A double slit is illuminated by the light of wavelength 12000A .The slits are 0.1 cm apart and the screen is placed one metre away.calculate the angular posiyion of 10 maximum in radians ?

Answer

To solve the problem of finding the angular position of the 10th maximum in a double-slit experiment, we will follow these steps:

### Step-by-Step Solution:

1. **Identify the Given Data:**
- Wavelength (\( \lambda \)) = 12000 Å (angstroms)
- Distance between slits (\( d \)) = 0.1 cm
- Distance to the screen (\( D \)) = 1 m
- Order of maximum (\( n \)) = 10

2. **Convert Units:**
- Convert the wavelength from angstroms to meters:
\[ \lambda = 12000 \, \text{Å} = 12000 \times 10^{-10} \, \text{m} = 12 \times 10^{-7} \, \text{m} \]
- Convert the distance between slits from centimeters to meters:
\[ d = 0.1 \, \text{cm} = 0.1 \times 10^{-2} \, \text{m} = 1 \times 10^{-3} \, \text{m} \]

3. **Use the Formula for Angular Position:**
- The formula for the angular position of the \( n \)-th maximum in a double-slit experiment is:
\[ d \sin \theta = n \lambda \]
- For small angles, \( \sin \theta \approx \theta \) (in radians), so we can rewrite the equation as:
\[ \theta = \frac{n \lambda}{d} \]

4. **Substitute the Values:**
- Substitute \( n = 10 \), \( \lambda = 12 \times 10^{-7} \, \text{m} \), and \( d = 1 \times 10^{-3} \, \text{m} \) into the equation:
\[ \theta = \frac{10 \times (12 \times 10^{-7})}{1 \times 10^{-3}} \]

5. **Calculate \( \theta \):**
- Perform the calculation:
\[ \theta = \frac{120 \times 10^{-7}}{10^{-3}} = 120 \times 10^{-4} = 12 \times 10^{-3} \, \text{radians} \]

6. **Final Result:**
- The angular position of the 10th maximum is:
\[ \theta = 0.012 \, \text{radians} \]