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Answer :
Final answer:
The speed of light in a crystal with a refractive index of 1.70 is approximately 1.76 x 10^8 m/s, while in a crystal with a refractive index of 2.14 it is approximately 1.40 x 10^8 m/s.
Explanation:
The speed of light in a vacuum is approximately 3.00 x 10^8 m/s. The index of refraction (n) of a material is defined as the ratio of the speed of light in a vacuum to the speed of light in that material. Therefore, the speed of light in a crystal with a refractive index of 1.70 would be (3.00 x 10^8 m/s) / 1.70 = 1.7647 x 10^8 m/s. Similarly, the speed of light in a crystal with a refractive index of 2.14 would be (3.00 x 10^8 m/s) / 2.14 = 1.4018 x 10^8 m/s.
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Rewritten by : Jeany
Light travels approximately 114,046,693 meters per second faster in a crystal with a refractive index of 1.70 compared to another crystal with a refractive index of 2.14.
The speed of light in a medium is given by the equation v = c/n, where v is the speed of light in the medium, c is the speed of light in a vacuum (approximately 299,792,458 meters per second), and n is the refractive index of the medium. By calculating the speed of light in each crystal using their respective refractive indices, we can determine the difference in their speeds.
Let's break down the calculations:
For the crystal with a refractive index of 1.70: [tex]v1 = c/n1 = 299,792,458 m/s / 1.70 = 176,347,924 m/s.[/tex]
For the crystal with a refractive index of 2.14: [tex]v2 = c/n2 = 299,792,458 m/s / 2.14 = 139,745,571 m/s.\\[/tex]
To find the difference in speed, we subtract the speed of light in the crystal with the higher refractive index from the speed of light in the crystal with the lower refractive index: [tex]Δv = v1 - v2 = 176,347,924 m/s - 139,745,571 m/s = 36,602,353 m/s.[/tex]
Therefore, light travels approximately 114,046,693 meters per second faster in the crystal with a refractive index of 1.70 compared to the crystal with a refractive index of 2.14.
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