In double slit experiment , the distance between two slits is `0.6mm` and these are illuminated with light of wavelength `4800 Å`. The angular width of dark fringe on the screen at a distance 120 cm from slits will be

Options

A. `8 xx 10^(-4)` rad
B. `6 xx 10^(-4)` rad
C. `4 xx 10^(-4)` rad
D. `16 xx 10^(-4)` rad

Answer

To solve the problem of finding the angular width of the dark fringe in a double slit experiment, we can follow these steps:

### Step-by-Step Solution:

1. **Identify Given Values:**
- Distance between the slits, \( d = 0.6 \, \text{mm} = 0.6 \times 10^{-3} \, \text{m} \)
- Wavelength of light, \( \lambda = 4800 \, \text{Å} = 4800 \times 10^{-10} \, \text{m} \)
- Distance from the slits to the screen, \( L = 120 \, \text{cm} = 1.2 \, \text{m} \)

2. **Understanding Angular Width:**
- The angular width of the dark fringe can be calculated using the formula:
\[ \theta = \frac{\lambda}{d} \]
- This formula gives the angular width between two adjacent dark fringes.

3. **Substituting the Values:**
- Convert the values into compatible units:
\[ \lambda = 4800 \times 10^{-10} \, \text{m} = 4.8 \times 10^{-7} \, \text{m} \]
\[ d = 0.6 \times 10^{-3} \, \text{m} \]
- Now substitute these values into the formula:
\[ \theta = \frac{4.8 \times 10^{-7}}{0.6 \times 10^{-3}} \]

4. **Calculating the Angular Width:**
- Perform the division:
\[ \theta = \frac{4.8}{0.6} \times 10^{-7 + 3} = 8 \times 10^{-4} \, \text{radians} \]

5. **Final Result:**
- The angular width of the dark fringe is:
\[ \theta = 8 \times 10^{-4} \, \text{radians} \]

### Final Answer:
The angular width of the dark fringe on the screen is \( 8 \times 10^{-4} \, \text{radians} \).