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Visualizing video at the speed of light – MIT researchers created a video where you can see photons traveling through a medium.

Finding the speed of light with peeps – Use your favorite marshmallow candy and a microwave to calculate the speed of light!

Table of SI Prefixes


Video Transcript

Hello there! Welcome to lecture 26: light.

Light is all around us: some of it we can see, and some if it we cannot. From the Wi-Fi or cellular signal you’re using to connect to the Internet to watch this video, to the light waves emanating out of your laptop or smart phone screen, to the infrared you are emitting as heat, the electromagnetic spectrum is possibly one of the most important aspects of our daily lives.

Each of the following concepts will be discussed in this video: electromagnetism, SI prefixes, the electromagnetic spectrum, radio waves, microwaves, ionizing radiation, and light waves.


As we’ve learned in lectures 24 and 25, electricity can generate magnetism and magnetism can generate electricity. As fields, an electric field can generate a magnetic field, and so on. This process does not require the presence of a magnet or an electronic circuit. An electromagnetic wave is a transverse wave composed of both an oscillating electric field and an oscillating magnetic field, both at right angles to each other. Those oscillating electromagnetic fields propagate through space. We’ll discuss all the different types of electromagnetic waves in just a few moments.

The speed of light is 3 times 10 to the 8 meters per second. That is, 300 million meters per second! The speed of light is represented by the lowercase letter c. When discussing electromagnetic waves, the equation v equals lambda f becomes c equals lambda f. 

In the mid 1800s, James Clerk Maxwell discovered that the speed of electromagnetic waves is equal to the speed of light, leading him to conclude that light is simply a type of electromagnetic radiation. Maxwell’s equations are used today by scientists, engineers, and students all around the world to study electromagnetism.

In the early twentieth century, Albert Einstein postulated that the speed of light is constant, and acts as something like a universal speed limit. As far as we know, nothing can travel faster than the speed of light.

Electromagnetic waves are capable of travelling through the vacuum of space. This makes them very different from waves such as sound and water waves that require a medium to travel through. In fact, light travels through the vacuum of space between stars and our planet. Notably, the sun produces most of the electromagnetic radiation we experience here on Earth.

We can use the speed of light to calculate how long it takes light waves to travel between the Sun and the Earth. Because the velocity is constant throughout the trip, we can use the equation velocity equals distance over time to solve for the time. The distance between the Earth and Sun is approximately 150 billion meters, or 150 times 10 to the 9 meters. The speed of light is 3 times 10 to the 8 meters per second. Therefore, the amount of time it takes light to travel this distance is 150 times 10 to the 9 meters divided by 3 times 10 to the 8 meters per second, which is 500 seconds. Dividing by 60 we see that is equal to 8.3 minutes. If the sun were to somehow disappear, we wouldn’t know until 8.3 minutes later when the light stopped reaching the Earth’s surface.

SI prefixes

Our discussion of electromagnetic waves will require us to discuss quantities that are both extremely small and extremely large. Instead of using scientific notation to deal with these quantities, we can instead use prefixes. The SI prefixes have been standardized for use with the International System of Units (SI). These prefixes can be used with any type of SI unit: meter, volt, second, gram, and so on.

Let’s say we’re defining a quantity with units of meters. That is the regular unit. When we have thousands of meters, we use the prefix kilo, defined by the lowercase letter k. The prefix kilo means we are multiplying something by ten to the three, one thousand. When used with the base of meter, we get units of kilometer.

The next prefix is mega, defined by the capital letter M. The prefix mega means we are multiplying something by ten to the six: one million.

Next is giga, defined by the capital letter G. The prefix giga means that a quantity is being multiplied by ten to the nine: one billion.

Next is tera, defined by the capital letter T. The prefix tera means that something is multiplied by ten to the twelve: one trillion.

Next is peta, defined by the capital letter P. Peta indicates that we are multiplying by ten to the fifteen: one quadrillion.

While there are more after exa, we will stop here. Exa is defined by the capital letter E, and denotes multiplication by ten to the eighteen: one quintillion.

