Question
As light travels through a medium, it interacts with the particles of the medium and slows down. Use the graph to determine the ratios of the speeds of light in different media to one another and to the speed of light in a vacuum.
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Speed (10' m/s)
The ratio of the speed of light through diamond to the speed of light through a vacuum is [Select]
The ratio of the
speed of light through glass to the speed of light
through a vacuum is
(Select ]|
The ratio of the speed of light through diamond to the speed of light through
63)
Diamond &
Glass
Water F
Calendar
吧
Inbox
History.
Mastery.
Studio
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Speed (10' m/s)
The ratio of the speed of light through diamond to the speed of light through a vacuum is [Select]
The ratio of the
speed of light through glass to the speed of light
through a vacuum is
(Select ]|
The ratio of the speed of light through diamond to the speed of light through
Answers
Answered by
GPT-4o mini
To determine the ratios of the speeds of light in different media to one another and to the speed of light in a vacuum, we typically use the values of the speed of light in various media. The value of the speed of light in a vacuum (denoted as \(c\)) is approximately \(3.00 \times 10^8 \, \text{m/s}\).
To illustrate how to analyze this without the graph itself, I can provide the typical values for the speed of light in various media:
1. **Diamond**: \(c \approx 1.24 \times 10^8 \, \text{m/s}\)
2. **Glass**: \(c \approx 2.0 \times 10^8 \, \text{m/s}\)
3. **Water**: \(c \approx 2.25 \times 10^8 \, \text{m/s}\)
### To Calculate the Ratios:
1. **Ratio of the speed of light through diamond to the speed of light in a vacuum**:
\[
\text{Ratio (Diamond)} = \frac{\text{Speed in diamond}}{\text{Speed in vacuum}} = \frac{1.24 \times 10^8}{3.00 \times 10^8} \approx 0.413
\]
2. **Ratio of the speed of light through glass to the speed of light in a vacuum**:
\[
\text{Ratio (Glass)} = \frac{2.0 \times 10^8}{3.00 \times 10^8} \approx 0.667
\]
3. **Ratio of the speed of light through diamond to the speed of light through glass**:
\[
\text{Ratio (Diamond to Glass)} = \frac{\text{Speed in diamond}}{\text{Speed in glass}} = \frac{1.24 \times 10^8}{2.0 \times 10^8} \approx 0.620
\]
### Summary of Ratios:
- Ratio of speed of light through diamond to vacuum: **0.413**
- Ratio of speed of light through glass to vacuum: **0.667**
- Ratio of speed of light through diamond to glass: **0.620**
If you have specific values from the graph you're looking at, you can replace the given numbers with those values to find the corresponding ratios.
To illustrate how to analyze this without the graph itself, I can provide the typical values for the speed of light in various media:
1. **Diamond**: \(c \approx 1.24 \times 10^8 \, \text{m/s}\)
2. **Glass**: \(c \approx 2.0 \times 10^8 \, \text{m/s}\)
3. **Water**: \(c \approx 2.25 \times 10^8 \, \text{m/s}\)
### To Calculate the Ratios:
1. **Ratio of the speed of light through diamond to the speed of light in a vacuum**:
\[
\text{Ratio (Diamond)} = \frac{\text{Speed in diamond}}{\text{Speed in vacuum}} = \frac{1.24 \times 10^8}{3.00 \times 10^8} \approx 0.413
\]
2. **Ratio of the speed of light through glass to the speed of light in a vacuum**:
\[
\text{Ratio (Glass)} = \frac{2.0 \times 10^8}{3.00 \times 10^8} \approx 0.667
\]
3. **Ratio of the speed of light through diamond to the speed of light through glass**:
\[
\text{Ratio (Diamond to Glass)} = \frac{\text{Speed in diamond}}{\text{Speed in glass}} = \frac{1.24 \times 10^8}{2.0 \times 10^8} \approx 0.620
\]
### Summary of Ratios:
- Ratio of speed of light through diamond to vacuum: **0.413**
- Ratio of speed of light through glass to vacuum: **0.667**
- Ratio of speed of light through diamond to glass: **0.620**
If you have specific values from the graph you're looking at, you can replace the given numbers with those values to find the corresponding ratios.