Question

The refractive index of a medium is 2. The speed of light in that medium is

• A. \(6 × 10^8 m/s\)
• B. \(10^8 m/s\)
• C. \(5 × 10^8 m/s\)
• D. \(1·5 × 10^8 m/s\)

Answer 1

The Correct Option is D

To find the speed of light in the medium, we use the formula for the refractive index \(n\):

\(n = \frac{c}{v}\)

where \(n\) is the refractive index of the medium, \(c\) is the speed of light in a vacuum (approximately \(3 \times 10^8 \text{ m/s}\)), and \(v\) is the speed of light in the medium.

Given that \(n = 2\), we can rearrange the formula to solve for \(v\):

\(v = \frac{c}{n}\)

Substitute the known values into the equation:

\(v = \frac{3 \times 10^8}{2} \text{ m/s}\)

Calculating this gives:

\(v = 1.5 \times 10^8 \text{ m/s}\)

Therefore, the speed of light in the medium is \(1.5 \times 10^8 \text{ m/s}\).

Answer 2

Given: Refractive index of the medium n = 2

Formula: The refractive index is given by 

n = c / v

where:

• c is the speed of light in vacuum = 3 × 10⁸ m/s
• v is the speed of light in the medium

Substitute the values:

2 = (3 × 10⁸) / v

⇒ v = (3 × 10⁸) / 2 = 1.5 × 10⁸ m/s

Correct Answer: 1.5 × 10⁸ m/s