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# Trigonometry in Light Waves

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## Fatimah Khan

on 2 March 2016

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#### Transcript of Trigonometry in Light Waves

History of Light
Light Waves
Humans are able to see light in a narrow spectrum known as the visible light spectrum. The visible light spectrum contains a range of wavelengths and
frequencies of different colors of light that can be seen by the human eye. This spectrum covers the colors that range in wavelength from 700 nanometers (nm) to 400 nm. The only colors that fall in this sprectrum are the band of colors in the rainbow, also known as
R
O
Y
G
B
I
V
(
Red
,
orange
,

yellow
,

green
,

blue
,
indigo
, and
violet
).

Light Waves
When light is shining through a prism, the colors of visible light are shown and separated for each color. In physics, this is known as dispersion. Each color on this spectrum has its own varying wavelength and frequency. The color with the longest wavelength is red. Each color after red in the visible light spectrum has shorter and shorter wavelengths, with violet having the shortest wavelength. Similarly, the frequency is highest at violet and becomes lower as you go backwards in ROYGBIV, making red light have the lowest frequency.
Data for Light Waves
In order to find the function for the graphs of light waves of varying colors, the information from the table above was used.
The following graphs show the light waves for the three colors, red, green, and violet, respectively.
Basics of Trignometry In Light Waves
The frequency is the number of cycles per time. (measured in Hertz)
Thus, one cycle is one full wave before repeating itself.
The volume of the light wave is determined by the height of the wave.
The height is called the amplitude of the wave.
The amplitude of light waves are determined by the speed of the light wave.
The speed is determined by the period of the wave, which is the time it takes for the wave to go through a full.
The period of sin(x) is 2π. This means at every 2π unit the sine wave repeats. So the function sin (2π/
b
.) has period
b
λ.
Trigonometry in Light Waves and Color
In the history of the discovery of how lights are seen, reknowned scientists including the likes of Isaac Newton, Christian Huygens, and Thomas Young provided the world with the first explanations.

Until Thomas Young provided the first concrete piece of evidence in his theory that light travels in waves, there were vast amounts of theories between light being seen because of particles and waves. Since then, scientists have agreed that lights are seen because of both tiny particles as well as waves.

Today, trigonometry can be used to understand these light waves.

The graph above shows the light waves of the three colors, red, green, and violet together. As you can see, the red light wave has the lowest frequency and the higest wavelengt, while Violet has the highest frequency and lowest wavelength, as stated before.
On the previous slide, the graph with the light waves for red, green, and violet are shown. The function for the violet light wave is
y=(π/200)x
. This is found using the data given in the table in slide 6. The data says that the violet wavelength is between 430 nm to 380 nm. So, if you have a wavelength (
b
), for example, of 400 nm, the light will be seen as violet. In order to find the period, you must follow the (2π /b) format. In the case of a wavelength of 400 nm, you would have (2π/400), which simplifies to (π/200). This is the period for the graph.

According to the data table in slide 6, the green wavelength is between 565 nm and 520 nm. So, if you use a wavelength of 540 nm, you will see green light. In order to find the period, you must use (2π /b). This equals to (2π/540), which simplifies to (π/270). This is the period for the green light. The function that represents this scenario is
y=(π/270)x
.

According to the data table, the red wavelength is between 740 to 625 nm. So, if you use a wavelength of 700 nm, you will see red light. In order to find the period, you must use (2π /b). With a wavelength of 700 nm, you would have (2π/700). This simplifies to (π/350), giving you the period of this graph for the red wavelength. The function of the graph is represented by
y=(π/350)x
.

Functions of Red, Green, and Violet Wavelengths
Fatimah Khan & Jasmine Sawh
Bibliography
http://www.relativitycalculator.com/Albert_Michelson_Part_I.shtml

http://www.physicsclassroom.com/class/light/Lesson-2/The-Electromagnetic-and-Visible-Spectra

http://www.timaras.com/science/light1.html

https://graphsketch.com/?eqn1_color=1&eqn1_eqn&eqn2_color=2&eqn2_eqn=sin%28.009x%29&eqn3_color=3&eqn3_eqn=sin%28.012x%29&eqn4_color=4&eqn4_eqn&eqn5_color=5&eqn5_eqn=sin%28.016x%29&eqn6_color=6&eqn6_eqn&x_min=-500&x_max=500&y_min=-1&y_max=1&x_tick=1&y_tick=1&x_label_freq=50&y_label_freq=.5&do_grid=0&bold_labeled_lines=1&line_width=4&image_w=1600&image_h=525
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