 2b) + f
f = 4b – a
f=e+a
e=f–a
e = 4b – 2 a
sin (a) = h/r = M
a = (1/sin)M
Rainbow angle
• n*sin(b) = sin(a)
• b= (1/sin)(M/n)
™Finally we have final formula
• e= 4 * (1/sin) (M) – 2*(1/sin)(M)
™Take derivative of e with respect to (M) and find
where it has an extreme by setting the derivative
Equal 0 and solve for (M) we get the final result for
M = ((4-n^2)/3)^(1/2)
(a)
Rainbow Angle
• e has a maximum value given by
• e = (4*(1/sin)(((4-n^2)/3)^(1/2))/n- 2*(1/sin)(((4n^2)/3)^(1/2)). (b)
• n water= 1.333
• Substitute n = 1.33 into (a) and (b) we have
• M = 0.8608
• e = 42.0 degree
Nature Rainbow
• Nature rainbow is created by nature. We can see
the rainbow when it rains or at the waterfall under
the sunshine.
Nature Rainbow
Nature Rainbow
Manmade Rainbows
• Manmade Rainbows are the rainbows that are
created by human.
• We can make our own rainbows in many ways
• We can use a garden hose, a sprinkler, and a water
spout out, and the sunlight to make our own
rainbows.
• We can use a prism and a flashlight to make a
rainbow
• We can also make a rainbow by using a flashlight,
a round container, and a large piece of cardboard.
Stern, an artist and visual arts professor, uses fire trucks,
boats, pumps, and hoses to create rainbows at Germany.
I used a spherical bottle, a flashlight, water, and a piece of
cardboard to create a simple rainbow
References
• http://brantancan.co.uk/rainbow.htm
• http://www.albemarle.cc.nc.us/~aaldridg/mat172/proje
ct2.html
• http://www.psupress.org/samplechapters/justataste_lee.
html
• http://www.unidata.ucar.edu/staff/blynds/rnbw.html
• Overheim, R.Daniel and Wagner, David L. Light and
Color.1982.
• Reese, Ronald Lane. University of Physics.1998.
Thanks for your listening