The speed of light in water is 2.25 x 10^8 m/s. If the speed of light in a vacuum be 3.00 x 10^8 m/s, what is the refractive index of water?
Understand the Problem
The question is asking for the refractive index of water, which can be calculated using the formula: refractive index = speed of light in vacuum / speed of light in medium (water). We will apply this formula using the provided speeds.
Answer
The refractive index of water is approximately $1.33$.
Answer for screen readers
The refractive index of water is approximately $1.33$.
Steps to Solve
- Identify the formula for refractive index
The formula for calculating the refractive index ($n$) is given by:
$$ n = \frac{c}{v} $$
Where:
- $c$ = speed of light in vacuum
- $v$ = speed of light in the medium (water)
- Substitute the values into the formula
Given:
- $c = 3.00 \times 10^8$ m/s (speed of light in vacuum)
- $v = 2.25 \times 10^8$ m/s (speed of light in water)
We substitute these values into the formula:
$$ n = \frac{3.00 \times 10^8 \text{ m/s}}{2.25 \times 10^8 \text{ m/s}} $$
- Perform the division
Now, we calculate:
$$ n = \frac{3.00}{2.25} $$
- Calculate the refractive index
Dividing the two numbers gives us:
$$ n = 1.3333... $$
- Round to appropriate significant figures
Since typical refractive indices are given to two decimal places, we round:
$$ n \approx 1.33 $$
The refractive index of water is approximately $1.33$.
More Information
The refractive index is a dimensionless number that indicates how much light bends or refracts when entering a medium from a vacuum. A value of around $1.33$ is commonly accepted for water, indicating that light travels slower in water than in vacuum.
Tips
- Incorrectly substituting the values into the formula. Always double-check the values being used.
- Forgetting to properly perform the division can lead to mistakes in the final answer. It’s important to ensure accurate calculations.
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