According to the equation for the energy of light, which statement is true? (1) The energy of light increases as its wavelength increases. (2) The energy of light decreases as its wavelength increases. Explain how the equation for the energy of light tells you which is true.

The relationship between the wavelength of light and its energy is fundamental to understanding how light behaves. The two are inversely related, meaning that as one increases, the other decreases. This inverse relationship is captured mathematically in the equation:
\[E = \frac{hc}{\lambda}\] where \(E\) represents the energy of the photon, \(h\) is Planck's constant, \(c\) is the speed of light, and \(\lambda\) is the wavelength of the photon. When you look at this equation, notice that energy (E) is directly proportional to Planck's constant ((h)) and the speed of light ((c)), but inversely proportional to wavelength ((\lambda)).
To put it simply, shorter wavelengths of light have higher energy photons, and longer wavelengths have lower energy photons. This is why ultraviolet light, which has very short wavelengths, can be energetic enough to cause sunburns, while infrared light, with its longer wavelengths, is only felt as heat. Understanding this principle is also crucial for various applications, including spectroscopy, where scientists analyze light to detect chemical substances based on their energy levels.

Planck's constant is a fundamental constant in physics that represents the relationship between energy and frequency for photons, the particles of light. Represented by the symbol (h), its value is approximately 6.626 x 10^{-34} joule-seconds. This constant is named after the physicist Max Planck, who was a pivotal figure in the development of quantum mechanics.
Planck's constant allows us to calculate the energy of a photon when its frequency ((f)) is known through the equation: \[E = h\cdot f\] In combination with the speed of light ((c)), it also connects energy with wavelength as shown in the earlier relationship, where wavelength and frequency are inversely related. It's an incredibly small number, but it represents a huge concept in physics that energy is quantized, meaning it can be divided into discrete amounts, rather like counting in whole numbers. This principle is a cornerstone of quantum theory and has extensive implications for our understanding of the atomic and subatomic world.

The speed of light, denoted as (c), is another fundamental physical constant and is the speed at which light travels in a vacuum. Its accepted value is approximately 299,792,458 meters per second. This constant is not just important for the propagation of light; it also serves as a speed limit for information and matter in the universe. In equations relating to light energy, like the one featured in this exercise, (c) works hand-in-hand with Planck's constant to determine the energy of a photon based on its wavelength.
Einstein's theory of relativity hinges on the constancy of the speed of light, regardless of the observer's perspective. In practical terms, the speed of light affects how we perceive the universe, governs the laws of reflection and refraction, and is integral to technologies such as lasers and optical fibers. As a content creator for an educational platform, we stress the concept's significance not just in physics but in understanding how we interact with technology and perceive the cosmos.