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Wavelength is the distance between consecutive peaks of a wave and is usually denoted by the Greek letter \( \lambda \). In the context of light, it represents the color or type of light. Wavelengths of light that we can see, also known as visible light, typically range from 380 nm to 750 nm. \(1 \text{ nm} = 1 \times 10^{-9} \text{ m} \). The wavelength of light changes when it enters a different medium, such as moving from air into water, due to its interaction with the medium's atomic structure. Yet, the frequency remains the same across different media. Understanding wavelength helps in identifying the type of wave and how it will behave when passing through different materials.

Frequency refers to the number of wave cycles that pass a given point per unit of time and is usually measured in hertz (Hz). In optics, it relates to the color of the light; higher frequencies correspond to blue light, while lower frequencies correspond to red light. The relationship between wavelength \( \lambda \) and frequency \( f \) is given by the formula \( c = f \cdot \lambda \), where \( c \) is the speed of light in a vacuum (\(3 \times 10^8 \text{ m/s}\)). In any medium, the frequency of light does not change when it crosses from one medium to another, which is a fundamental principle in optics. This allows us to predict how light behaves across different media without altering its frequency.

The refractive index \( n \) of a medium describes how much the light slows down when it enters that medium. It is a dimensionless number indicative of how fast light travels through the material compared to its speed in a vacuum. When light enters a material like water, which has a refractive index of \( 1.33 \), it slows down compared to its speed in air. The equation \( v = \frac{c}{n} \) where \( v \) is the speed of light in the medium, shows how to calculate the new speed of light in the medium. Media with higher refractive indices slow down light more significantly and bend it more sharply.

The speed of light is a fundamental constant of nature, usually denoted as \( c \). In a vacuum, it is approximately \(3 \times 10^8 \text{ m/s}\). However, when light travels through different media, its speed changes due to interactions with the atoms in the medium. This change in speed is dictated by the refractive index \( n \). Thus, the speed of light in any medium is calculated using \( v = \frac{c}{n} \). For example, in water with a refractive index of \( 1.33 \), the speed of light is slowed to approximately \( 2.26 \times 10^8 \text{ m/s} \). Hence, understanding the speed of light in various media helps in many practical applications including optics and telecommunications.