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 enters a different medium, its wavelength changes according to the refractive index of the new medium. The relationship between the wavelength in air (\( \lambda_{\text{air}} \)) and the wavelength in a medium (\( \lambda_{\text{medium}} \)) is given by: \[ \lambda_{\text{medium}} = \frac{\lambda_{\text{air}}}{n} \] Where:
- \( \lambda_{\text{air}} = 720 \, \text{nm} \) is the wavelength of light in air,
- \( n = \frac{4}{3} \) is the refractive index of water. Substitute the known values: \[ \lambda_{\text{water}} = \frac{720}{\frac{4}{3}} = 720 \times \frac{3}{4} = 540 \, \text{nm} \] Thus, the wavelength of the light in water is \( 540 \, \text{nm} \).