The two slits are 1 mm apart from each other and illuminated with a light of wavelength `5xx10^(-7)` m. If the distance of the screen is 1 m from the slits, then the distance between third dark fringe and fifth bright fringe is

Options

A. 1.2 mm
B. 0.75 mm
C. 1.25 mm
D. 0.625 mm

Explanation

To find the distance between the third dark fringe and the fifth bright fringe in a double-slit experiment, we can follow these steps:

### Step 1: Identify the given values
- Distance between the slits (d) = 1 mm = \(1 \times 10^{-3}\) m
- Wavelength of light (\(\lambda\)) = \(5 \times 10^{-7}\) m
- Distance from the slits to the screen (D) = 1 m

### Step 2: Calculate the position of the fifth bright fringe
The position of the nth bright fringe from the center is given by the formula:
\[ y_n = \frac{n \cdot D \cdot \lambda}{d} \]
For the fifth bright fringe (\(n = 5\)):
\[ y_5 = \frac{5 \cdot D \cdot \lambda}{d} \]
Substituting the values:
\[ y_5 = \frac{5 \cdot 1 \cdot 5 \times 10^{-7}}{1 \times 10^{-3}} = \frac{25 \times 10^{-7}}{10^{-3}} = 25 \times 10^{-4} \text{ m} = 2.5 \times 10^{-3} \text{ m} = 2.5 \text{ mm} \]

### Step 3: Calculate the position of the third dark fringe
The position of the nth dark fringe from the center is given by the formula:
\[ y_{n} = \frac{(n - 0.5) \cdot D \cdot \lambda}{d} \]
For the third dark fringe (\(n = 3\)):
\[ y_3 = \frac{(3 - 0.5) \cdot D \cdot \lambda}{d} = \frac{2.5 \cdot D \cdot \lambda}{d} \]
Substituting the values:
\[ y_3 = \frac{2.5 \cdot 1 \cdot 5 \times 10^{-7}}{1 \times 10^{-3}} = \frac{12.5 \times 10^{-7}}{10^{-3}} = 12.5 \times 10^{-4} \text{ m} = 1.25 \times 10^{-3} \text{ m} = 1.25 \text{ mm} \]

### Step 4: Calculate the distance between the fifth bright fringe and the third dark fringe
The distance between the fifth bright fringe and the third dark fringe is given by:
\[ \text{Distance} = y_5 - y_3 \]
Substituting the values:
\[ \text{Distance} = 2.5 \text{ mm} - 1.25 \text{ mm} = 1.25 \text{ mm} \]

### Final Answer
The distance between the third dark fringe and the fifth bright fringe is **1.25 mm**.

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