A microscope is focussed on a point object, and then its objective is raised through a height of 2cm when a glass slab of refractive index 1.5 is placed over this point object such that it is focussed again. The thickness of the glass slab is

Options

A. 6 cm
B. 3 cm
C. 2 cm below P
D. 1.5 cm

Answer

To solve the problem, we need to find the thickness of the glass slab when the objective of the microscope is raised by 2 cm after placing the slab over the point object. The refractive index of the glass slab is given as 1.5.

### Step-by-Step Solution:

1. **Understand the Problem**:
- The microscope is initially focused on a point object.
- When the objective is raised by 2 cm, a glass slab with a refractive index of 1.5 is placed over the object.
- The goal is to find the thickness of the glass slab that allows the microscope to be focused again.

2. **Identify the Relationship**:
- When a glass slab is placed over the object, the apparent position of the object changes due to refraction.
- The relationship between the actual thickness of the glass slab (t), the refractive index (μ), and the shift in the apparent position (Δx) can be expressed as:
\[ \Delta x = t \left(1 - \frac{1}{\mu}\right) \]

3. **Substitute Known Values**:
- Given that Δx = 2 cm and μ = 1.5, we can substitute these values into the equation:
\[ 2 = t \left(1 - \frac{1}{1.5}\right) \]

4. **Calculate the Factor**:
- First, calculate \(1 - \frac{1}{1.5}\):
\[ 1 - \frac{1}{1.5} = 1 - \frac{2}{3} = \frac{1}{3} \]

5. **Set Up the Equation**:
- Now substitute this back into the equation:
\[ 2 = t \left(\frac{1}{3}\right) \]

6. **Solve for Thickness (t)**:
- To find t, multiply both sides by 3:
\[ t = 2 \times 3 = 6 \text{ cm} \]

7. **Conclusion**:
- The thickness of the glass slab is 6 cm.

### Final Answer:
The thickness of the glass slab is **6 cm**.