A light source emits infrared radiation at a wavelength of \(1150 \mathrm{~nm}\). What is the frequency of this radiation?

The speed of light, often denoted by the symbol 'c', is a fundamental constant that is vital to understanding the nature of the universe. It is the speed at which all electromagnetic radiation, including infrared radiation, travels in a vacuum. The value of the speed of light is approximately \( 3 \times 10^8 \) meters per second (m/s).
The speed of light is not just some arbitrary number; it's deeply woven into the fabric of space and time. In fact, according to Einstein’s theory of relativity, \( c \) serves as a cosmic speed limit—nothing can travel faster than light in a vacuum. In our context of studying the properties of infrared radiation, understanding that this is a universal constant helps us derive other important characteristics such as frequency and energy.
For educational purposes, it is crucial to remember that when solving problems involving electromagnetic waves, the value of \( c \) is a key component, and its large numerical value often means careful consideration to units is required to ensure correct calculations.

Converting wavelength to frequency is a common practice when analyzing electromagnetic waves. It's important to understand that these two properties, wavelength and frequency, are inversely related—this is expressed in the formula \( f = c / \lambda \) where \( f \) is the frequency, \( c \) is the speed of light, and \( \lambda \) is the wavelength.

Understanding the Formula

To grasp this concept, imagine a wave. The wavelength (\( \lambda \) ) is the distance between two consecutive peaks of the wave. Frequency (\( f \) ), on the other hand, refers to the number of waves that pass a given point within one second. So when you have a longer wavelength, there are fewer wave peaks passing a point per second, which means a lower frequency. Conversely, a shorter wavelength has more peaks passing, implying a higher frequency.

Application in Calculations

When dealing with electromagnetic radiation like the infrared radiation in our exercise, it's crucial to convert the wavelength from nanometers to meters (since the speed of light is in meters per second) to perform wavelength to frequency conversion. It’s this relationship that allows scientists and engineers to accurately describe and manipulate electromagnetic waves for various applications, such as communications and medical imaging.

The electromagnetic spectrum encompasses all types of electromagnetic radiation, ranging from very short wavelengths (high-frequency gamma rays) to very long wavelengths (low-frequency radio waves). Infrared radiation, which is the focus of our exercise, lies between the visible light and microwave regions of the spectrum.

Diversity of the Spectrum

Each part of the electromagnetic spectrum has unique properties and uses. For example, X-rays are used in medical imaging to see inside the body, while radio waves are used for broadcasting audio and data signals. Infrared radiation itself is often used in remote controls, thermal imaging cameras, and even in astronomy to observe celestial objects obscured by dust.

Education and Practical Implications

For students, understanding the electromagnetic spectrum is essential, not just for academic exercises but also for comprehending how various technologies in our daily lives work. Recognizing where infrared sits on this spectrum, helps clarify why, for instance, it can be felt as heat (because it has a shorter wavelength than microwaves) and why it cannot be seen by the naked eye (it has a longer wavelength than visible light). The concept of the electromagnetic spectrum is foundational in fields like physics, engineering, and even environmental science, where understanding radiation is key to topics ranging from climate change to communication technology.