Light from a sodium lamp with a wavelength in a vacuum of...

Light from a sodium lamp with a wavelength in a vacuum of 590 nm enters diamond in which the speed of light is $1.24 \times 10^{8} \mathrm{m} / \mathrm{s} .$ What is the wavelength of this light in diamond?

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Key Concepts

Wavelength Change in a Medium

The wavelength of light changes when it enters a medium with a different refractive index, even though its frequency stays constant. The relationship between wavelength and speed in the medium is given by lambda = v/f, which can also be expressed as lambda = lambda_vacuum/n, where lambda_vacuum is the wavelength in vacuum and n is the refractive index. This concept explains why light, such as that from a sodium lamp, has a different wavelength in diamond than in vacuum.

Conservation of Frequency

When light passes from one medium to another, its frequency remains unchanged. This is because the frequency is determined by the source and is not affected by the medium change. The conservation of frequency is key to connecting the speed of light in the new medium with its altered wavelength.

Index of Refraction

This concept measures how much the speed of light is reduced in a 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 in the medium. This parameter is crucial for understanding how light propagates through materials and how its wavelength changes.

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