As a quantity such as a meter becomes smaller, we can use prefixes that indicate fractions of ten. The prefix milli, defined by the lowercase letter m, is used to define a multiplication by ten to the negative three: one thousandth. You may be familiar with the unit of millimeter: one thousandth of a meter.

Next is micro, defined by the lowercase Greek letter mu. Micro indicates that a number is being multiplied by ten to the negative six: one millionth.

Next is nano, defined by a lowercase n. Nano is a multiplication by ten to the negative nine: one billionth.

Next is pico, defined by a lowercase p. Pico denotes that a quantity is being multiplied by ten to the negative twelve: one trillionth.

Femto, defined by a lowercase f, means that we are multiplying by ten to the negative fifteen: one quadrillionth.

And while numbers can get smaller than atto, we will stop here. Atto is defined by the lowercase letter a, and denotes multiplication by ten to the negative eighteen: one quintillionth.

The electromagnetic spectrum

There are many types of waves in the electromagnetic spectrum. Each of these waves can be defined in different categories, and each wave has different properties. The electromagnetic spectrum defines each type of wave based on its frequency or wavelength. Because the speed of electromagnetic waves is a constant, wavelength and frequency are inversely related to each other. If frequency is known, the wavelength of an electromagnetic wave equals c over f. If wavelength is known, the frequency of an electromagnetic wave is c over lambda.

The energy of each wave is proportional to frequency, and inversely proportional to wavelength. We will discuss the equation used to define the energy of electromagnetic waves in lecture 31.

At the lowest energy, lowest frequency, longest wavelength end of the spectrum are radio waves. We’ll discuss the uses of radio waves in a few moments. These waves have wavelengths greater than 3 meters, which corresponds to frequencies less than 100 megahertz.

Next along the spectrum are microwaves. Microwaves have lots of interesting uses that we’ll discuss in several minutes. Microwaves have wavelengths between 3 meters and 1 millimeter, and frequencies ranging from 100 megahertz to 300 gigahertz.

Infrared radiation, or IR, has wavelengths between 1 millimeter and 750 nanometers. The frequencies range from 300 gigahertz to 400 terahertz. 

As we learned in lecture 16, one of the mechanisms of heat transfer is via electromagnetic radiation. Most “cool” objects such as humans, plants, and animals emit heat in the infrared region of the electromagnetic spectrum. Therefore, the infrared region of the electromagnetic spectrum is extremely helpful in any types of science and technology that require us to study heat.

Thermal cameras have a sensor that collects infrared radiation rather than visible light. This allows us to use IR for night vision, thermal imaging, and many other applications. For example, satellite imagery of cloud coverage is used as weather observations that aid in forecasting. After sunset and before sunrise, visible satellite images cannot record any meaningful data. However, IR satellites can take images corresponding to the heat reflected from the planet’s surface, which correlates to cloud coverage.

This is a visual satellite image taken just after sunset in Illinois on October 11, 2019. The entire east coast and most of the Midwest is dark, due to the fact that there was no light present to create an image. The IR satellite view shows a very different picture: that of a tropical storm that had recently made landfall on the east coast!

Visible light is the light we can see. Visible light is a very tiny portion of the electromagnetic spectrum, encompassing wavelengths from 750 nanometers to 400 nanometers. The longest wavelength of visible light corresponds to red, and the shortest wavelength of visible light corresponds to violet. The frequencies of visible light span from 400 terahertz to 750 terahertz.

The next three types of waves along the electromagnetic spectrum are high energy, collectively referred to as ionizing radiation, which we’ll discuss in more detail in a few moments.

Ultraviolet, or UV, radiation has wavelengths between 400 nanometers and 10 nanometers. These correspond to frequencies between 750 terahertz and 30 petahertz.

Next are x-rays. X-rays have wavelengths between 10 nanometers and 10 picometers, and frequencies between 30 petahertz and 30 exahertz.

Any electromagnetic radiation with wavelengths less than 10 picometers and frequencies above 30 exahertz are known as gamma radiation. These are the highest energy waves on the electromagnetic spectrum.

Radio waves

Radio waves, as mentioned, comprise the lowest-energy region of the electromagnetic spectrum. Contrary to what the name implies, radio waves are not only comprised of the waves we tune into to listen to music or talk radio.

