91Ó°ÊÓ

The speed of light is a fundamental constant in physics, symbolized as \(c\). It represents how fast light travels through a vacuum, specifically at \(3.00 \times 10^8\) meters per second. This speed is constant for all electromagnetic waves in a vacuum, which include not only visible light but also radio waves, microwaves, infrared, ultraviolet, X-rays, and gamma rays. Knowing the speed of light is essential for understanding wave behavior and calculations related to light and other electromagnetic phenomena. This constant allows us to connect other properties of light, such as wavelength and frequency, through mathematical relations.

Wavelength, symbolized as \(\lambda\), is a measure of the distance between consecutive crests (or troughs) of a wave. In the context of light, it's a key characteristic that determines the color we perceive. Wavelengths of light are usually measured in meters but can also be expressed in nanometers for precision, with 1 meter equaling 1 billion nanometers. The given wavelength in our exercise is a crucial piece of information—it refers to the yellow-green light, specifically \(5.45 \times 10^{-7} \, \text{m}\), which determines where the wave falls on the electromagnetic spectrum. For light waves traveling through different mediums, the speed and wavelength may vary, even though their frequency remains constant.

Calculating the frequency of light involves using a fundamental equation that relates wavelength, frequency, and the speed of light: \(c = f \lambda\). Here, \(f\) represents frequency. By rearranging the formula, frequency can be isolated as \(f = \frac{c}{\lambda}\). In our exercise, with a given speed of light \(c = 3.00 \times 10^8 \, \text{m/s}\) and wavelength \(\lambda = 5.45 \times 10^{-7} \, \text{m}\), substituting these values into the equation allows us to calculate the frequency of the yellow-green light. The calculated frequency is \(5.50 \times 10^{14}\ \text{Hz}\). This high frequency indicates the rapid oscillations of the electromagnetic wave in this part of the spectrum, essential for its specific color characteristics.

The visible spectrum is a small part of the electromagnetic spectrum that human eyes can perceive. It ranges approximately from wavelengths of 400 to 700 nanometers, or \(4.00 \times 10^{-7}\) to \(7.00 \times 10^{-7} \, \text{meters}\). Each wavelength within this range corresponds to a different color, starting from violet at the shorter wavelengths to red at the longer wavelengths. Yellow-green light, with a wavelength around \(5.45 \times 10^{-7} \, \text{m}\), lies in the range where human vision is most sensitive. Understanding the position of a wavelength within the visible spectrum helps us link the physical properties of light to what we see and experience in everyday life.