Light travels at a speed of 2.201 ×10^8 m / s in a certain substance. What substance from Table

step 1 As we all know that the refractive index of a medium is the ratio of speed of light in vacuum to

Light travels at a speed of 2.201 ×10^8 m / s in a certain...

Light travels at a speed of $2.201 \times 10^{8} \mathrm{~m} / \mathrm{s}$ in a certain substance. What substance from Table $26-1$ could this be? For the speed of light in a vacuum use $2.998 \times 10^{8} \mathrm{~m} / \mathrm{s},$ and support your answer with a calculation.

Key Concepts

Refractive Index

The refractive index is a dimensionless number that indicates how much the speed of light is reduced in a particular medium compared to its speed in a vacuum. It is defined by the ratio n = c/v, where c is the speed of light in a vacuum and v is the speed of light in the medium. This concept is fundamental in optics because it explains phenomena such as refraction and dispersion when light passes from one medium to another.

Speed of Light in a Medium

The speed of light in a medium is determined by the medium’s optical properties, notably its refractive index. When light enters a substance other than vacuum, its speed decreases from approximately 3.00 x 10^8 m/s to a lower value, which depends on how strongly the medium interacts with the light. Calculating the speed change using the refractive index is essential for understanding how light behaves in different materials.

Calculation of the Refractive Index from Measured Speed

Using the relationship n = c/v, where c is the speed of light in a vacuum and v is the measured speed in the medium, one can compute the refractive index. In this context, substituting the given values gives n = (2.998 x 10^8 m/s) / (2.201 x 10^8 m/s) ? 1.363. This calculated refractive index can then be used to identify the substance from standard reference tables, as each material has a characteristic refractive index.

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