2. The speed of light in a certain substance is 82% of its value in water. What is the index of refraction of that substance 1

The index of refraction of a substance is calculated using the formula:<br /><br />\[ n = \frac{c}{v} \]<br /><br />where \( c \) is the speed of light in a vacuum and \( v \) is the speed of light in the substance.<br /><br />Given that the speed of light in the substance is 82% of its value in water, we can use the fact that the speed of light in water is approximately 0.75 times the speed of light in a vacuum. Therefore, the speed of light in the substance is:<br /><br />\[ v = 0.82 \times 0.75c \]<br /><br />Sub this into the formula for the index of refraction, we get:<br /><br />\[ n = \frac{c}{0.82 \times 0.75c} = \frac{1}{0.615} \approx 1.62 \]<br /><br />Therefore, the index of refraction of the substance is approximately 1.62.