In Yonung's double-slit experiment, two slits which are separated by 1.2 mm are illuminated with a monochromatic light of wavelength `6000 Å` The interference pattern is observed on a screen placed at a distance of 1 m from the slits. Find the number of bright fringes formed over 1 cm width on the screen.

Options

A. 25
B. 12
C. 15
D. 20

Answer

To solve the problem of finding the number of bright fringes formed over a 1 cm width on the screen in Young's double-slit experiment, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Given Values:**
- Distance between the slits, \( d = 1.2 \, \text{mm} = 1.2 \times 10^{-3} \, \text{m} \)
- Wavelength of light, \( \lambda = 6000 \, \text{Å} = 6000 \times 10^{-10} \, \text{m} = 6 \times 10^{-7} \, \text{m} \)
- Distance from the slits to the screen, \( D = 1 \, \text{m} \)
- Width over which bright fringes are counted, \( \Delta x = 1 \, \text{cm} = 1 \times 10^{-2} \, \text{m} \)

2. **Use the Formula for Bright Fringe Position:**
The position of the nth bright fringe is given by:
\[ x_n = \frac{n \lambda D}{d} \]
We need to find the maximum value of \( n \) such that \( x_n \leq \Delta x \).

3. **Rearranging the Formula:**
To find \( n \):
\[ n = \frac{x_n d}{\lambda D} \]
Substitute \( x_n = \Delta x \):
\[ n = \frac{\Delta x \cdot d}{\lambda D} \]

4. **Substituting the Values:**
\[ n = \frac{(1 \times 10^{-2}) \cdot (1.2 \times 10^{-3})}{(6 \times 10^{-7}) \cdot (1)} \]

5. **Calculating the Value:**
\[ n = \frac{1.2 \times 10^{-5}}{6 \times 10^{-7}} = 20 \]

6. **Conclusion:**
The number of bright fringes formed over a 1 cm width on the screen is \( n = 20 \).