Question

The wavelength of light while it is passing through water is \(540\,\text{nm}\). The refractive index of water is \( \frac{4}{3} \). The wavelength of the same light when it is passing through a transparent medium having refractive index of \( \frac{3}{2} \) is _________ nm.

• A. \(480\)
• B. \(840\)
• C. \(380\)
• D. \(540\)

Hint:

Frequency of light remains unchanged when it passes from one medium to another; only wavelength changes.

Answer 1

The Correct Option is A

Step 1: Use relation between wavelength and refractive index.
Wavelength in a medium is given by \[ \lambda = \frac{\lambda_0}{\mu}, \] where \( \lambda_0 \) is wavelength in vacuum and \( \mu \) is refractive index.

Step 2: Find wavelength in vacuum.
For water, \[ \lambda_0 = \mu_{\text{water}} \times \lambda_{\text{water}} = \frac{4}{3} \times 540 = 720\,\text{nm}. \]

Step 3: Find wavelength in the second medium.
For refractive index \( \frac{3}{2} \), \[ \lambda = \frac{720}{\frac{3}{2}} = 720 \times \frac{2}{3} = 480\,\text{nm}. \]

Final Answer: \[ \boxed{480} \]