Question

If the speed of light in a medium is \(2 \times 10^8 \, \text{m/s}\), what is the refractive index of the medium?

• A. \(1.2\)
• B. \(1.3\)
• C. \(1.5\)
• D. \(2\)

Hint:

The refractive index indicates how much light slows down in a medium. Higher refractive index means the speed of light in that medium is lower.

Answer 1

The Correct Option is C

Step 1: Understanding the Question:
The question provides the speed of light inside a specific optical medium.
We need to determine the refractive index of this medium based on how much it slows down the light.
Step 2: Key Formula or Approach:
The absolute refractive index (\(n\)) of a medium is defined as the ratio of the speed of light in a vacuum (\(c\)) to the speed of light in that medium (\(v\)):
\[ n = \frac{c}{v} \] Step 3: Detailed Solution:
The constant for the speed of light in a vacuum is universally known as:
\[ c = 3 \times 10^8\,\text{m/s} \] The given speed of light in the medium is:
\[ v = 2 \times 10^8\,\text{m/s} \] Substitute these values into the refractive index formula:
\[ n = \frac{3 \times 10^8}{2 \times 10^8} \] The \(10^8\) terms cancel out completely:
\[ n = \frac{3}{2} \] \[ n = 1.5 \] Step 4: Final Answer:
The refractive index of the given medium is \(1.5\).