Interactive Solution 26.7 at www.wiley.com/college/cutnell...

Interactive Solution 26.7 at www.wiley.com/college/cutnell offers one model for problems like this one. In a certain time, light travels $6.20 \mathrm{~km}$ in a vacuum. During the same time, light travels only $3.40 \mathrm{~km}$ in a liquid. What is the refractive index of the liquid?

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Key Concepts

Refractive Index

The refractive index is a dimensionless number that quantifies how much the speed of light is reduced in a material compared to its speed in a vacuum. It is central to understanding how light bends and slows down when it enters different media.

Speed of Light in Different Media

Light travels at its maximum speed in a vacuum, but in other media it slows down due to interactions with the material. This variation in speed underlies many optical phenomena, such as refraction and dispersion.

Time Equivalence in Propagation

When the travel time is held constant for light in different media, the distances covered directly reflect the speeds in those media. This principle allows us to compare how much slower light travels in a particular medium relative to its speed in a vacuum.

Applying Ratio Relationships in Optics

By comparing the speed of light in a vacuum to its speed in another medium (using the distance traveled in the same time), one can calculate the refractive index. This ratio, defined as the speed of light in vacuum divided by that in the medium, is a fundamental relationship in optics.

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