If the speed of light in air is represented by e and the speed in a medium is u, then the refractive index of the medium can be calculated using the formula_______.
e/u
Calculating Refractive Index of a Medium
The question asks for the formula to calculate the refractive index of a medium when given the speed of light in air and the speed of light in the medium.
The refractive index is a fundamental property of a medium that describes how light propagates through it. Specifically, the absolute refractive index of a medium is defined as the ratio of the speed of light in a vacuum (or air, which is very close to a vacuum) to the speed of light in that medium.
In this problem, we are given:
- Speed of light in air = \(e\)
- Speed of light in the medium = \(u\)
The formula for the refractive index (\(\mu\)) of the medium is:
\[ \mu = \frac{\text{Speed of light in vacuum (or air)}}{\text{Speed of light in the medium}} \] Substituting the given variables into the formula:
\[ \mu = \frac{e}{u} \]
Therefore, the refractive index of the medium can be calculated using the formula \(e/u\).
Analyzing the Options
Let's look at the provided options based on the formula for refractive index:
- Option 1: \(u/e\) - This is the inverse ratio, representing the ratio of speed in the medium to speed in air. This is not the definition of refractive index.
- Option 2: \(e/u\) - This matches the definition of refractive index: speed in air divided by speed in the medium.
- Option 3: \(e/(2.u)\) - This formula is not consistent with the definition of refractive index.
- Option 4: \((e-u)/e\) - This formula represents the difference in speeds relative to the speed in air, which is not the formula for refractive index.
Based on the definition, the correct formula is \(e/u\).
Revision Table: Refractive Index Calculation
| Concept | Definition | Formula (using given variables) |
|---|---|---|
| Refractive Index (\(\mu\)) of a Medium | Ratio of the speed of light in air (or vacuum) to the speed of light in the medium. | \(\mu = e/u\) |
| Speed of light in air | \(e\) | Numerator in the formula |
| Speed of light in the medium | \(u\) | Denominator in the formula |
Additional Information: Understanding Refractive Index
The refractive index is a dimensionless quantity (it has no units). It tells us how much the speed of light is reduced when it passes from air (or vacuum) into the medium. A higher refractive index means light travels slower in that medium, and the medium is said to be optically denser.
The refractive index is also related to how much light bends when it passes from one medium to another. This bending is described by Snell's Law:
\[ n_1 \sin \theta_1 = n_2 \sin \theta_2 \]
where \(n_1\) and \(n_2\) are the refractive indices of the two media, and \(\theta_1\) and \(\theta_2\) are the angles of incidence and refraction, respectively, measured from the normal to the boundary.
The refractive index of vacuum is exactly 1. The refractive index of air is very close to 1 (about 1.0003 at standard conditions), which is why we often use the speed of light in air (\(e\)) as a proxy for the speed of light in vacuum when calculating refractive indices.
Different materials have different refractive indices. For example, water has a refractive index of about 1.33, and glass has a refractive index typically ranging from 1.5 to 1.7.
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