Find the angular fringe width in a Young's double slits experiment with blue-green light of wavelength `6000 A.` The separation between the slits is `3.0xx10^(-3)m.`

Explanation

To find the angular fringe width in a Young's double slit experiment, we can follow these steps:

### Step 1: Understand the formula for angular fringe width
In the Young's double slit experiment, the angular fringe width (θ) is given by the formula:
\[ \theta = \frac{\lambda}{d} \]
where:
- \( \lambda \) is the wavelength of the light,
- \( d \) is the separation between the slits.

### Step 2: Convert the wavelength from angstroms to meters
The given wavelength is \( 6000 \) angstroms. We need to convert this to meters:
\[ \lambda = 6000 \, \text{A} = 6000 \times 10^{-10} \, \text{m} = 6.0 \times 10^{-7} \, \text{m} \]

### Step 3: Identify the separation between the slits
The separation between the slits is given as:
\[ d = 3.0 \times 10^{-3} \, \text{m} \]

### Step 4: Substitute the values into the formula
Now we can substitute the values of \( \lambda \) and \( d \) into the formula for angular fringe width:
\[ \theta = \frac{6.0 \times 10^{-7}}{3.0 \times 10^{-3}} \]

### Step 5: Calculate the angular fringe width
Perform the calculation:
\[ \theta = \frac{6.0 \times 10^{-7}}{3.0 \times 10^{-3}} = 2.0 \times 10^{-4} \, \text{radians} \]

### Step 6: Convert the angular fringe width to degrees (if necessary)
To convert from radians to degrees, we can use the conversion factor \( \frac{180}{\pi} \):
\[ \theta \, (\text{in degrees}) = 2.0 \times 10^{-4} \times \frac{180}{\pi} \approx 0.0115 \, \text{degrees} \]

### Final Answer
The angular fringe width is approximately \( 2.0 \times 10^{-4} \, \text{radians} \) or \( 0.0115 \, \text{degrees} \).

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