Four transparent slabs having thickness `t_(1)= 2cm, t_(2)= 4 cm, t_(3)= 3 cm" and "t_(4)= 5cm` are introduced in one of the paths of light emitted by two narrow slits the ascending order of shift of the central fringe

Options

A. `t_(1), t_(2), t_(3), t_(4)`
B. `t_(4), t_(3), t_(2), t_(1)`
C. `t_(3), t_(2), t_(4), t_(1)`
D. `t_(1), t_(3), t_(2), t_(4)`

Answer

To find the ascending order of shift of the central fringe caused by four transparent slabs of different thicknesses, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Thicknesses of the Slabs:**
- The thicknesses of the slabs are given as:
- \( t_1 = 2 \, \text{cm} \)
- \( t_2 = 4 \, \text{cm} \)
- \( t_3 = 3 \, \text{cm} \)
- \( t_4 = 5 \, \text{cm} \)

2. **Understand the Relationship Between Thickness and Fringe Shift:**
- The shift in the central fringe (\( \Delta t \)) due to a slab is directly proportional to its thickness. The formula can be simplified to:
\[ \Delta t \propto t \]
- This means that the larger the thickness of the slab, the greater the shift in the fringe.

3. **Arrange the Thicknesses in Ascending Order:**
- We will now arrange the thicknesses from smallest to largest:
- \( t_1 = 2 \, \text{cm} \)
- \( t_3 = 3 \, \text{cm} \)
- \( t_2 = 4 \, \text{cm} \)
- \( t_4 = 5 \, \text{cm} \)

4. **Determine the Order of Shift:**
- Based on the thicknesses, the order of shift of the central fringe will be:
- First: \( t_1 \) (2 cm)
- Second: \( t_3 \) (3 cm)
- Third: \( t_2 \) (4 cm)
- Fourth: \( t_4 \) (5 cm)

5. **Final Ascending Order of Shift:**
- Therefore, the ascending order of shift of the central fringe due to the slabs is:
\[ t_1 < t_3 < t_2 < t_4 \]

### Conclusion:
The ascending order of shift of the central fringe is:
- \( t_1 (2 \, \text{cm}) < t_3 (3 \, \text{cm}) < t_2 (4 \, \text{cm}) < t_4 (5 \, \text{cm}) \)