A ray of light passes through two slabs of same thickness. In the first slab `n_(1)` waves are formed and in the second slab `n_2`. Find refractive `
` index of second medium with respect to first.

Explanation

To find the refractive index of the second medium with respect to the first, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Problem**: We have two slabs of the same thickness, and we know the number of waves formed in each slab. Let \( n_1 \) be the number of waves formed in the first slab, and \( n_2 \) be the number of waves formed in the second slab.

2. **Relate Wave Number to Thickness and Wavelength**: The relationship between the number of waves, thickness of the slab, and wavelength is given by:
\[ n = \frac{T}{\lambda} \]
where \( n \) is the number of waves, \( T \) is the thickness of the slab, and \( \lambda \) is the wavelength of light in that medium.

3. **Express Wavelength in Terms of Refractive Index**: The wavelength in a medium is related to the refractive index \( n \) by the equation:
\[ \lambda = \frac{\lambda_0}{n} \]
where \( \lambda_0 \) is the wavelength in vacuum (or air).

4. **Set Up the Equations for Both Slabs**:
- For the first slab (medium 1):
\[ n_1 = \frac{T}{\lambda_1} \]
- For the second slab (medium 2):
\[ n_2 = \frac{T}{\lambda_2} \]

5. **Substitute Wavelengths**: Substitute the expressions for \( \lambda_1 \) and \( \lambda_2 \):
\[ n_1 = \frac{T}{\frac{T}{n_1}} \quad \text{and} \quad n_2 = \frac{T}{\frac{T}{n_2}} \]

6. **Relate the Two Refractive Indices**: From the equations for the two slabs, we can express the refractive indices:
\[ \frac{n_1}{n_2} = \frac{\lambda_2}{\lambda_1} \]

7. **Rearranging for Refractive Index of Second Medium**: We can rearrange this to find the refractive index of the second medium with respect to the first:
\[ \frac{n_2}{n_1} = \frac{\lambda_1}{\lambda_2} \]

8. **Final Result**: Thus, the refractive index of the second medium with respect to the first is:
\[ n_{21} = \frac{n_2}{n_1} \]

### Summary:
The refractive index of the second medium with respect to the first is given by the ratio of the wavelengths in the two media:
\[ n_{21} = \frac{n_2}{n_1} = \frac{\lambda_1}{\lambda_2} \]