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Light frequency is a fundamental characteristic of light, measuring how many wave cycles occur in one second. Frequency, often denoted by \( u \), is measured in hertz (Hz). It tells us how frequently the light's electric and magnetic fields oscillate. The higher the frequency, the more energy the photons carry, and the visible light appears more towards the blue/violet end of the spectrum.

To calculate the frequency of light, one needs to know its wavelength and the speed of light, which is a constant \( c = 3 \times 10^8 \ \text{m/s} \). The formula to find frequency is:

• \( u = \frac{c}{\lambda} \)

Where \( \lambda \) is the wavelength of the light. In this exercise, we calculated that a 75-W light source emitting light at a wavelength of 600 nm has a frequency of approximately \( 5.00 \times 10^{14} \ \text{Hz} \). This frequency indicates how quickly the light waves are occurring.

Wavelength is the distance between successive peaks of a wave. In the context of light, it is a critical factor in determining the color and type of light within the electromagnetic spectrum.

Wavelength is usually measured in meters (m), but for light studies, it is often expressed in nanometers (nm), where 1 nm equals \( 10^{-9} \) meters. For example, visible light wavelengths range from about 400 nm (violet) to 700 nm (red).

• Shorter wavelengths equate to higher frequencies and energies.
• Longer wavelengths equate to lower frequencies and energies.

In this exercise, the given wavelength was 600 nm, corresponding to orange/yellow light in the visible spectrum. This wavelength was used to find the frequency of the emitted light, demonstrating the inverse relationship between wavelength and frequency—shorter wavelengths have higher frequencies, and longer wavelengths have lower frequencies.

Planck's constant is a fundamental physical constant that relates a photon's energy to its frequency. It is denoted by the symbol \( h \) and approximately equals \( 6.63 \times 10^{-34} \ \text{J} \cdot \text{s} \). This constant is pivotal in quantum mechanics and was first introduced by Max Planck.

Planck's equation \( E = h u \) allows physicists to compute the energy of a photon when its frequency is known.

• \( E \) represents the energy of the photon in joules.
• \( h \) is Planck's constant.
• \( u \) is the frequency of the light.

In our exercise, Planck's equation was used to determine that the energy of a single photon emitted by the 75-W light source was approximately \( 3.315 \times 10^{-19} \ \text{J/photon} \). This small yet significant quantity shows how energy is quantized at a microscopic scale.

The electromagnetic spectrum encompasses all types of electromagnetic radiation, which vary by their wavelengths and frequencies. Visible light, which is only a small part of this spectrum, ranges from about 380 to 750 nm in wavelength.

The spectrum includes other forms of electromagnetic radiation, such as:

• Radio waves with the longest wavelengths and lowest frequencies.
• Microwaves, which are shorter than radio waves and used in communications and cooking.
• Infrared waves, experienced as heat, just beyond visible red light.
• Ultraviolet light, with shorter wavelengths than visible light, known for causing sunburns.
• X-rays and gamma rays, which have progressively shorter wavelengths and higher frequencies.

This wide range of wavelengths shows how diverse electromagnetic radiation is. In our exercise, we explored a specific point on this spectrum—light with a wavelength of 600 nm, demonstrating the interplay between wavelength, frequency, and the type of electromagnetic radiation observed.