The Wavelength of Green Light in Water: Exploring the Physics of Refraction

Green light has a wavelength of approximately 504 nm in a vacuum. When it travels through different media, such as water, the wavelength changes. This phenomenon is described by the refractive index of the medium, which affects the speed of light. This article explores how the wavelength of green light in water can be calculated using the refractive index, and provides a deeper understanding of the physics behind refraction.

Understanding the Refractive Index

Refraction is the bending of light as it passes from one medium to another. The amount of bend depends on the refractive index of the medium. The refractive index n is defined as the ratio of the speed of light in a vacuum c to the speed of light in the medium v. For water, the refractive index is typically around 1.33, meaning that light travels about 33% slower in water compared to a vacuum.

The Formula for Wavelength in a Medium

When light travels through a medium other than a vacuum, its wavelength changes. The relationship between the wavelength in the medium lambda;n and the wavelength in vacuum lambda;0 is given by the formula:

lambda;n lambda;0 / n

This formula can be used to determine the new wavelength of green light when it travels through water. Given that the wavelength in a vacuum for green light is 504 nm (or 504 times; 10-9 m) and the refractive index of water is 1.33, we can calculate the new wavelength in water as follows:

Calculation of Wavelength in Water

To find the new wavelength, we use the provided formula:

lambda;n (504 times; 10-9 m) / 1.33

Performing the calculation:

lambda;n approx; 378.95 times; 10-9 m

Converting this to nanometers:

lambda;n approx; 379 nm

Thus, the new wavelength of green light in water is approximately 379 nm.

The Role of Speed and Frequency in Refraction

Understanding the relationship between the speed, wavelength, and frequency of light is crucial to comprehending refraction. The speed of a wave (such as light) is given by the product of its wavelength and frequency, which is expressed in the equation:

c L times; F

where:

c is the speed of light in a vacuum, L is the wavelength of the light, F is the frequency of the light.

When light passes from one medium to another, the frequency remains constant, but both the speed and wavelength change. This is because the refractive index of the medium affects the speed of light while the wavelength is inversely proportional to the speed.

The refractive index of a medium can be seen as the factor by which the speed and the wavelength of the radiation are reduced with respect to their vacuum values. The formula for the wavelength in the medium is:

lambda;n lambda;0 / n

Given the wavelength of green light in a vacuum, lambda;0 504 times; 10-9 m, and the refractive index of water, n 1.33, the calculation can be performed as:

lambda;n (504 times; 10-9 m) / 1.33 378.95 times; 10-9 m approx; 379 nm

Conclusion

The change in the wavelength of light as it passes from one medium to another is a fascinating aspect of physics, especially relevant in fields such as optics and photonics. The calculation of the new wavelength of green light in water showcases the interplay between the speed of light, the refractive index, and the medium through which the light travels. Understanding these principles has numerous applications, from designing optical devices to advancing our knowledge of light behavior in various media.