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Difficulty: MediumWaves, Sound, and Light

The speed at which light travels depends directly on the optical density and refractive index of the medium through which it passes. Arrange the following media in order of the speed of light within them, from slowest to fastest.

  1. 1Diamond
  2. 2Crown glass
  3. 3Liquid water
  4. 4Vacuum

Answer

Diamond, Crown glass, Liquid water, Vacuum (from slowest to fastest)
Light travels fastest through empty space (c≈3.00×108 m/sc \approx 3.00 \times 10^8\text{ m/s}) where the refractive index is 1.001.00. When entering denser transparent media, the wave interacts with the electromagnetic fields of atoms, causing an apparent slowdown proportional to the medium's index of refraction (v=cnv = \frac{c}{n}). Diamond has the highest index of refraction among the options (n≈2.42n \approx 2.42), making it the slowest, followed by crown glass (n≈1.52n \approx 1.52), liquid water (n≈1.33n \approx 1.33), and vacuum (n=1.00n = 1.00).

Step-by-Step Solution

1
Identify the relationship between the index of refraction and the speed of light.
The speed of light in a medium is inversely proportional to its refractive index, given by v=cnv = \frac{c}{n}, where cc is the speed of light in a vacuum and nn is the refractive index.
Higher refractive indices indicate greater optical density and slower wave propagation speeds.
2
Rank the media by their refractive indices from highest to lowest.
Diamond (n≈2.42n \approx 2.42) > Crown glass (n≈1.52n \approx 1.52) > Liquid water (n≈1.33n \approx 1.33) > Vacuum (n=1.00n = 1.00).
Ranking from highest index to lowest index establishes the reverse order of speed.
3
Invert the refractive index ranking to order the media from slowest speed to fastest speed.
Diamond (slowest, ≈1.24×108 m/s\approx 1.24 \times 10^8\text{ m/s}) →\rightarrow Crown glass (≈1.97×108 m/s\approx 1.97 \times 10^8\text{ m/s}) →\rightarrow Liquid water (≈2.25×108 m/s\approx 2.25 \times 10^8\text{ m/s}) →\rightarrow Vacuum (fastest, ≈3.00×108 m/s\approx 3.00 \times 10^8\text{ m/s}).
Matches the required sequence criteria from slowest to fastest.

Key Concept

Inverse relationship between index of refraction and wave speed in optical media (v=cnv = \frac{c}{n})
Estimated Time:1m 0s
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Topics

Waves, Sound, and Light

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