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 will follow these steps:

### Step-by-Step Solution:

1. **Identify the given values:**
- Distance between the slits (d) = 1.2 mm = 1.2 × 10^-3 m
- Wavelength of light (λ) = 6000 Å = 6000 × 10^-10 m = 6 × 10^-7 m
- Distance from slits to screen (D) = 1 m
- Width of the region on the screen (y₀) = 1 cm = 0.01 m

2. **Calculate the fringe width (β):**
The formula for fringe width (β) in Young's double-slit experiment is given by:
\[ β = \frac{λD}{d} \]
Substituting the values:
\[ β = \frac{(6 \times 10^{-7} \text{ m})(1 \text{ m})}{1.2 \times 10^{-3} \text{ m}} \]
\[ β = \frac{6 \times 10^{-7}}{1.2 \times 10^{-3}} = 5 \times 10^{-4} \text{ m} = 0.5 \text{ mm} \]

3. **Determine the number of fringes (n) over the width (y₀):**
The number of fringes (n) that fit into the width (y₀) can be calculated using:
\[ n = \frac{y₀}{β} \]
Substituting the values:
\[ n = \frac{0.01 \text{ m}}{5 \times 10^{-4} \text{ m}} = \frac{0.01}{0.0005} = 20 \]

4. **Conclusion:**
Therefore, the number of bright fringes formed over a 1 cm width on the screen is **20**.