First, let’s talk about why we need to use radio waves to transmit sound over long distances. What is the difference between sound waves and radio waves? As we discussed in lecture 20, sound waves are longitudinal pressure waves. They require some type of medium through which to travel. In addition, sound waves don’t travel very far before they become inaudible. To hear the sound of somebody’s voice over long distances, another method for transmitting that sound is required.

To that end, a sound wave can be encoded onto a radio wave and transmitted by means of some electric circuitry and an antenna. Radio waves are part of the electromagnetic spectrum, travel at the speed of light, and can easily transmit through the Earth’s atmosphere over much longer distances than sound waves. These radio waves are received by something like a radio or walkie-talkie and decoded back into vibrations through a speaker into sound waves.

The radio wave portion of the electromagnetic spectrum is used for a lot of applications. This is because long-wavelength light can travel over very long distances. Some radio waves can reflect off of the Earth’s ionosphere and travel nearly around the globe. Many radio waves can travel through clouds and storms, which means that their transmission will not be affected by weather. The longest wavelengths of radio waves are only limited by the difficulty in generating these waves, which would require extremely large antennas.

The applications of radio waves include telephone signals; military, aircraft, and maritime communication; aircraft navigation; WWVB and other similar time signals; CB and amateur radio; TV broadcasts; and AM/FM radio.

AM and FM refer to the two methods of sending radio waves to a radio receiver. These are amplitude modulation and frequency modulation. These two modulation methods describe how a sound wave is converted into a radio wave. 

In amplitude modulation (AM), the amplitude of the radio wave (known as the carrier wave) is modified to reflect changes in the sound wave.

In this animation, the high frequency wave, shown in red, is the carrier wave. This is the radio wave used to transmit the signal. The sound wave source is shown in blue. The amplitude of the carrier wave is multiplied by the amplitude of the sound wave, creating an amplitude-modulated wave.

The frequencies of AM radio stations in the US vary from 540 kilohertz to 1700 kilohertz. AM radio, while popular in the early twentieth century, is now used very infrequently, and may be considered by some to be obsolete. Many AM radio stations consist of talk or sports radio. Because of the long wavelengths of AM radio, the signals travel very far. However, because the wavelengths are physically large, they do not transmit well through small spaces like tunnels. AM radio reception will therefore become blocked when driving through tunnels, underpasses, or possibly even parking garages.

Using frequency modulation (FM), the frequency of the carrier wave is modified to reflect changes in the sound wave.

In this animation, the carrier wave is shown in red and the sound wave source is shown in blue. The frequency of the carrier wave is equal to the amplitude of the sound wave, creating a frequency-modulated wave.

The frequencies of FM radio stations in the US vary from 88.1 megahertz to 107.9 megahertz. FM radio is much more popular than AM radio as it is less susceptible to noise, and has much higher sound quality than AM radio. However, due to the shorter wavelengths, FM radio signals cannot travel as far.


Microwaves travel line-of-sight distances. Unlike radio waves, they cannot bounce off the ionosphere or travel along the curvature of the Earth. For this reason, microwaves are used in applications where the signals only need to travel over short distances. Some, but not all, microwaves can transmit through buildings, but again, only over short distances.

Much of our modern life is transmitted over microwaves: wifi, Bluetooth, cellular, and GPS and other satellite signals. In addition, things such as garage door openers, collision detectors in cars, and radar use microwaves.

Perhaps when you heard the word microwave, you thought about cooking food. In fact, microwave ovens do use microwaves to cook food. At just the right frequency, microwaves can cause the water and fat molecules in food to heat up. Microwave ovens emit microwave radiation at a 2.45 gigahertz frequency, usually with power levels between 600 watts and 1200 watts.

Most microwave ovens contain a sticker inside the door that shows the frequency of operation and power level. My microwave oven emits at 2.45 gigahertz and has a power rating of 950 watts.

