A narrow beam of sodium yellow light, with wavelength 589...

A narrow beam of sodium yellow light, with wavelength $589 \mathrm{~nm}$ in vacuum, is incident from air onto a smooth water surface at an angle $\theta_{1}=35.0^{\circ} .$ Dctermine the angle of refraction $\theta_{2}$ and the wavelength of the light in water.

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Key Concepts

Refractive Index

The refractive index of a medium quantifies how much the speed of light is reduced within that medium compared to its speed in a vacuum. It is a dimensionless number that influences the bending of light rays at the interface between different materials, as well as other properties such as the wavelength of light within the medium.

Wavelength Change in a Medium

When light enters a medium with a different refractive index, its speed and consequently its wavelength change, while its frequency remains constant. The new wavelength can be determined by dividing the original wavelength in vacuum by the refractive index of the medium, reflecting the proportional reduction in speed and wavelength due to the medium's optical density.

Snell's Law

Snell's Law is a fundamental principle in optics that relates the angles of incidence and refraction to the refractive indices of two media. It states that the product of the refractive index and the sine of the angle of incidence in the first medium is equal to the product of the refractive index and the sine of the angle of refraction in the second medium. This law is used to determine how light bends when transitioning from one medium to another.

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