A layer of benzene `(mu=1.5)` 12 cm thick floats on water layer `(mu=4//3)` 8 cm thick in a vessel. When viewed from the top, the apparent depth of bottom of vessel below the surface of benzene will be

Options

A. 20 cm
B. 14 cm
C. 7 cm
D. 21 cm

Answer

To find the apparent depth of the bottom of the vessel below the surface of benzene, we need to consider the refractive indices and the actual depths of the layers of benzene and water.

### Step-by-Step Solution:

1. **Identify the Given Data:**
- Refractive index of benzene, \( \mu_{benzene} = 1.5 \)
- Thickness of benzene, \( d_{benzene} = 12 \, \text{cm} \)
- Refractive index of water, \( \mu_{water} = \frac{4}{3} \)
- Thickness of water, \( d_{water} = 8 \, \text{cm} \)

2. **Calculate the Apparent Depth of Benzene:**
The formula for apparent depth when viewing through a medium is given by:
\[ \text{Apparent Depth} = \frac{\text{Actual Depth}}{\text{Refractive Index}} \]
For benzene:
\[ \text{Apparent Depth}_{benzene} = \frac{d_{benzene}}{\mu_{benzene}} = \frac{12 \, \text{cm}}{1.5} = 8 \, \text{cm} \]

3. **Calculate the Apparent Depth of Water:**
Using the same formula for the water layer:
\[ \text{Apparent Depth}_{water} = \frac{d_{water}}{\mu_{water}} = \frac{8 \, \text{cm}}{\frac{4}{3}} = 8 \, \text{cm} \times \frac{3}{4} = 6 \, \text{cm} \]

4. **Calculate the Total Apparent Depth:**
The total apparent depth from the top of the benzene to the bottom of the vessel is the sum of the apparent depths of both layers:
\[ \text{Total Apparent Depth} = \text{Apparent Depth}_{benzene} + \text{Apparent Depth}_{water} = 8 \, \text{cm} + 6 \, \text{cm} = 14 \, \text{cm} \]

5. **Conclusion:**
Thus, the apparent depth of the bottom of the vessel below the surface of benzene is \( 14 \, \text{cm} \).

### Final Answer:
The apparent depth of the bottom of the vessel below the surface of benzene is \( 14 \, \text{cm} \).

---