Electromagnetic radiation of frequency v, velocity v and wavelength `lambda` in air, enters a glass slab of refractive index μ . The frequency, wavelength and velocity of light in the glass slab will be, respectively

Options

A. `(v)/mu,(lamda)/mu'v`
B. `v,lamda(v)/mu`
C. `v'(lamda)/mu'(v)/(mu)`
D. `(v)/(mu)'(lamda)/(mu)'(v)/(mu)`

Answer

To solve the problem, we need to determine the frequency, wavelength, and velocity of light as it passes from air into a glass slab with a refractive index \( \mu \).

### Step-by-Step Solution:

1. **Understanding Frequency in Different Mediums**:
- The frequency \( \nu \) of electromagnetic radiation remains constant when it passes from one medium to another. This is because the energy of the light does not change, and frequency is directly related to energy by the equation \( E = h\nu \).
- Therefore, in the glass slab, the frequency \( \nu' \) will be the same as in air:
\[ \nu' = \nu \]

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

3. **Understanding Wavelength in Different Mediums**:
- The relationship between wavelength \( \lambda \), frequency \( \nu \), and velocity \( v \) is given by the equation:
\[ v = \lambda \nu \]
- Since the frequency remains constant and the velocity changes, we can find the new wavelength \( \lambda' \) in the glass slab using the relationship:
\[ v' = \lambda' \nu \]
- Substituting for \( v' \):
\[ \frac{v}{\mu} = \lambda' \nu \]
- Rearranging gives us:
\[ \lambda' = \frac{v}{\mu \nu} \]
- Since \( v = \lambda \nu \), we can substitute \( v \) in terms of \( \lambda \) and \( \nu \):
\[ \lambda' = \frac{\lambda \nu}{\mu \nu} = \frac{\lambda}{\mu} \]

### Final Results:
- The frequency in the glass slab: \( \nu' = \nu \)
- The velocity in the glass slab: \( v' = \frac{v}{\mu} \)
- The wavelength in the glass slab: \( \lambda' = \frac{\lambda}{\mu} \)

Thus, the frequency, wavelength, and velocity of light in the glass slab will be:
\[ \text{Frequency: } \nu, \quad \text{Wavelength: } \frac{\lambda}{\mu}, \quad \text{Velocity: } \frac{v}{\mu} \]