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

Options

A. `n/mu, lambda/mu, v/mu`
B. `n, lambda/mu, v/mu`
C. `n, lambda, v/mu`
D. `n/mu, lambda/mu, v`

Answer

To solve the problem step by step, we will analyze the behavior of electromagnetic radiation as it transitions from air to a glass slab.

### Step 1: Understanding Frequency
When electromagnetic radiation travels from one medium to another, its frequency remains constant. Therefore, the frequency of the light in the glass slab will be the same as that in air.

**Solution:**
- Frequency in glass, \( n' = n \)

### Step 2: Understanding Velocity
The velocity of light in a medium is given by the formula:
\[ v' = \frac{c}{\mu} \]
where \( c \) is the speed of light in vacuum (or air, approximately) and \( \mu \) is the refractive index of the medium. Since we are given the velocity \( v \) in air, we can express the velocity in the glass slab as:
\[ v' = \frac{v}{\mu} \]

**Solution:**
- Velocity in glass, \( v' = \frac{v}{\mu} \)

### Step 3: Understanding Wavelength
The relationship between velocity, frequency, and wavelength is given by:
\[ v = n \cdot \lambda \]
When light enters a different medium, the wavelength changes according to the refractive index. The wavelength in the medium can be calculated using the formula:
\[ \lambda' = \frac{v'}{n'} \]
Substituting the values we found earlier:
\[ \lambda' = \frac{v/\mu}{n} = \frac{\lambda}{\mu} \]

**Solution:**
- Wavelength in glass, \( \lambda' = \frac{\lambda}{\mu} \)

### Final Summary of Results
- Frequency in glass: \( n' = n \)
- Velocity in glass: \( v' = \frac{v}{\mu} \)
- Wavelength in glass: \( \lambda' = \frac{\lambda}{\mu} \)