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

step 1 The speed of light in a medium is given by the product of frequency and wavelength. The frequenc

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? Show your calculations.

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Key Concepts

Wave Propagation Equation

The equation v = ?f relates the speed (v) of a wave to its wavelength (?) and its frequency (f). This fundamental relationship is pivotal in understanding the behavior of waves, including light, and is used to compute one of the quantities when the other two are known.

Refractive Index

The refractive index (n) of a medium is defined as the ratio of the speed of light in a vacuum (c) to the speed of light in the medium (v): n = c/v. This concept is critical for understanding how light slows down as it travels through different substances, altering its wavelength while its frequency remains constant.

Calculation of Speed and Determination of n

By calculating the speed of light in the medium using v = ?f, and then applying n = c/v, one can determine the refractive index of the substance. Once the index is known, it can be compared with known values from tables or literature to identify the substance.

Comparison with Standard Tabulated Values

After determining the refractive index through calculations, the final step involves comparing this value with standard indexed values typically provided in reference tables (such as Table 26.1). Matching the computed refractive index with a tabulated value allows for the identification of the medium through which the light is passing.

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