A tank of height 50 m is filled with oil fully. If the bottom of the tank appears to be 40 m below its top, the refractive index of the oil should be

Options

A. `4/5`
B. `1/5`
C. `1/4`
D. `5/4`

Answer

To solve the problem, we need to find the refractive index of the oil based on the given information about the tank's height and the apparent depth of the bottom of the tank.

### Step-by-Step Solution:

1. **Identify Given Values:**
- Actual height of the tank (H_actual) = 50 m
- Apparent depth of the bottom of the tank (H_apparent) = 40 m

2. **Understand the Relationship:**
The relationship between the apparent depth (H_apparent), actual depth (H_actual), and the refractive index (μ) of the medium is given by the formula:
\[ H_{apparent} = \frac{H_{actual}}{\mu} \]

3. **Rearrange the Formula:**
To find the refractive index (μ), we can rearrange the formula:
\[ \mu = \frac{H_{actual}}{H_{apparent}} \]

4. **Substitute the Known Values:**
Now, substitute the known values into the rearranged formula:
\[ \mu = \frac{50 \, \text{m}}{40 \, \text{m}} \]

5. **Calculate the Refractive Index:**
Perform the division:
\[ \mu = \frac{50}{40} = \frac{5}{4} \]

6. **Final Result:**
The refractive index of the oil is:
\[ \mu = 1.25 \]

### Conclusion:
The refractive index of the oil is \( \frac{5}{4} \) or 1.25.

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