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# Chapter 3: Basic Physics SE-Light Nature

Difficulty Level: At Grade Created by: CK-12

PART I: Nature of Light, Polarization, Color

The Big Idea

Light is a wave of changing electric and magnetic fields. Light waves are caused by disturbances in the electromagnetic field that permeates the universe, for example, the acceleration of charged particles (such as electrons). Light has a dual nature: at times, it acts like waves; at other times it acts like particles, called photons. Light travels through space at the maximum speed allowed by the laws of physics, called the speed of light. Light has no mass, but it carries energy and momentum. Of all possible paths light rays will always take the path that takes the least amount of time (not distance). This is known as Fermat’s Principle.

Light, more generally known as Electromagnetic Waves (EM Waves), can be produced in many different wavelengths that can be very large to extremely small. EM waves can be polarized when produced or after going through a filter (natural or man-made). Polarization of light, means that the light wave oscillates in only one direction rather than unpolarized light that oscillates in two directions as it moves forward.

The visible range of light (i.e. the range of wavelengths that our eyes can detect) is a very narrow piece of the full EM spectrum. In the visible range our eyes differentiate between the different wavelengths by producing ‘color’ for them. When we observe something that is green, it is green to us, because the wavelength of the light hitting our eyes is around 550 nm. If the wavelength of light is slightly larger than this it starts to look red, if it is slightly smaller it looks blue. White light is the combination of all the colors. Black light is the absence of EM waves in the visible spectrum for human beings.

Key Concepts

• Light is produced when charged particles accelerate. As a result changing electric and magnetic fields radiate outward. The traveling electric and magnetic fields of an accelerating (often oscillating) charged particle are known as electromagnetic radiation or light.
• The color of light that we observe is nothing more than the wavelength of the light: the longer the wavelength, the redder the light.
• Light can have any wavelength at all. Our vision is restricted to a very narrow range of colors between red and violet.
• The spectrum of electromagnetic radiation can be roughly broken into the following ranges:
Color Wavelength range Comparison size
gamma-ray (\begin{align*}\gamma\end{align*} - ray) \begin{align*}10 ^{- 11} \ m\end{align*} and shorter atomic nucleus
\begin{align*}x\end{align*}-ray \begin{align*}10^{-11} \ m - 10^{-8} \ m\end{align*} hydrogen atom
ultraviolet (UV) \begin{align*}10^{-8} \ m - 10^{-7} \ m\end{align*} small molecule
violet (visible) \begin{align*}\sim 4 \times 10^{-7} \ m \ (400 \ nm)^*\end{align*} typical molecule
blue (visible) \begin{align*}\sim 450 \ nm\end{align*} typical molecule
green (visible) \begin{align*}\sim 500 \ nm\end{align*} typical molecule
red (visible) \begin{align*}\sim 650 \ nm\end{align*} typical molecule
infrared (IR) \begin{align*}10^{-6} \ m - 1 \ mm\end{align*} human hair
microwave \begin{align*}1 \ mm - 10 \ cm\end{align*} human finger
radio Larger than 10 cm car antenna
• The brightness, or intensity, of light is inversely proportional to the square of the distance between the light source and the observer. This is just one of many inverse square laws in physics; others include gravitational and electrical forces.
• Fermat’s Principle makes the angle of incident light equal to the angle of reflected light. This is the law of reflection.
• When light travels from one type of material (like air) into another (like glass), the speed changes due to interactions between photons and electrons. Transparent materials transmit the electromagnetic energy at a speed slower than \begin{align*}c\end{align*}; opaque materials absorb that EM energy and convert it into heat. A material may be transparent to some wavelengths of light but opaque to others.
• Polarized light is made of waves oscillating in only one direction: horizontal or vertical. The direction of the oscillation of the light waves is the same as the direction of oscillation of the electron creating the light. Unpolarized light can be polarized selectively by reflections from surfaces (glare); the orientation of the reflected light polarization is the same as that of the surface.
• White light consists of a mixture of all the visible colors: red, orange, yellow, green, blue, indigo, and violet (ROYGBIV). Our perception of the color black is tied to the absence of light.
• Our eyes include color-sensitive and brightness-sensitive cells. The three different color-sensitive cells (cones) can have sensitivity in three colors: red, blue, and green. Our perception of other colors is made from the relative amounts of each color that the cones register from light reflected from the object we are looking at. Our brightness-sensitive cells (rods) work well in low light. This is why things look ‘black and white’ at night.
• The chemical bonds in pigments and dyes – like those in a colorful shirt – absorb light at frequencies that correspond to certain colors. When you shine white light on these pigments and dyes, some colors are absorbed and some colors are reflected. We only see the colors that objects reflect.