The interesting thing to note is that most of our Bluetooth and Wi-Fi communication also occur right around that 2.4 to 2.5 gigahertz frequency range. Our mobile devices communicate using complex protocols that ensure that one signal does not get confused for another. My laptop’s Wi-Fi receiver will not get confused when I receive a cellphone call or send a text message. And the reason that a microwave oven is dangerous enough to require metal shielding, and a cellphone and wireless router is not, is due to the power rating. A microwave oven uses microwave radiation at power levels about one thousand times stronger than those used by our modern telecommunication devices!

Ionizing radiation

Electromagnetic radiation with frequencies greater than that of visible light: short-wavelength UV, x-rays, and gamma rays, is known as ionizing radiation. That’s because the energy of these waves is so great that it can ionize atoms. This can be very dangerous for humans, plants, and animals as it can cause damage to our DNA and other tissues.

Ultraviolet radiation is emitted by the sun. Some of this UV transmits through the Earth’s atmosphere, and is the reason why our skin becomes darker with sun exposure. Sunscreen can help block the damage caused by UV light. Higher frequencies of UV are blocked by the Earth’s ozone layer and do not reach the surface of the planet.

While ultraviolet radiation can be damaging to us, that doesn’t mean it isn’t useful. Mercury vapor lights generate UV, which then is converted by a phosphor to visible light. This is how fluorescent lamps work, as we’ll discuss in lecture 30. The integrated circuits comprising your computer processor are fabricated in clean rooms using a photolithography process that uses UV rays to pattern the transistors in the processor hardware. UV is also used in medical imaging, sterilization, bug zappers, and curing lamps.

X-rays are used widely in medical imaging. Their ability to permeate through soft tissue and be blocked by our bones makes it an extremely helpful diagnostic tool. However, x-rays are dangerous and they should not be used without medical justification. We’ll discuss x-rays in more detail in lecture 33.

Finally, gamma rays reside at the highest energy end of the electromagnetic spectrum. Gamma rays are produced by radioactive decay, a process we’ll discuss in lecture 33. Gamma radiation is extremely hazardous to humans, as it can cause damage to our internal organs and bone marrow. Gamma radiation, while dangerous, does have its applications. Its ability to travel through many objects makes it useful for scanning objects in container trucks at border checkpoints, irradiating objects from harmful bacteria, and gamma rays do have limited use in nuclear medicine. 

Light waves

Light waves have lots of interesting properties. In fact, we’ll learn later on that light isn’t even really just a wave, there’s a lot more to it!

There are a lot of things that can happen to electromagnetic waves as they travel between two points. Reflection and refraction have to do with bending and bouncing, which we’ll discuss in lecture 28. If you’ve ever looked in a mirror, you’ve experienced the reflection of light waves.

Light can also be transmitted and absorbed. When I look out a window, visible light transmits through and I’m able to see what’s going on outside. When I look at a wall in my house, visible light does not transmit through, and I cannot see through the wall. A combination of reflection and absorption on the other side of the wall prevents the light from getting to my side. We’ll discuss how transmission and absorption play a role in the colors of objects in lecture 27.

Whether or not objects allow light waves to pass through gives them different properties. We say that an object that does not transmit any visible light to through it is opaque. This piece of cardboard is opaque. When I hold it up between the camera and my face, I cannot see the camera, and as a result, you cannot see my face.

An object that allows visible light to pass through without getting scattered is known as transparent. This sheet of plastic is transparent, as you can see my face through the object.

An object that allows light to pass through, but scatters the light in the process, is known as translucent. This means the image becomes blurry or otherwise hard to make out entirely. This piece of plastic is translucent. You can see that there’s definitely something on the other side of it, but may not be able to give any detail about it.

One of the fascinating things about light is that something transparent to one type of electromagnetic radiation may be opaque to another! My eyeglasses have glass lenses. This glass allows visible light to transmit through, they are transparent to visible light. However, when you take an infrared photo of me wearing my glasses, the glasses block the infrared emissions from getting to the camera sensor. Glass is opaque to infrared.

Similarly, our atmosphere is transparent to some types of light and opaque to others. This is why some radio waves can travel over long distances due to being reflected by the atmosphere. And it’s also why satellites using microwaves can send information to our smart phones and GPS devices, as the atmosphere is transparent to many microwave frequencies.

Thanks for taking the time to learn about light! Until next time, stay well.