Absolute refractive index of a medium is X. Refractive index of same medium w.r.t to air is Y and absolute refractive index to air is Z. Then the relation between them is

Options

A. X=Y/Z
B. Y=X/Z
C. Z=Y/X
D. Y=1/XZ

Answer

To solve the problem, we need to establish the relationships between the absolute refractive index of a medium (X), the refractive index of the same medium with respect to air (Y), and the absolute refractive index of air (Z).

### Step-by-Step Solution:

1. **Understanding Refractive Index**:
- The absolute refractive index of a medium (X) is defined as the speed of light in vacuum divided by the speed of light in that medium.
- The refractive index of a medium with respect to air (Y) is defined as the speed of light in air divided by the speed of light in that medium.

2. **Establishing Relationships**:
- The refractive index of the medium with respect to air (Y) can be expressed using the absolute refractive index of the medium (X) and the absolute refractive index of air (Z):
\[ Y = \frac{X}{Z} \]
- Here, Z is the absolute refractive index of air, which is approximately equal to 1 (since the speed of light in air is very close to that in vacuum).

3. **Rearranging the Equation**:
- From the equation \( Y = \frac{X}{Z} \), we can rearrange it to express the relationship between X, Y, and Z:
\[ X = Y \cdot Z \]

4. **Conclusion**:
- Therefore, the relationship between the absolute refractive index of the medium (X), the refractive index of the medium with respect to air (Y), and the absolute refractive index of air (Z) is:
\[ Y = \frac{X}{Z} \]
- This implies that \( X = Y \cdot Z \).

### Final Answer:
The relation between the absolute refractive index of a medium (X), the refractive index of the same medium with respect to air (Y), and the absolute refractive index of air (Z) is:
\[ Y = \frac{X}{Z} \]