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 relationship between the speed of light, frequency, and wavelength in a medium. The speed of light in a medium is given by the equation: $v=f\lambda$, where $v$ is the speed of light in the medium, $f$ is the frequency, and $\lambda$ is the wavelength.
2. Understand that the frequency of light remains constant when it travels from one medium to another. Therefore, the frequency of light in water is the same as in benzene.
3. Use the refractive index to relate the speed of light in different media. The refractive index $n$ of a medium is defined as $n=\frac{c}{v}$, where $c$ is the speed of light in vacuum and $v$ is the speed of light in the medium.
4. Calculate the speed of light in water using its refractive index. For water, the refractive index is approximately 1.33. Thus, $v$_water = c1.33.
5. Determine the wavelength of light in benzene using its refractive index. For benzene, the refractive index is approximately 1.50. Use the relationship $\lambda$_benzene = λ_watern_water n_benzene to find the wavelength in benzene.

Key Concepts

Refraction and Refractive Index

Refraction is the bending of light as it passes from one medium to another, due to a change in its speed. The refractive index is a measure of how much the speed of light is reduced inside a medium compared to vacuum. It is crucial for determining how light's wavelength changes when moving between different substances.

Wavelength and Frequency Relationship

The wavelength of light is inversely proportional to its frequency, given by the equation c = λν, where c is the speed of light, λ is the wavelength, and ν is the frequency. In different media, while the speed and wavelength change, the frequency remains constant, which is key to finding the new wavelength in benzene.

Speed of Light in Different Media

The speed of light varies in different media, being slower in denser materials. This speed is calculated using v = c/n, where v is the speed of light in the medium, c is the speed of light in vacuum, and n is the refractive index. Understanding this helps in determining how the wavelength changes as light enters benzene from water.