A monochromatic beam of bright of light of wavelength `5000 Å` is used in Young's double slit experiment. If one of the slits is covered by a transparent sheet of thikness `1.4 xx 10^(-5) m`, having refractive index of its medium 1.25. Then the number of fringes shifted is

Explanation

To solve the problem step by step, we will follow the principles of Young's double slit experiment and the effect of a transparent sheet on the path difference.

### Step 1: Understand the Given Information
- Wavelength of light, \( \lambda = 5000 \, \text{Å} = 5000 \times 10^{-10} \, \text{m} \)
- Thickness of the transparent sheet, \( t = 1.4 \times 10^{-5} \, \text{m} \)
- Refractive index of the sheet, \( n = 1.25 \)

### Step 2: Calculate the Optical Path Length
The optical path length (OPL) is given by the formula:
\[ \text{OPL} = n \cdot t \]
Substituting the values:
\[ \text{OPL} = 1.25 \times 1.4 \times 10^{-5} \, \text{m} = 1.75 \times 10^{-5} \, \text{m} \]

### Step 3: Calculate the Geometrical Path Length
The geometrical path length (GPL) is simply the thickness of the sheet:
\[ \text{GPL} = t = 1.4 \times 10^{-5} \, \text{m} \]

### Step 4: Determine the Path Difference
The path difference \( \Delta x \) introduced by the sheet is given by:
\[ \Delta x = \text{OPL} - \text{GPL} = (1.25 \times 1.4 \times 10^{-5}) - (1.4 \times 10^{-5}) \]
Calculating this gives:
\[ \Delta x = (1.75 \times 10^{-5}) - (1.4 \times 10^{-5}) = 0.35 \times 10^{-5} \, \text{m} \]

### Step 5: Calculate the Number of Fringes Shifted
The number of fringes shifted \( N \) can be calculated using the formula:
\[ N = \frac{\Delta x}{\lambda} \]
Substituting the values:
\[ N = \frac{0.35 \times 10^{-5}}{5000 \times 10^{-10}} = \frac{0.35 \times 10^{-5}}{5 \times 10^{-7}} = \frac{0.35}{5} \times 10^{2} = 7 \]

### Final Answer
The number of fringes shifted is \( N = 7 \).

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