Find the angular separation between the consecutive bright fringes in a Young's double slit experiment with blue-green light of wavelength 500 nm. The separation between the slits is `2.0 x 10^ -3` m.

Explanation

To find the angular separation between consecutive bright fringes in a Young's double slit experiment, we can follow these steps:

### Step 1: Understand the relationship between angular separation and fringe width
In a Young's double slit experiment, the angular separation (θ) between consecutive bright fringes can be expressed as:
\[ \theta = \frac{\lambda}{d} \]
where:
- \( \lambda \) is the wavelength of the light used,
- \( d \) is the distance between the slits.

### Step 2: Convert the wavelength from nanometers to meters
The given wavelength is 500 nm. We need to convert this to meters:
\[ \lambda = 500 \, \text{nm} = 500 \times 10^{-9} \, \text{m} \]

### Step 3: Identify the distance between the slits
The distance between the slits is given as:
\[ d = 2.0 \times 10^{-3} \, \text{m} \]

### Step 4: Substitute the values into the angular separation formula
Now we can substitute the values of \( \lambda \) and \( d \) into the formula for angular separation:
\[ \theta = \frac{500 \times 10^{-9}}{2.0 \times 10^{-3}} \]

### Step 5: Calculate the angular separation
Perform the calculation:
\[ \theta = \frac{500 \times 10^{-9}}{2.0 \times 10^{-3}} = \frac{500}{2.0} \times 10^{-9 + 3} = 250 \times 10^{-6} \, \text{radians} \]
\[ \theta = 2.5 \times 10^{-4} \, \text{radians} \]

### Final Answer
The angular separation between consecutive bright fringes is:
\[ \theta = 2.5 \times 10^{-4} \, \text{radians} \]

---