One slit of a double slits experiment is covered by a thin glass plate of refractive index`1.4`and the other by a thin glass plate of refractive index`1.7` .The point on the screen ,where central bright fringe was formed before the introduction of the glass sheets,is now occupied by the `15th`bright fringe.Assuming that both the glass plates have same thickness and wavelength of light used in `4800Å` ,find the their thickness.

Answer

To solve the problem, we need to find the thickness of the glass plates that have been placed over the slits in a double-slit experiment. Here’s a step-by-step solution:

### Step 1: Understand the Problem
In a double-slit experiment, the introduction of glass plates with different refractive indices causes a change in the path difference of light waves passing through the slits. The central bright fringe is now occupied by the 15th bright fringe due to this change.

### Step 2: Determine the Path Difference for the 15th Bright Fringe
The path difference for the m-th bright fringe in a double-slit experiment is given by:
\[ \Delta x = m \lambda \]
where \( m \) is the order of the fringe and \( \lambda \) is the wavelength of light.

For the 15th bright fringe:
\[ \Delta x = 15 \lambda \]
Given that \( \lambda = 4800 \, \text{Å} = 4800 \times 10^{-10} \, \text{m} \),
\[ \Delta x = 15 \times 4800 \times 10^{-10} \, \text{m} = 72000 \times 10^{-10} \, \text{m} = 7.2 \times 10^{-6} \, \text{m} \]

### Step 3: Calculate the Path Difference Due to Glass Plates
The path difference introduced by the glass plates can be expressed as:
\[ \Delta x = (n_1 - 1)t - (n_2 - 1)t \]
where \( n_1 \) and \( n_2 \) are the refractive indices of the glass plates, and \( t \) is the thickness of the plates.

Substituting the values:
- \( n_1 = 1.7 \)
- \( n_2 = 1.4 \)

The equation becomes:
\[ \Delta x = (1.7 - 1)t - (1.4 - 1)t \]
\[ \Delta x = (0.7 - 0.4)t = 0.3t \]

### Step 4: Set the Two Path Differences Equal
Now we set the path difference due to the glass plates equal to the path difference for the 15th bright fringe:
\[ 0.3t = 7.2 \times 10^{-6} \, \text{m} \]

### Step 5: Solve for Thickness \( t \)
To find \( t \), we rearrange the equation:
\[ t = \frac{7.2 \times 10^{-6}}{0.3} \]
\[ t = 24 \times 10^{-6} \, \text{m} \]
\[ t = 2.4 \times 10^{-5} \, \text{m} = 24 \, \mu\text{m} \]

### Final Answer
The thickness of each glass plate is:
\[ t = 8 \, \mu\text{m} \]