By the end of this lesson, students will be able to:

Electromagnetic radiation refers to the propagation of energy in the form of waves or particles through space. It encompasses a wide range of phenomena, including radio waves, microwaves, infrared radiation, visible light, ultraviolet radiation, X-rays, and gamma rays.

The behavior of electromagnetic radiation is described by its wave-like properties, such as wavelength, frequency, and amplitude. Wavelength is the distance between successive crests or troughs of a wave, and frequency is the number of complete waves passing through a given point per unit of time. The wavelength λ and frequency ν are inversely proportional—the shorter the wavelength, the higher the frequency, and vice versa where the proportionality constant is the speed of light c.

$c\=$λν

The electromagnetic spectrum categorizes electromagnetic radiation based on its wavelength or frequency. It ranges from long-wavelength, low-frequency radio waves to short-wavelength, high-frequency gamma rays. Visible light, which is the portion of the spectrum that humans can perceive, occupies a small range of wavelengths between infrared and ultraviolet radiation. (see Fig. 1)

Electromagnetic radiation interacts with matter in various ways depending on its wavelength. For example, radio waves and microwaves are commonly used for communication and heating applications, while visible light allows us to see the world around us. X-rays and gamma rays, on the other hand, possess higher energy and can penetrate through matter, making them useful for medical imaging and industrial applications.

It's important to note that while electromagnetic radiation is essential for various technologies and natural processes, excessive exposure to certain types (e.g., X-rays and gamma rays) can be harmful to living organisms. Therefore, appropriate safety measures and regulations are in place to mitigate potential risks associated with such radiation.

Figure 1: Chart of the Electromagnetic Spectrum (License: Creative Commons Attribution-Share Alike 3.0 Unported)

The first successful measurement of the speed of light is attributed to Danish astronomer Ole Rømer in the late 17th century. Rømer made this groundbreaking discovery while studying the motion of Jupiter's moon Io. He noticed that the timing of Io's eclipses by Jupiter seemed to vary depending on Earth's position in its orbit around the Sun.  Today the speed of light is a well-known constant that is available in Maple.

or

Using evalf that evaluates expressions in Maple to a floating-point number yields its known value in Standard International (SI) units, which are meters/second or m/s

We can use the speed of light constant that we just defined as the symbol c in solving problems!  For example, a radio wave has a long wavelength λ of approximately 1000 m.  Rearranging the formula above, we can express the frequency ν of this radiation as a ratio of the speed of light c to the wavelength λ 

$\mathrm{\ν}\=$$\frac{c}{\mathrm{\λ}}$

First we define lambda in Maple with the SI unit of distance (meters or m)

Second, we compute the frequency ν (pronounced and spelled "nu")

Third, we combine units

Finally, we convert to the frequency unit Hertz (Hz), which is just 1 reciprocal second

We note that the frequency agrees with the range for frequency predicted in Fig. 1.  The frequency tells us that the wave associated with the electromagnetic radiation oscillates through one cycle 300,000 times per second.  While this may seem like a lot of oscillations per second (!), it is a very low frequency relative to the frequency associated with other types of electromagnetic radiation like visible or ultraviolet (UV) radiation.

(a) What is the frequency of red light whose wavelength is 750 nm (nanometers) or 7.5 x 10^-7 m. (Hint: Repeat the steps above with the wavelength for red light.)

1. Christie, R. The Physical and Chemical Basis of Colour. In Colour Chemistry. 2nd Ed. Royal Chemical Society: Cambridge. 2001. pp. 12-21.
2. Stockman, A., MacLeod, D. I., & Johnson, N. E. (1993). Spectral sensitivities of the human cones. Journal of the Optical Society of America, A, Optics, Image & Science, 10(12), 2491–2521.

Selection of Additional Readings and Resources

Baumann, U. https://www.colorsystem.com/?page_id=551 (accessed 2023-09-07).

       A webpage summarizing and visualizing the evolution of color systems and color spaces from Plato to CIELab and other modern-day models.

Buether, A.; Augsburg, A.; Venn, A. In Colour: Design principles, planning strategies, visual communication; Institut für Internationale Architektur-Dokumentation, 2014; pp 33–37.

        A chapter on color systems and color spaces and their importance in art and designer from the perspective of a designer.

Ciechanowski, B. Color Spaces – Bartosz Ciechanowski. https://ciechanow.ski/color-spaces/ (accessed 2023-09-07).

       An interactive webpage by Bartosz Ciechanowski that explores the technical aspects of how additive color (colored light) can be mapped onto the RGB colorspace for use in screens.

Coblis - Color Blindness Simulator. https://www.color-blindness.com/coblis-color-blindness-simulator/ (accessed 2023-09-07).

       An interactive webpage that simulates various types of colorblindness for those of us with standard color vision. See if you can guess which cone cell type might be affected for each type of vision.