Light of frequency n, wave length x travelling with a velocity v enters into a glass slab of R.I n then frequency, wave length and velocity of the wave in glass slab respectively are

Options

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

Answer

To solve the problem, we need to analyze how the frequency, wavelength, and velocity of light change when it enters a glass slab with a given refractive index. Here’s a step-by-step solution:

### Step 1: Understand the given parameters
We are given:
- Frequency of light in vacuum: \( n \)
- Wavelength of light in vacuum: \( \lambda \)
- Velocity of light in vacuum: \( v \)
- Refractive index of the glass slab: \( \mu \)

### Step 2: Determine the velocity of light in the glass slab
The refractive index \( \mu \) is defined as the ratio of the speed of light in vacuum \( c \) to the speed of light in the medium \( v_m \):
\[ \mu = \frac{c}{v_m} \]
Since we are considering the speed of light in vacuum as \( v \), we can express the speed of light in the glass slab as:
\[ v_m = \frac{v}{\mu} \]

### Step 3: Analyze the frequency of light in the glass slab
The frequency of light does not change when it enters a different medium. Therefore, the frequency of light in the glass slab remains the same:
\[ \text{Frequency in glass} = n \]

### Step 4: Determine the wavelength of light in the glass slab
The relationship between the speed of light, frequency, and wavelength is given by:
\[ v = f \cdot \lambda \]
In the glass slab, the speed of light is \( v_m \) and the wavelength is \( \lambda_m \). Therefore, we can write:
\[ v_m = n \cdot \lambda_m \]
Substituting \( v_m \) from Step 2 into this equation:
\[ \frac{v}{\mu} = n \cdot \lambda_m \]
From this, we can solve for the wavelength in the glass slab:
\[ \lambda_m = \frac{v}{\mu \cdot n} \]

### Step 5: Summarize the results
Now we have:
- Frequency in glass: \( n \)
- Wavelength in glass: \( \frac{\lambda}{\mu} \) (since \( \lambda = \frac{v}{n} \))
- Velocity in glass: \( \frac{v}{\mu} \)

### Final Answer
Thus, the frequency, wavelength, and velocity of the wave in the glass slab are:
- Frequency: \( n \)
- Wavelength: \( \frac{\lambda}{\mu} \)
- Velocity: \( \frac{v}{\mu} \)