Question

If the speed of light in a medium is \( 200 \times 10^8 \, \text{cm/s} \), calculate the refractive index for this medium given that \( c = 3 \times 10^{10} \, \text{m/s} \).

• A. 1.33
• B. 1.5
• C. 1.0
• D. 2.42

Hint:

The refractive index is a measure of how much the speed of light is reduced inside a medium compared to its speed in a vacuum.

Answer 1

The Correct Option is B

Step 1: Formula for refractive index.
The refractive index \( n \) is given by the formula: \[ n = \frac{c}{v} \] where: - \( c = 3 \times 10^{10} \, \text{m/s} \) (speed of light in vacuum), - \( v = 200 \times 10^8 \, \text{cm/s} = 2 \times 10^{9} \, \text{m/s} \) (speed of light in the medium).
Step 2: Calculate the refractive index.
Substituting the values: \[ n = \frac{3 \times 10^{10}}{2 \times 10^9} = 1.5 \]
Step 3: Conclusion.
Thus, the refractive index for this medium is 1.5, so the correct answer is (B).