Given that the speed of light in a vacuum is approximately $3.0 \times 10^8$ m/s and the refractive index of a certain material is 1.5, what is the approximate speed of light in th... Given that the speed of light in a vacuum is approximately $3.0 \times 10^8$ m/s and the refractive index of a certain material is 1.5, what is the approximate speed of light in that material?
Understand the Problem
The question is asking us to calculate the speed of light in a material given its refractive index and the speed of light in a vacuum. We can use the formula: speed of light in material = speed of light in vacuum / refractive index.
Answer
$2.0 \times 10^8 \, \text{m/s}$
Answer for screen readers
The speed of light in the material is $2.0 \times 10^8 , \text{m/s}$.
Steps to Solve
- Identify the given values
The refractive index, $n = 1.5$
The speed of light in a vacuum, $c = 3.0 \times 10^8 , \text{m/s}$
- Apply the formula to calculate the speed of light in the material, $v$
The formula relating refractive index, speed of light in a vacuum, and the speed of light in a material is: $$ n = \frac{c}{v} $$ We need to solve for $v$, so rearrange the formula: $$ v = \frac{c}{n} $$
- Substitute the given values into the formula
Substitute $c = 3.0 \times 10^8 , \text{m/s}$ and $n = 1.5$ into the equation: $$ v = \frac{3.0 \times 10^8 , \text{m/s}}{1.5} $$
- Calculate the speed of light in the material $$ v = 2.0 \times 10^8 , \text{m/s} $$
The speed of light in the material is $2.0 \times 10^8 , \text{m/s}$.
More Information
The speed of light is slower in a material than in a vacuum. This is because light interacts with the atoms in the material, which slows it down. The refractive index tells us how much slower light is in a material compared to a vacuum.
Tips
A common mistake is to multiply the speed of light in a vacuum by the refractive index instead of dividing. Remember that the speed of light in a material is always less than the speed of light in a vacuum, so if you get a value greater than $3.0 \times 10^8 , \text{m/s}$, you've made a mistake.
AI-generated content may contain errors. Please verify critical information