Red Green Blue Perceived color
\begin{align*}\checkmark\end{align*} \begin{align*}\checkmark\end{align*} \begin{align*}\checkmark\end{align*} white
black
\begin{align*}\checkmark\end{align*} \begin{align*}\checkmark\end{align*} magenta
\begin{align*}\checkmark\end{align*} \begin{align*}\checkmark\end{align*} yellow
\begin{align*}\checkmark\end{align*} \begin{align*}\checkmark\end{align*} cyan

Key Applications

• Rayleigh scattering occurs when light interacts with our atmosphere. The shorter the wavelength of light, the more strongly it is disturbed by collisions with atmospheric molecules. So blue light from the Sun is preferentially scattered by these collisions into our line of sight. This is why the sky appears blue.
• Beautiful sunsets occur when light travels long distances through the atmosphere. The blue light and some green is scattered away, leaving only red and a little green, making the sun appear red.

Key Equations

• \begin{align*}c = \lambda f\end{align*} ; The product of the wavelength \begin{align*}\lambda\end{align*} of the light (in meters) and the frequency \begin{align*}f\end{align*} of the light (in Hz, or \begin{align*}\frac{1}{sec}\end{align*}) is always equal to a constant, namely the speed of light \begin{align*}c = 300,000,000 \ m/s\end{align*}.

