In a Young's double slit experiment, light of 500 nm is used to produce an interference pattern. When the distance between the slits is 0.05 mm, the angular width (in degree) of the fringes formed on the distance screen is close to:

Options

A. `0.17 ^@`
B. `0.07^@`
C. `0.57 ^@`
D. `1.7^@`

Explanation

To solve the problem of finding the angular width of the fringes in a Young's double slit experiment, we can follow these steps:

### Step-by-Step Solution:

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

2. **Understand the Concept of Angular Width:**
- The angular width \( \beta \) of the fringes is defined as the angle subtended by the distance between two adjacent bright fringes at the screen.

3. **Use the Formula for Angular Width:**
- The angular width \( \beta \) can be calculated using the formula:
\[ \beta = \frac{\lambda}{d} \]
- This formula gives the angular separation between the bright fringes.

4. **Substitute the Values:**
- Plugging in the values:
\[ \beta = \frac{500 \times 10^{-9} \, \text{m}}{0.05 \times 10^{-3} \, \text{m}} \]

5. **Calculate the Angular Width:**
- Performing the calculation:
\[ \beta = \frac{500 \times 10^{-9}}{0.05 \times 10^{-3}} = \frac{500 \times 10^{-9}}{5 \times 10^{-5}} = \frac{500}{5} \times 10^{-4} = 100 \times 10^{-4} = 1 \times 10^{-2} \, \text{radians} \]

6. **Convert Radians to Degrees:**
- To convert radians to degrees, use the conversion factor \( \frac{180}{\pi} \):
\[ \beta \text{ (in degrees)} = 1 \times 10^{-2} \times \frac{180}{\pi} \approx 0.57 \, \text{degrees} \]

7. **Final Result:**
- The angular width of the fringes formed on the distant screen is approximately \( 0.57 \, \text{degrees} \).