we know that the speed of light in a vacuum is 3.0 x 10^8 m/s (18,000 mi/sec). If light travels through thick plastic with a speed of 1.75 x 10^8 m/s, what is the index of refraction through plastic?

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To find the index of refraction through plastic, we need to use the formula relating the speed of light in a vacuum (c) to the speed of light in a medium (v) and the index of refraction (n). The formula is:

n = c / v

Given that the speed of light in a vacuum is 3.0 x 10^8 m/s and the speed of light in the plastic is 1.75 x 10^8 m/s, we can substitute these values into the formula:

n = (3.0 x 10^8 m/s) / (1.75 x 10^8 m/s)

Now, we can simplify this expression:

n = 1.7142857

Therefore, the index of refraction through the plastic is approximately 1.71.