Light Questions

1. Which travels faster - a radio wave or a sound wave? What’s the fundamental difference between the two? (bonus: name another fundamental difference between the two)
2. Light does not travel infinitely fast – its speed in a vacuum is \begin{align*}3 \times 10^8 \ m/s\end{align*}. We measure very large astronomical distances in “light years” (LY) – the distance light travels in one year. The closest star beyond our sun is Alpha Centauri, 4 LY away. Some distant quasars are 2 billion LY away. Why do astronomers say that to look at these distant objects is to look back in time? Explain briefly.
3. When light impinges upon an object three things can happen to it: absorption, transmission, or reflection. Discuss an example of each.
4. Which corresponds to light of longer wavelength, UV rays or IR rays?
5. Which corresponds to light of lower frequency, \begin{align*}x-\end{align*}rays or millimeter-wavelength light?
6. Approximately how many blue wavelengths would fit end-to-end within a space of one millimeter?
7. Approximately how many short (“hard”) \begin{align*}x-\end{align*}rays would fit end-to-end within the space of a single red wavelength?
8. Calculate the frequency in Hz of a typical green photon emitted by the Sun. What is the physical interpretation of this (very high) frequency? (That is, what is oscillating)?
9. FM radio stations list the frequency of the light they are emitting in MHz, or millions of cycles per second. For instance, 90.3 FM would operate at a frequency of \begin{align*}90.3 \times 10^6 \ Hz\end{align*}. What is the wavelength of the radio-frequency light emitted by this radio station? Compare this length to the size of your car’s antenna, and make an argument as to why the length of a car’s antenna should be about the wavelength of the light you are receiving.
10. Our sun is 8 “light minutes” from earth.
1. Using the speed of light as \begin{align*}c\end{align*} calculate the earth-sun distance in \begin{align*}m\end{align*}, then convert it to miles (one mile = 1609 m)
2. The nearest galaxy to our Milky Way is the Andromeda Galaxy, 2 million light years away. How far away is the Andromeda Galaxy in miles?
11. Consult the color table for human perception under the ‘Key Concepts’ section and answer the questions which follow.
1. Your coat looks magenta in white light. What color does it appear in blue light? In green light?
2. Which secondary color would look black under a blue light bulb?
3. You look at a cyan-colored ribbon under white light. Which of the three primary colors is your eye not detecting?
12. The primary colors of light are red, green, and blue. This is due to the way our eyes see color and the chemical reactions in the cone cells of the retina. Mixing these colors will produce the secondary, or complementary colors: magenta, cyan and yellow, as well as white. On the diagram below label colors to show how this works:
13. Color printers use a different method of color mixing: color mixing by subtraction. What colors are used in this process? (HINT: look at the ink colors in an ink-jet printer, CYMB). The idea here is that each color subtracts from the reflected light – for example, cyan ink reflects blue and green but SUBTRACTS red. If Explain with diagrams how CYM can be combined to produce red, blue, and green.
14. Answer the following light transmission questions
1. A beam of cyan light passes into a yellow filter. What color emerges?
2. A beam of yellow light passes into a magenta filter. What color emerges?
3. What color results when two beams of light, one cyan and one magenta, are made to overlap on a white screen?
4. White light passes through a cyan filter followed by a magenta filter. What color emerges?
15. Describe the function of the dye in blue jeans. What does the dye do to each of the various colors of visible light?
16. Why is the sky blue? Find a family member who doesn’t know why the sky is blue and explain it to them. Ask them to write a short paragraph explaining the situation and include a sketch.
17. Above is a graph of wavelength vs. intensity for sunlight reaching Earth.
1. Why does less light reach Earth’s surface than the top of the atmosphere?
2. Calculate the frequency of the most abundant light reaching the top of the atmosphere.
3. Which color of light is removed most in the atmosphere? How does this explain why the sky is the color it is? Explain this phenomenon with respect to the composition of the atmosphere.
18. Ocean water appears cyan because the microbes in the water preferentially absorb red light. What color does a red lobster appear on the ocean floor? How about a white shirt with blue stripes?
19. Explain how you could tell whether or not the light from a plasma screen TV is polarized.
20. A radio wave is emitted and bounces off some object, and returns in a total of \begin{align*}5.5 \ \mu s\end{align*}. How far away is the object?
21. Here on Earth you can run a solar calculator using a solar panel about \begin{align*}1 \ cm \times 2 \ cm\end{align*}. Suppose you take your calculator to Neptune, 30 AU from the sun. (The earth-sun distance is defined as 1 AU, or astronomical unit).
1. What fraction of sunlight intensity hits your solar panel at Neptune compared with at Earth?
2. Design a solar panel (size) that would allow you to collect the same amount of solar power (same amount of light energy in same time) on Neptune as on Earth.
22. You are reading two feet from a lamp with a 100 W (100 Watts) light bulb. For this problem, assume that a 100 W bulb is exactly half as bright as a 200 W bulb and that 50 W is half as bright as the 100 W bulb.
1. If you move 100 feet away from the lamp, how many 100-watt bulbs would you need to get the same amount of light to read as you had before?
2. Suppose you are reading 5 feet from a lamp with a 50 W bulb – it burns out and someone replaces the bulb with a 200-watt bulb. How far away from the lamp will you need to sit now to get the same amount of light?
23. A cell phone has an average power output of 1 watt, and you hold it about a cm from your brain. A strong TV signal from a transmitter like Sutro Tower has a power output of 1 million watts. Remembering the inverse-square law, how far could you stand from Sutro Tower to receive the same rate of radiation as from a cell phone? Express your answer in meters and in feet.
24. How do we know the universe is expanding? (hint: what is meant by ‘redshift’)
25. Explain why polarized sunglasses are often used by skiers, boaters, drivers, etc. Which way would the lenses be polarized? Draw a diagram to illustrate your answer.
26. Polarized filters block 50% of unpolarized light. If two filters are oriented so that their polarization axes are aligned, how much light is transmitted? What about if their axes are oriented perpendicular to each other? Draw two diagrams below to support your answers.
27. Polarized glasses are used to view 3-D movies. Do a little online research and explain below how these movies are projected to get the 3-D effect. How are the viewing glasses’ polarization axes oriented? A diagram may be helpful.
28. Stars may look mostly white to the naked eye, but they actually emit different colors depending upon their temperature. A HOT star (ie, Sirius) will emit more energetic light while a cooler star (ie, Betelgeuse) will emit light of lower energy. What color is each star? What would you infer about our yellow sun based upon this information?

1. IR
2. millimeter-wavelength light
3. 2200 blue wavelengths
4. 65000 \begin{align*}x-\end{align*}rays
5. \begin{align*}6 \times 10^{14} \ Hz\end{align*}
6. 3.32 m

1. \begin{align*}8.9 \times 10^7 \ miles\end{align*}
2. \begin{align*}1.9 \times 10^{22} \ m = 1.2 \times 10^{19} \ miles\end{align*}
1. blue, black
2. yellow
3. red

1. green
2. red
3. blue
4. blue

1. Light is scattered from the molecules in our atmosphere
2. \begin{align*}6.7 \times 10^{14} \ Hz\end{align*}
3. blue light, it’s scattering causes sky to be blue (see teacher for more thorough explanation)
1. black; cyan with blue stripes
2. using a polarizer, rotate it and if color darkens, then polarized
3. 825 m

1. \begin{align*}\frac{1}{900}\end{align*}
2. \begin{align*}1800 \ cm^2\end{align*} (ex. 60 cm by 30 cm)

1. 2500 light bulbs of 100W
2. 10 ft
1. 10 m

Chapter Outline