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Light travels incredibly fast, making it one of the swiftest phenomena in the universe. The speed of light in a vacuum is a constant value, approximately equal to \(3 \times 10^8 \text{ meters per second (m/s)}\). This means that light can travel 300,000 kilometers, roughly from the Earth to the Moon, in just about a second. Understanding the speed of light is fundamental in physics because it forms the basis for calculating other properties of light, such as frequencies and wavelengths. When it comes to light, any change in wavelength directly affects its frequency, given that the speed of light remains constant. This relationship is concisely expressed in the equation \(c = \lambda f\), where \(c\) is the speed of light, \(\lambda\) is the wavelength, and \(f\) is the frequency.

Violet light is the most energetic color within the visible light spectrum due to its short wavelengths, ranging from 400 nm to 440 nm. To convert these wavelengths from nanometers to meters, as required by physics equations, we multiply by \(10^{-9}\), giving us \( 400 \times 10^{-9} \text{ m} \) to \( 440 \times 10^{-9} \text{ m} \). Once converted, we use the formula \(f = \frac{c}{\lambda}\) to find the frequency range:

• Maximum frequency, using 400 nm: \( f_{max} = \frac{3 \times 10^8 \text{ m/s}}{400 \times 10^{-9} \text{ m}} = 7.5 \times 10^{14} \text{ Hz} \)
• Minimum frequency, using 440 nm: \( f_{min} = \frac{3 \times 10^8 \text{ m/s}}{440 \times 10^{-9} \text{ m}} = 6.82 \times 10^{14} \text{ Hz} \)

Thus, violet light has a frequency range of approximately \(6.82 \times 10^{14} \text{ Hz} \) to \(7.5 \times 10^{14} \text{ Hz}.\)

In contrast to violet light, red light represents the lowest energy portion of the visible spectrum with longer wavelengths ranging from 630 nm to 700 nm. Translating these into meters gives us \( 630 \times 10^{-9} \text{ m} \) and \( 700 \times 10^{-9} \text{ m} \). We apply the same frequency formula to determine the frequency range:

• Minimum frequency, for 700 nm: \( f_{min} = \frac{3 \times 10^8 \text{ m/s}}{700 \times 10^{-9} \text{ m}} = 4.29 \times 10^{14} \text{ Hz} \)
• Maximum frequency, for 630 nm: \( f_{max} = \frac{3 \times 10^8 \text{ m/s}}{630 \times 10^{-9} \text{ m}} = 4.76 \times 10^{14} \text{ Hz} \)

Therefore, red light occupies a frequency range from approximately \(4.29 \times 10^{14} \text{ Hz}\) to \(4.76 \times 10^{14} \text{ Hz}.\)

Wavelengths of light are commonly expressed in nanometers (nm), but physics calculations usually require meters (m). The basic conversion rule is: 1 nm equals \(10^{-9}\) meters.When working with light equations, it's critical to convert all wavelengths to meters to ensure consistency and correctness. For example:

• A wavelength of \(400 \text{ nm}\) becomes \(400 \times 10^{-9} \text{ m}\).
• A wavelength of \(700 \text{ nm}\) translates to \(700 \times 10^{-9} \text{ m}\).

Converting wavelength units carefully is important to avoid calculation errors in determining cost/off frequency.

The visible light spectrum is a small part of the electromagnetic spectrum that is visible to the human eye, ranging approximately from 380 nm to 750 nm. It represents all the colors we can see, each at a different wavelength. The spectrum starts with violet on the shorter wavelength end and extends to red on the longer wavelength side.

• Violet wavelengths: 380 - 450 nm
• Blue wavelengths: 450 - 495 nm
• Green wavelengths: 495 - 570 nm
• Yellow wavelengths: 570 - 590 nm
• Orange wavelengths: 590 - 620 nm
• Red wavelengths: 620 - 750 nm

Each color has its own unique wavelength that determines its color in the spectrum. This range enables us to see the world in a rainbow of colors, all due to variations in wavelength.