Suppose a beam of light of average wavelength 600nm  is incident on a glass prism from air, and on entering into the prism, it splits into different colours. One of the colours has wavelength 380nm. The refractive index of the medium for this particular wavelength is:

Correct option is A

The correct answer is: (A) 1.58

Explanation:

To find the refractive index of the medium (the glass prism) for a particular wavelength of light, we use the relationship between the wavelength of light in air and in the medium:

​$$n = \frac{\lambda_{\text{air}}}{\lambda_{\text{medium}}}$$​​

Where:

• n is the refractive index of the medium.
• λair is the wavelength of light in air.
• λmedium is the wavelength of light in the medium (glass prism).

Here:

• The wavelength of light in air is λair=600 nm.
• The wavelength of light in the prism is λmedium=380 nm.

Now, applying the formula:

​$$n = \frac{\lambda_{\text{air}}}{\lambda_{\text{medium}}} = \frac{600}{380} \approx 1.58$$​​

Therefore, the refractive index of the prism for the wavelength of 380 nm is approximately 1.58.

Information Booster:

• The refractive index increases as the wavelength decreases. This explains why shorter wavelengths (like 380 nm) have a higher refractive index than longer wavelengths (like 600 nm).
• This phenomenon leads to the dispersion of light, where different wavelengths of light bend by different amounts as they pass through a prism.