A glass slab of thickness 3 cm 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 2 cm above it, the distance of the mark will appear to be in cm

Options

A. 4 cm
B. 3 cm
C. 2 cm
D. 5cm

Answer

To solve the problem, we need to determine the apparent depth of the ink mark when viewed through a glass slab. Here’s a step-by-step breakdown of the solution:

### Step 1: Identify the Given Values
- Thickness of the glass slab (t) = 3 cm
- Refractive index of the glass (μ) = 3/2
- Height of the observer's eye above the slab = 2 cm

### Step 2: Calculate the Apparent Depth
The formula for apparent depth (d') when looking through a medium is given by:
\[ d' = \frac{d}{\mu} \]
where:
- \(d\) is the actual depth (thickness of the slab),
- \(\mu\) is the refractive index.

Substituting the known values:
\[ d' = \frac{3 \text{ cm}}{\frac{3}{2}} = 3 \text{ cm} \times \frac{2}{3} = 2 \text{ cm} \]

### Step 3: Calculate the Total Distance from the Observer's Eye to the Ink Mark
The total distance from the observer's eye to the ink mark is the sum of the apparent depth and the height of the observer's eye above the slab:
\[ \text{Total Distance} = d' + \text{Height of the observer's eye} \]
Substituting the values:
\[ \text{Total Distance} = 2 \text{ cm} + 2 \text{ cm} = 4 \text{ cm} \]

### Final Answer
The distance of the mark will appear to be **4 cm**.

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