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

The speed of light, denoted as c, is a fundamental physical constant that travels at approximately 3.00 × 10⁸ meters per second in a vacuum. This relationship can be expressed through the formula:

c = λ × μ

In this equation, λ (lambda) represents the wavelength, while μ (mu) signifies the frequency of the light wave. It is essential to note that frequency is measured in hertz (Hz), which is equivalent to seconds^-1, and wavelength is measured in meters. This ensures that the units are consistent with the speed of light.

Understanding the connection between wavelength and frequency is crucial, as it allows for the calculation of one when the other is known, reinforcing the fundamental principles of wave behavior in physics.

Calculate Frequency Example

To calculate the frequency of red light emitted by a neon sign with a wavelength of 663.8 nanometers, we start by using the relationship between the speed of light, wavelength, and frequency. The equation that connects these variables is:

$c^{=}\lambda \nu$

Where $c$ is the speed of light (approximately $\mathrm{3.00}\times \mathrm{10}^8$ m/s), $\lambda$ is the wavelength, and $\nu$ is the frequency.

First, we need to convert the wavelength from nanometers to meters. Since 1 nanometer is equal to $10^\{-9\}$ meters, we convert 663.8 nanometers as follows:

$663.8\; \backslash ,\; \backslash text\{nm\}\; =\; 663.8\; \backslash times\; 10^\{-9\}\; \backslash ,\; \backslash text\{m\}\; =\; 6.638\; \backslash times\; 10^\{-7\}\; \backslash ,\; \backslash text\{m\}$

Now that we have the wavelength in meters, we can rearrange the equation to solve for frequency:

$\backslash nu\; =\; \backslash frac\{c\}\{\backslash lambda\}$

Substituting the values:

$\backslash nu\; =\; \backslash frac\{3.00\; \backslash times\; 10^8\; \backslash ,\; \backslash text\{m/s\}\}\{6.638\; \backslash times\; 10^\{-7\}\; \backslash ,\; \backslash text\{m\}\}\; \backslash approx\; 4.519\; \backslash times\; 10^\{14\}\; \backslash ,\; \backslash text\{s\}^\{-1\}$

The frequency can also be expressed in hertz (Hz), where 1 Hz is equivalent to 1 s^-1. Therefore, the frequency of the red light is approximately $4.519\; \backslash times\; 10^\{14\}\; \backslash ,\; \backslash text\{Hz\}$.

It is important to note that the answer is reported with four significant figures, consistent with the precision of the given wavelength.

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.