Video: Refractive Index Relationship to Speed of Light Propagation

The refractive index of crown glass is 1.52. What is the speed of light in crown glass?

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Video Transcript

The refractive index of crown glass is 1.52. What is the speed of light in crown glass?

In our solution, we can refer to the refractive index of crown glass, 1.52, as 𝑛 sub 𝑔. We want to know the speed of light in crown glass, which we’ll call 𝑣.

And in this problem, we’ll assume that the speed of light, 𝑐, is exactly 3.00 times 10 to the eighth meters per second. Let’s start by recalling the mathematical relationship defining index of refraction. A material’s refractive index, 𝑛, is defined as the speed of light in vacuum, 𝑐, divided by the speed of light in that material.

When we apply this relationship to our situation, we see the refractive index of crown glass, 𝑛 sub 𝑔, equals 𝑐 divided by 𝑣, the speed of light in crown glass. Rearranging this equation to solve for 𝑣, we see that it’s equal to 𝑐 over 𝑛 sub 𝑔.

When we plug-in for these two values and calculate this fraction, we find that 𝑣 equals 1.97 times 10 to the eighth meters per second. That’s the speed of light in crown glass, roughly two-thirds the speed of light in vacuum.

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