In young`s double slit experiment the fringes are formed at a distance of 2m from double slits of sepration 0.12mm.calculate the distance of 12th bright band from the centre of screen ,given wavelength is 12000A.

Answer

To solve the problem of finding the distance of the 12th bright band from the center of the screen in Young's double slit experiment, we can follow these steps:

### Step-by-step Solution:

1. **Identify the Given Data:**
- Wavelength (λ) = 12000 Å (angstroms)
- Distance from slits to screen (D) = 2 m
- Slit separation (d) = 0.12 mm
- Bright band number (n) = 12

2. **Convert Units:**
- Convert the wavelength from angstroms to centimeters:
\[ 1 \text{ Å} = 10^{-10} \text{ m} \quad \Rightarrow \quad 12000 \text{ Å} = 12000 \times 10^{-10} \text{ m} = 12 \times 10^{-6} \text{ m} = 12 \times 10^{-5} \text{ cm} \]
- Convert the distance from slits to screen from meters to centimeters:
\[ D = 2 \text{ m} = 200 \text{ cm} \]
- Convert the slit separation from mm to cm:
\[ d = 0.12 \text{ mm} = 0.012 \text{ cm} \]

3. **Use the Formula for Bright Fringes:**
The position of the nth bright fringe (Xn) is given by the formula:
\[ X_n = \frac{n \lambda D}{d} \]
where:
- \( n \) = order of the bright fringe (in this case, 12)
- \( \lambda \) = wavelength
- \( D \) = distance from the slits to the screen
- \( d \) = slit separation

4. **Substitute the Values:**
\[ X_{12} = \frac{12 \times (12 \times 10^{-5} \text{ cm}) \times (200 \text{ cm})}{0.012 \text{ cm}} \]

5. **Calculate:**
- First, calculate the numerator:
\[ 12 \times (12 \times 10^{-5}) \times 200 = 12 \times 12 \times 200 \times 10^{-5} = 28800 \times 10^{-5} = 2.88 \text{ cm} \]
- Now divide by the slit separation:
\[ X_{12} = \frac{2.88 \text{ cm}}{0.012 \text{ cm}} = 240 \text{ cm} \]

6. **Final Result:**
The distance of the 12th bright band from the center of the screen is:
\[ X_{12} = 24 \text{ cm} \]