The length of the optical path of two media in contact of length `d_(1)` and `d_(2)` of refreactive indices `mu_(1)` and `mu_(2)` respectively, is

Options

A. `mu_(1)d_(1)+mu_(2)d_(2)`
B. `mu_(1)d_(2)+mu_(2)d_(1)`
C. `(d_(1)d_(2))/(mu_(1)mu_(2))`
D. `(d_(1)+d_(2))/(mu_(1)mu_(2))`

Explanation

To find the total length of the optical path when two media are in contact, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Concept of Optical Path Length**:
The optical path length (OPL) is defined as the product of the refractive index of a medium and the physical length of the path traveled through that medium. Mathematically, it is given by:
\[ \text{Optical Path Length} = \mu \times d \]
where \(\mu\) is the refractive index and \(d\) is the physical length.

2. **Identify the Two Media**:
We have two media in contact:
- Medium 1 with refractive index \(\mu_1\) and length \(d_1\)
- Medium 2 with refractive index \(\mu_2\) and length \(d_2\)

3. **Calculate the Optical Path Length for Each Medium**:
- For Medium 1, the optical path length is:
\[ \text{OPL}_1 = \mu_1 \times d_1 \]
- For Medium 2, the optical path length is:
\[ \text{OPL}_2 = \mu_2 \times d_2 \]

4. **Combine the Optical Path Lengths**:
Since the two media are in contact, the total optical path length is the sum of the optical path lengths of both media:
\[ \text{Total Optical Path Length} = \text{OPL}_1 + \text{OPL}_2 \]
Substituting the expressions we found:
\[ \text{Total Optical Path Length} = \mu_1 d_1 + \mu_2 d_2 \]

5. **Final Result**:
Thus, the total length of the optical path when two media are in contact is:
\[ \text{Total Optical Path Length} = \mu_1 d_1 + \mu_2 d_2 \]