A coin is dropped in a glass through containing benzene filled to a depth of 4cm. When viewed from the outside it appears to be raised by 2cm. The refractive index of benzene with respect to air is calculated as:

Options

A. dividing real depth by shift that is `[4//2]=2`
B. First finding the apparent depth as real depth-shift and then using the relation refractive index is real depth upon apparent depth = `[4//(4-2)]=2`
C. Finding the real depth and then using the relation refractive index is real depth/apparent depth
D. None of the above

Explanation

To calculate the refractive index of benzene with respect to air, we can follow these steps:

### Step 1: Identify the given values
- Real depth of benzene (d) = 4 cm
- Apparent shift (s) = 2 cm (the coin appears raised by this amount)

### Step 2: Understand the relationship between real depth, apparent depth, and refractive index
The refractive index (n) can be calculated using the formula:
\[ n = \frac{\text{Real Depth}}{\text{Apparent Depth}} \]
Where:
- Apparent Depth = Real Depth - Shift

### Step 3: Calculate the Apparent Depth
Using the values from Step 1:
\[ \text{Apparent Depth} = \text{Real Depth} - \text{Shift} = 4 \text{ cm} - 2 \text{ cm} = 2 \text{ cm} \]

### Step 4: Substitute the values into the refractive index formula
Now we can substitute the real depth and apparent depth into the refractive index formula:
\[ n = \frac{4 \text{ cm}}{2 \text{ cm}} = 2 \]

### Step 5: Conclusion
The refractive index of benzene with respect to air is \( n = 2 \).

---