Question

A light wave of wavelength 600 nm passes from air into a medium with refractive index 1.5. What is the wavelength of light in the medium?

• A. 400 nm
• B. 450 nm
• C. 500 nm
• D. 600 nm

Hint:

Wavelength of light in a medium = $\lambda/n$, where $\lambda$ is original wavelength and $n$ is the refractive index.

Answer 1

The Correct Option is A

When light enters a medium with refractive index \( n \), its speed and wavelength decrease, but frequency remains constant. The wavelength in the medium is given by: \[ \lambda' = \frac{\lambda}{n} \] Given: \[ \lambda = 600 \, \text{nm}, \quad n = 1.5 \] \[ \lambda' = \frac{600}{1.5} = 400 \, \text{nm} \]

Answer 2

To solve the problem, we need to find the wavelength of light in a medium with refractive index 1.5 when the light of wavelength 600 nm passes from air into the medium.

1. Relation Between Wavelength and Refractive Index: 
The wavelength of light in a medium is given by:
$ \lambda_{\text{medium}} = \frac{\lambda_{\text{air}}}{n} $
where $n$ is the refractive index of the medium, $\lambda_{\text{air}}$ is the wavelength in air, and $\lambda_{\text{medium}}$ is the wavelength in the medium.

2. Given Data:
$ \lambda_{\text{air}} = 600\, \text{nm} $
$ n = 1.5 $

3. Calculating Wavelength in Medium:
$ \lambda_{\text{medium}} = \frac{600}{1.5} = 400\, \text{nm} $

Final Answer:
The wavelength of light in the medium is $ {400\, \text{nm}} $.