A glass slab of thickness 12 cm is placed on a table. The level surface of the slab has a black spot. At what depth from the upper surface will the spot appear when viewed from above?
(Refractive index of glass = 1.5)

Options

A. 2 mm
B. 4 mm
C. 6 mm
D. 8 mm

Explanation

To find the apparent depth of the black spot when viewed from above the glass slab, we can use the formula for apparent depth in a medium with a refractive index. Here are the steps to solve the problem:

### Step 1: Identify the given values
- Thickness of the glass slab (real depth) = 12 cm
- Refractive index of glass (μ) = 1.5

### Step 2: Use the formula for apparent depth
The formula for apparent depth (d') when viewing an object through a medium is given by:
\[ d' = \frac{d}{\mu} \]
where:
- \( d \) is the real depth (thickness of the slab),
- \( \mu \) is the refractive index of the medium.

### Step 3: Substitute the values into the formula
Substituting the given values into the formula:
\[ d' = \frac{12 \, \text{cm}}{1.5} \]

### Step 4: Calculate the apparent depth
Now, perform the calculation:
\[ d' = \frac{12}{1.5} = 8 \, \text{cm} \]

### Step 5: Conclusion
The apparent depth of the black spot when viewed from above the glass slab is 8 cm.

### Final Answer
The spot will appear at a depth of 8 cm from the upper surface of the glass slab.

---