A young's double slit apporatus is immersed in a liquid of refractive index 1.33.It has slit separation of 1 mm and interference pattern is observed on the screen at a distance 1.33 m from plane of slits.The wavelength in air is `6300 Å`
Find the distance of seventh bright fringe from third bright fringe lying on the same side of central bright fringe.

Options

A. 2.52 mm
B. 4.41 mm
C. 1.89 mm
D. 1.26 mm

Explanation

To solve the problem, we need to find the distance between the seventh bright fringe and the third bright fringe in a Young's double slit experiment immersed in a liquid. Here’s a step-by-step solution:

### Step 1: Convert Given Values
- Wavelength in air: \( \lambda = 6300 \, \text{Å} = 6300 \times 10^{-10} \, \text{m} \)
- Slit separation: \( d = 1 \, \text{mm} = 1 \times 10^{-3} \, \text{m} \)
- Distance from slits to screen: \( D = 1.33 \, \text{m} \)
- Refractive index of liquid: \( \mu = 1.33 \)

### Step 2: Calculate the Wavelength in the Liquid
The wavelength of light in the liquid can be calculated using the formula:
\[ \lambda' = \frac{\lambda}{\mu} \]
Substituting the values:
\[ \lambda' = \frac{6300 \times 10^{-10}}{1.33} \approx 4744.36 \times 10^{-10} \, \text{m} \]

### Step 3: Calculate the Distance of the 7th Bright Fringe from the Central Maximum
The distance of the nth bright fringe from the central maximum is given by:
\[ y_n = \frac{n \lambda' D}{d} \]
For the 7th bright fringe (\( n = 7 \)):
\[ y_7 = \frac{7 \cdot 4744.36 \times 10^{-10} \cdot 1.33}{1 \times 10^{-3}} \]
Calculating this gives:
\[ y_7 \approx \frac{7 \cdot 4744.36 \times 10^{-10} \cdot 1.33}{1 \times 10^{-3}} \approx 0.0437 \, \text{m} = 43.7 \, \text{mm} \]

### Step 4: Calculate the Distance of the 3rd Bright Fringe from the Central Maximum
Using the same formula for the 3rd bright fringe (\( n = 3 \)):
\[ y_3 = \frac{3 \cdot 4744.36 \times 10^{-10} \cdot 1.33}{1 \times 10^{-3}} \]
Calculating this gives:
\[ y_3 \approx \frac{3 \cdot 4744.36 \times 10^{-10} \cdot 1.33}{1 \times 10^{-3}} \approx 0.0144 \, \text{m} = 14.4 \, \text{mm} \]

### Step 5: Calculate the Distance Between the 7th and 3rd Bright Fringe
The distance between the 7th and 3rd bright fringes is given by:
\[ \text{Distance} = y_7 - y_3 \]
Substituting the values:
\[ \text{Distance} = 43.7 \, \text{mm} - 14.4 \, \text{mm} = 29.3 \, \text{mm} \]

### Final Answer
The distance between the 7th bright fringe and the 3rd bright fringe is \( 29.3 \, \text{mm} \).

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