Question

A light ray incident on a slab of refractive index \( \frac{3}{2} \). If the wavelength of the refracted ray is 520 nm, find the wavelength of the incident ray.

• A. 460 nm
• B. 780 nm
• C. 360 nm
• D. 560 nm

Hint:

The wavelength of light decreases in a medium with a refractive index greater than 1. Use the refractive index to find the incident wavelength.

Answer 1

The Correct Option is B

Step 1: Use the relationship between refractive index and wavelength.
The refractive index \( n \) is related to the wavelength of light in air and the wavelength of light in the medium by the formula: \[ n = \frac{\lambda_{\text{incident}}}{\lambda_{\text{refracted}}}. \] Here, \( n = \frac{3}{2} \) and \( \lambda_{\text{refracted}} = 520 \, \text{nm} \). Step 2: Solve for \( \lambda_{\text{incident}} \).
Rearrange the formula to find the incident wavelength: \[ \lambda_{\text{incident}} = n \times \lambda_{\text{refracted}} = \frac{3}{2} \times 520 \, \text{nm} = 780 \, \text{nm}. \] Final Answer: \[ \boxed{780 \, \text{nm}}. \]