Two indentical beakers, one filled with water `mu = (4)/(3)` and the other filled with oil `(mu = 1.6)` are viewed from directly above. On comparison, which of the following statements is correct?

Options

A. Water filled beaker appears deeper by a factor of 1.2
B. Oil filled beaker appear deeper by a factor of 1.2.
C. Water filled beaker appears deeper by a factor of `(4)/(3)`
D. Oil filled beaker appears deeper by a factor of 1.6.

Answer

To solve the problem, we need to compare the effective heights of the water and oil in the beakers when viewed from directly above. The refractive indices of water and oil are given, and we will use these to determine how deep each liquid appears.

### Step-by-Step Solution:

1. **Identify the Refractive Indices**:
- Refractive index of water, \( \mu_{water} = \frac{4}{3} \)
- Refractive index of oil, \( \mu_{oil} = 1.6 \)

2. **Understand the Concept of Apparent Depth**:
- The apparent depth of a liquid when viewed from above is given by the formula:
\[ \text{Apparent Depth} = \frac{h}{\mu} \]
where \( h \) is the actual depth of the liquid.

3. **Calculate the Apparent Depth of Water**:
- Let the actual height of the water be \( h \).
- The apparent depth of water is:
\[ \text{Apparent Depth}_{water} = \frac{h}{\frac{4}{3}} = \frac{3h}{4} \]

4. **Calculate the Apparent Depth of Oil**:
- The apparent depth of oil is:
\[ \text{Apparent Depth}_{oil} = \frac{h}{1.6} \]

5. **Compare the Apparent Depths**:
- To compare the two apparent depths, we can express them in terms of \( h \):
- For water: \( \frac{3h}{4} \)
- For oil: \( \frac{h}{1.6} \)
- To find out which is deeper, we can set up the ratio:
\[ \frac{\text{Apparent Depth}_{water}}{\text{Apparent Depth}_{oil}} = \frac{\frac{3h}{4}}{\frac{h}{1.6}} = \frac{3h \cdot 1.6}{4h} = \frac{3 \cdot 1.6}{4} = \frac{4.8}{4} = 1.2 \]

6. **Conclusion**:
- The apparent depth of water is 1.2 times the apparent depth of oil. Thus, when viewed from above, the water appears deeper than the oil.

### Final Answer:
The water beaker will appear 1.2 times deeper than the oil beaker.