In YDSE wavelength of light used is 500 nm and slit width is `0.05 mm`. then the angular fringe width will be.

Options

A. `1.8^@`
B. `3.2^@`
C. `0.57^@`
D. `0.48^@`

Answer

To find the angular fringe width in the Young's Double Slit Experiment (YDSE), we can follow these steps:

### Step-by-Step Solution:

1. **Identify Given Values:**
- Wavelength of light, \( \lambda = 500 \, \text{nm} = 500 \times 10^{-9} \, \text{m} \)
- Slit width (distance between the two slits), \( d = 0.05 \, \text{mm} = 0.05 \times 10^{-3} \, \text{m} \)

2. **Understand the Formula for Angular Fringe Width:**
- The angular fringe width \( \theta \) can be derived from the formula for fringe width \( \beta \):
\[ \beta = \frac{\lambda D}{d} \]
where \( D \) is the distance from the slits to the screen. However, for angular fringe width, we can simplify it to:
\[ \theta = \frac{\lambda}{d} \]

3. **Substitute the Values into the Formula:**
- Substitute \( \lambda \) and \( d \) into the formula for angular fringe width:
\[ \theta = \frac{500 \times 10^{-9} \, \text{m}}{0.05 \times 10^{-3} \, \text{m}} \]

4. **Calculate the Angular Fringe Width:**
- Calculate the value:
\[ \theta = \frac{500 \times 10^{-9}}{0.05 \times 10^{-3}} = \frac{500 \times 10^{-9}}{5 \times 10^{-5}} = \frac{500}{5} \times 10^{-9 + 5} = 100 \times 10^{-4} = 10^{-2} \, \text{radians} \]

5. **Convert Radians to Degrees:**
- To convert radians to degrees, use the conversion factor \( \frac{180}{\pi} \):
\[ \theta \text{ (in degrees)} = 10^{-2} \times \frac{180}{\pi} \approx 0.01 \times 57.3 \approx 0.573 \, \text{degrees} \]

6. **Final Answer:**
- The angular fringe width \( \theta \) is approximately \( 0.57 \, \text{degrees} \).