Speed of Light: Videos & Practice Problems

Understanding the relationship between the speed of light, wavelength, and frequency is crucial in the study of electromagnetic radiation. The speed of light (c) is a fundamental physical constant with a value of approximately 3.0 x 10⁸ meters per second in a vacuum. It can be expressed using the equation:

$c=\lambda \nu$

where λ (lambda) represents the wavelength in meters, and ν (mu) denotes the frequency in hertz (Hz), which is equivalent to seconds^-1. This equation highlights that as the wavelength increases, the frequency decreases, and vice versa, while the speed of light remains constant. This concept is a cornerstone in fields such as physics and chemistry, where the behavior of light and other forms of electromagnetic radiation is analyzed.

Speed of Light Formula

So here we say the speed of light is the product of wavelength and frequency, and in a vacuum it travels at a speed of 3.00×108 meters per second. And we're going to say here it is a physical constant and uses the variable C. So we know that C now represents the speed of light and with it we have our speed of light formula.

Here, see our speed of light equals wavelength, which we said was Lambda, times our frequency, which we said was MU. O. Here we're going to say remember frequency uses MU and wavelength uses Lambda. And remember frequency is in units of seconds inverse, which is equivalent or equal to Hertz, and that wavelength is in units of meters.

Remember it's in these units so that it matches the units of our speed of light. Now that we know how wavelength and frequency are connected to the speed of light, move on to the next video and take a look at the example question.

Calculate Frequency Example

In this example, it says to calculate the frequency of the red light emitted by a neon sign with a wavelength of 663.8 nanometers. All right, so we need to determine what our frequency is, which is mu. They're giving us our wavelength, which is Lambda. Remember, the equation that connects them together is that the speed of light equals them multiplying one another.

Now remember, wavelength needs to be in units of meters, so we need to do a metric prefix conversion where we have 663.8 nanometers. We're going to say here that for every one nanometer it's 10 to the -9 meters. So here meters will come out to be 6.638 * 10^-7 meters. Now that we have that, we can plug it in.

We have the speed of light we have. We're looking for our frequency. We have our wavelength in meters, so divide both sides now by meters. So when we do that we're going to get left at the end our seconds inverse. So here we're going to say frequency equals 4.519 * 10¹⁴ seconds^-1. Because remember meters cancel out here, so we're left with one over seconds, which is the same thing as seconds inverse.

OK, so your units can be either one over seconds or seconds inverse or Hertz. All of them mean the same thing. And here answer has four sig figs because our wavelength was given to us also within 4 sigfix.

Even the music we listen to deals with how energy travels to get to our car radio. If an FM Radio station broadcasts its music at 97.7 MHz find the wavelength in angstroms of the radio waves. One angstrom is equal to 10^-10 m.

• A. 4.01 x 10¹⁰ Å
• B. 3.07 x 10¹⁰ Å
• C. 6.53 x 10¹¹ Å
• D. 2.54 x 10¹¹ Å

Answer: (B)

The distance between the earth and the sun is 1.496 x 10¹⁷ μm. How long (in mins) will it take for light to go from the sun to earth?

• A. 5.192 min
• B. 11.524 min
• C. 8.311 min
• D. 7.968 min

Answer: (C)

When they are burned, certain elements emit light at a specific wavelength. Some wavelengths for certain elements are provided below:

When burned, an unknown element emits light at a frequency of 9.23 x 10¹⁴ s^-1. What is the identity of this unknown element?

• A. 326 nm
• B. 585 nm
• C. 325 nm
• D. 454 nm

Answer: (C)

Here’s what students ask on this topic:

What is the speed of light?

The speed of light, denoted as "c," is a fundamental physical constant that represents the maximum speed at which all energy, matter, and information in the universe can travel. It is also the speed at which light waves propagate through a vacuum. The exact value of the speed of light is 299,792,458 meters per second (approximately 300,000 kilometers per second or roughly 186,282 miles per second). This incredible speed is used as a baseline in the theory of relativity and has profound implications for our understanding of space and time. It's important to note that while light can travel slower than this speed when passing through various mediums like water or glass due to refraction, it cannot exceed this speed in a vacuum.

How do you calculate wavelength from frequency?

To calculate the wavelength from frequency, you can use the formula that relates wavelength (λ), frequency (f), and the speed of light (c):

$\lambda =\frac{c}{f}$

Here, λ (lambda) represents the wavelength, c is the speed of light in a vacuum (approximately 3 x 10⁸ meters per second), and f is the frequency of the wave in hertz (Hz), which is equivalent to cycles per second.

For example, if you have a wave with a frequency of 2 x 10⁶ Hz (2 MHz), you would calculate the wavelength like this:

$\lambda =\frac{3\times 108^{}\text{m/s}}{2\times 106^{}\text{Hz}}$

λ = 150 meters

So, the wavelength of a wave with a frequency of 2 MHz is 150 meters. Remember that this formula is specific to electromagnetic waves in a vacuum. If the medium changes, such as air or water, the speed of light changes accordingly, and you would need to use the speed of light for that medium in your calculation.