Question

A beam of light of wavelength 720 nm in air enters water (refractive index \( n = \frac{4}{3} \)). Its wavelength in water will be:

• A. 540 nm
• B. 480 nm
• C. 420 nm
• D. 720 nm

Hint:

The wavelength of light decreases when it passes from a less dense medium (like air) to a denser medium (like water), according to the refractive index.

Answer 1

The Correct Option is A

When light passes into a new medium, its wavelength is altered based on the refractive index of that medium. The formula relating the wavelength in air (\( \lambda_{\text{air}} \)) to the wavelength in a medium (\( \lambda_{\text{medium}} \)) is: \[ \lambda_{\text{medium}} = \frac{\lambda_{\text{air}}}{n} \] In this equation:
- \( \lambda_{\text{air}} = 720 \, \text{nm} \) represents the light's wavelength in air.
- \( n = \frac{4}{3} \) is the refractive index of water. Plugging in the given values yields: \[ \lambda_{\text{water}} = \frac{720}{\frac{4}{3}} = 720 \times \frac{3}{4} = 540 \, \text{nm} \] Therefore, the light's wavelength in water is \( 540 \, \text{nm} \).