Light has a wavelength of 340.0 nm and a frequency of 5.403 ×10^14 Hz when traveling through a

step 1 As we all know that the speed of light in a medium is related to wavelength of light is given by

Light has a wavelength of 340.0 nm and a frequency of 5.403...

Light has a wavelength of $340.0 \mathrm{nm}$ and a frequency of $5.403 \times 10^{14} \mathrm{~Hz}$ when traveling through a certain substance. What substance from Table $26-1$ could this be? Support your answer with calculations.

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Key Concepts

Index of Refraction

The index of refraction (n) is defined as the ratio of the speed of light in vacuum (c) to the speed of light in a medium (v), given by n = c/v. This parameter quantifies how much the medium slows down light compared to vacuum, and it is essential for determining the optical properties of the medium, such as bending of light at interfaces.

Wave Relationship

This concept establishes that for any wave, the product of its wavelength (?) and frequency (f) is equal to its speed (v) in that medium, expressed as v = ?f. It is a foundational relationship in wave physics that applies to electromagnetic waves as well as other types, enabling calculations involving any one of these quantities when the other two are known.

Speed of Light in a Medium

When light travels through a medium other than vacuum, its speed decreases according to the medium’s index of refraction. The reduced speed can be calculated by multiplying the wavelength of light in the medium by its frequency, which remains unchanged during the transition. This concept is critical for analyzing how light behaves as it passes through various materials.

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