Light of a certain frequency has a wavelength of 526 nm in water. What is the wavelength of this light in benzene?

Verified step by step guidance

1. Identify the refractive indices of water and benzene. The refractive index (n) is a measure of how much the speed of light is reduced inside a medium compared to the speed of light in a vacuum.
2. Use the formula for the speed of light in a medium: v = c/n, where c is the speed of light in vacuum and v is the speed of light in the medium. Since the frequency (f) of light remains constant when transitioning between media, the relationship between wavelength (\(\lambda\)) and speed is given by \(\lambda = v/f\).
3. Express the wavelength in water in terms of its refractive index: \(\lambda_{water} = \frac{c}{n_{water} \times f}\).
4. Set up the equation to find the wavelength in benzene using its refractive index: \(\lambda_{benzene} = \frac{c}{n_{benzene} \times f}\).
5. Since the frequency of light does not change, equate the expressions for speed of light in both media and solve for \(\lambda_{benzene}\) using the known value of \(\lambda_{water}\) and the refractive indices: \(\lambda_{benzene} = \lambda_{water} \times \frac{n_{water}}{n_{benzene}}\).

Key Concepts

Wavelength and Frequency Relationship

The wavelength of light is inversely related to its frequency, as described by the equation c = λν, where c is the speed of light, λ is the wavelength, and ν is the frequency. This means that as the wavelength increases, the frequency decreases, and vice versa. Understanding this relationship is crucial for converting between different media.

Refraction and Snell's Law

Refraction occurs when light passes from one medium to another, changing its speed and direction. Snell's Law describes this phenomenon mathematically, stating that n1 * sin(θ1) = n2 * sin(θ2), where n is the refractive index of the media and θ is the angle of incidence or refraction. This principle is essential for determining how the wavelength of light changes in different substances.

Refractive Index

The refractive index of a medium is a dimensionless number that describes how much light slows down in that medium compared to a vacuum. It is defined as n = c/v, where c is the speed of light in a vacuum and v is the speed of light in the medium. The refractive index affects the wavelength of light, as the wavelength in a medium is given by λ_medium = λ_vacuum/n.