The table lists the index of refraction for various substances at `20^(@)C` for light with a wavelength of `589nm` in a vacuum. Through which substance will light with a vacuum wavelength of 589nm travel with the greatest speed ?
`{:("Substance",,n),("Fused quartz",,1.458),("Ethyl alcohol",,1.362),("Crown glass",,1.520),("Carbon tetrachloride",,1.461),("Crystalline quartz",,1.544):}`

Options

A. Fused quartz
B. Ethyl alcohol
C. Crown glass
D. Carbon tetrachloride

Answer

To determine through which substance light with a vacuum wavelength of 589 nm travels with the greatest speed, we will follow these steps:

### Step 1: Understand the relationship between speed of light and refractive index
The speed of light in a medium (V) is related to the speed of light in a vacuum (c) and the refractive index (n) of that medium by the formula:
\[ V = \frac{c}{n} \]
where:
- \( c \) is the speed of light in vacuum (approximately \( 3 \times 10^8 \) m/s),
- \( n \) is the refractive index of the medium.

### Step 2: Identify the refractive indices from the table
From the table provided, we have the following refractive indices for different substances:
- Fused quartz: \( n = 1.458 \)
- Ethyl alcohol: \( n = 1.362 \)
- Crown glass: \( n = 1.520 \)
- Carbon tetrachloride: \( n = 1.461 \)
- Crystalline quartz: \( n = 1.544 \)

### Step 3: Determine which substance has the lowest refractive index
To find the substance through which light travels the fastest, we need to identify the substance with the minimum refractive index, as a lower refractive index corresponds to a higher speed of light in that medium.

Comparing the refractive indices:
- Fused quartz: \( 1.458 \)
- Ethyl alcohol: \( 1.362 \) (lowest)
- Crown glass: \( 1.520 \)
- Carbon tetrachloride: \( 1.461 \)
- Crystalline quartz: \( 1.544 \)

### Step 4: Conclude which substance allows the greatest speed of light
From the comparison, ethyl alcohol has the lowest refractive index of \( 1.362 \). Therefore, light with a vacuum wavelength of 589 nm will travel through ethyl alcohol with the greatest speed.

### Final Answer
The substance through which light with a vacuum wavelength of 589 nm travels with the greatest speed is **Ethyl Alcohol**.

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