Question

An electromagnetic radiation of frequency n, wavelength $\lambda $, travelling with velocity v in air, enters a glass slab of refractive index \mu . The frequency, wavelength and velocity of light in the glass slab will be respectively

• A. $ n, 2 \lambda \, \, and \, \, \frac{v}{\mu }$
• B. $ \frac{2n}{\mu}, \frac{\lambda}{\mu} $ and $ v $
• C. $\frac{n}{\mu } , \frac{\lambda}{ \mu }$ and $\frac{v }{\mu }$
• D. $\frac{n}{\mu } $ and $ \frac{v}{\mu } $

Answer 1

The Correct Option is D

To solve this problem, we need to understand how the frequency, wavelength, and velocity of electromagnetic radiation change when it moves from one medium to another.

Step 1: Understanding the Concepts:

1. Frequency: The frequency (\( n \)) of electromagnetic radiation remains constant when light enters from one medium to another. This is because frequency is a property determined by the source of the light, and changing mediums does not affect it.

2. Velocity: The speed of light decreases in a denser medium. The relationship is given by:

v_{\text{glass}} = \frac{v}{\mu}

where \( v \) is the speed of light in air, and \( \mu \) is the refractive index of the glass.

3. Wavelength: Since the velocity changes and frequency remains the same, the wavelength (\(\lambda_{\text{glass}}\)) in the new medium (glass) can be calculated using the relation:

\lambda_{\text{glass}} = \frac{v_{\text{glass}}}{n} = \frac{\lambda}{\mu}

We derive this from the formula for the speed of light: \(v = n \times \lambda\).

Step 2: Calculating Values:

• The frequency remains the same, \( n \).
• The velocity of light in glass is \( \frac{v}{\mu} \).
• The wavelength in glass is \( \frac{\lambda}{\mu} \).

Step 3: Analyzing the Options:

After applying the above concepts:

1. n, 2\lambda, \text{and} \frac{v}{\mu} - Frequency changes, incorrect.
2. \frac{2n}{\mu}, \frac{\lambda}{\mu} \text{and} v - Frequency and velocity incorrect.
3. \frac{n}{\mu}, \frac{\lambda}{\mu} \text{and} \frac{v}{\mu} - The frequency value is incorrect.
4. n, \frac{\lambda}{\mu} \text{and} \frac{v}{\mu} - Correct option.

Conclusion:

In a glass medium with a refractive index \( \mu \), the frequency \( n \) remains the same, the wavelength becomes \( \frac{\lambda}{\mu} \), and the velocity of light becomes \( \frac{v}{\mu} \). Therefore, the fourth option n, \frac{\lambda}{\mu}, \text{and} \frac{v}{\mu} is correct.