You can calculate the speed of light in a material by dividing the speed of light in a vacuum by the material's index of refraction.
Understanding the Relationship
The speed of light changes when it passes through different materials compared to how fast it travels in a vacuum. This change is quantified by the index of refraction of the material.
- Speed of light in a vacuum (c): This is the universal speed limit, approximately 3.00 × 10⁸ meters per second (m/s). Light travels fastest in a vacuum.
- Speed of light in a material (v): This is the speed of light as it passes through a specific medium like water, glass, or air. It is always slower than the speed of light in a vacuum.
- Index of refraction (n): This dimensionless value represents how much a material slows down light. It is defined as the ratio of the speed of light in a vacuum to the speed of light in the material.
The Calculation Formula
According to the definition, the relationship between the index of refraction ($n$), the speed of light in a vacuum ($c$), and the speed of light in a material ($v$) is given by the formula:
$$n = \frac{c}{v}$$
To calculate the speed of light in the material ($v$), you need to rearrange this equation. By multiplying both sides by $v$ and then dividing by $n$, you get:
$$v = \frac{c}{n}$$
This rearranged formula allows you to find the speed of light in any material if you know the speed of light in a vacuum and the material's index of refraction.
Applying the Formula: An Example
Let's use the example provided in the reference to see this formula in action.
Problem: Calculate the speed of light in a material with an index of refraction of 1.923.
Solution:
- Identify the known values:
- Speed of light in a vacuum, $c \approx 3.00 \times 10^8 \, \text{m/s}$
- Index of refraction of the material, $n = 1.923$
- Use the formula $v = c/n$.
- Substitute the values into the formula:
$$v = \frac{3.00 \times 10^8 \, \text{m/s}}{1.923}$$
- Calculate the result:
$$v \approx 1.56 \times 10^8 \, \text{m/s}$$
So, the speed of light in a material with an index of refraction of 1.923 is approximately $1.56 \times 10^8$ meters per second. This calculation directly reflects the method shown in the reference ("v=3.00×10⁸m/s1.923=1.56×10⁸m/s").
Key Takeaways
- The index of refraction is a measure of how much a material slows down light.
- A higher index of refraction means light travels slower in the material.
- The speed of light in a material ($v$) is always less than the speed of light in a vacuum ($c$) for materials with $n > 1$.
Summary Table:
| Variable | Symbol | Description | Approximate Value (Vacuum) |
|---|---|---|---|
| Speed of light (vacuum) | $c$ | Speed of light in free space | $3.00 \times 10^8$ m/s |
| Speed of light (material) | $v$ | Speed of light within a specific medium | $v < c$ (for $n>1$) |
| Index of refraction | $n$ | Ratio of $c$ to $v$ ($n = c/v$) | Unitless |
By knowing the index of refraction, you can easily determine how fast light propagates through a specific substance.
