A mark at the bottom of a liquid appears to rise by `0.1m`. The depth of the liquid is `1m`. The refractive index of the liquid is

Options

A. 1.33
B. 43718
C. `10/9`
D. 1.5

Explanation

To find the refractive index of the liquid based on the information provided, we can follow these steps:

### Step 1: Understand the problem
We have a mark at the bottom of a liquid that appears to rise by 0.1 m. The actual depth of the liquid is 1 m. We need to find the refractive index of the liquid.

### Step 2: Identify the real and apparent depths
- **Real Depth (d)**: This is the actual depth of the liquid, which is given as 1 m.
- **Apparent Depth (d')**: Since the mark appears to rise by 0.1 m, the apparent depth can be calculated as:
\[ d' = d - 0.1 \, \text{m} = 1 \, \text{m} - 0.1 \, \text{m} = 0.9 \, \text{m} \]

### Step 3: Use the formula for refractive index
The refractive index (\( \mu \)) of the liquid can be calculated using the formula:
\[ \mu = \frac{\text{Real Depth}}{\text{Apparent Depth}} = \frac{d}{d'} \]
Substituting the values we have:
\[ \mu = \frac{1 \, \text{m}}{0.9 \, \text{m}} = \frac{10}{9} \]

### Step 4: Conclusion
Thus, the refractive index of the liquid is:
\[ \mu = \frac{10}{9} \]