Question

For a colour of light the wavelength for air is 6000 \AA\ and in water the wavelength is 4500 \AA. Then the speed of light in water will be

• A. \(5 \times 10^4\) m/s
• B. \(2.25 \times 10^8\) m/s
• C. \(4.0 \times 10^8\) m/s
• D. zero

Hint:

Refractive index \(n = \lambda_{vacuum}/\lambda_{medium} = c/v_{medium}\). Frequency remains unchanged when light passes through different media.

Answer 1

The Correct Option is B

Step 1: Basic Principle
\(n = \lambda_{air}/\lambda_{water}\) and \(v = c/n\).
Step 2: Solution Procedure:
\[ n = \frac{\lambda_{air}}{\lambda_{water}} = \frac{6000}{4500} = \frac{4}{3} \] \[ v = \frac{c}{n} = \frac{3 \times 10^8}{4/3} = \frac{3 \times 10^8 \times 3}{4} = 2.25 \times 10^8 \text{ m/s} \]
Step 3: Required Answer:
Speed of light in water \(= \mathbf{2.25 \times 10^8}\) m/s.