A glass slab of thickness `3cm` and refractive index `3//2` is placed on ink mark on a piece of paper. For a person looking at the mark at a distance `5.0 cm` above it, the distance of the mark will appear to be

Options

A. `3.0 cm`
B. `4.0 cm`
C. `4.5 cm`
D. `5.0 cm`

Explanation

To solve the problem, we need to find the apparent depth of the ink mark when viewed through the glass slab. We will use the formula for apparent depth, which is given by:

\[ \text{Apparent Depth} = \frac{\text{Actual Depth}}{\text{Refractive Index}} \]

### Step-by-Step Solution:

1. **Identify the Given Values:**
- Thickness of the glass slab (Actual Depth) = \(3 \, \text{cm}\)
- Refractive Index of the glass slab = \(\frac{3}{2} = 1.5\)
- Distance from the observer to the ink mark (above the slab) = \(5.0 \, \text{cm}\)

2. **Calculate the Apparent Depth of the Ink Mark:**
- Using the formula for apparent depth:
\[ \text{Apparent Depth} = \frac{3 \, \text{cm}}{1.5} = 2 \, \text{cm} \]

3. **Determine the Total Distance from the Observer to the Ink Mark:**
- The observer is looking from a distance of \(5.0 \, \text{cm}\) above the slab. Since the apparent depth of the ink mark is \(2 \, \text{cm}\), the total distance from the observer to the ink mark is:
\[ \text{Total Distance} = \text{Distance above the slab} + \text{Apparent Depth} = 5.0 \, \text{cm} - 2 \, \text{cm} = 3 \, \text{cm} \]

4. **Final Calculation:**
- Therefore, the distance of the mark as perceived by the observer is:
\[ \text{Distance of the mark} = 5.0 \, \text{cm} - 2 \, \text{cm} = 3 \, \text{cm} \]

### Conclusion:
The distance of the mark will appear to be \(3 \, \text{cm}\).