To find the separation between the slits in a double-slit experiment, we can use the formula for the position of bright spots (fringes) on the screen:
\[ y_m = \frac{m \lambda L}{d} \]
Where:
- \( y_m \) is the position of the m-th order bright spot from the central maximum,
- \( m \) is the order of the bright spot (for the first order, \( m = 1 \)),
- \( \lambda \) is the wavelength of the light,
- \( L \) is the distance from the slits to the screen,
- \( d \) is the separation between the slits.
From the problem:
- \( y_1 = 0.0655 , \text{m} \) (first order fringe),
- \( \lambda = 3.9 \times 10^{-7} , \text{m} \),
- \( L = 1.00 , \text{m} \),
- \( m = 1 \).
Plugging in the values for the first-order bright spot:
\[ 0.0655 = \frac{1 \cdot (3.9 \times 10^{-7}) \cdot 1.00}{d} \]
Now we can solve for \( d \):
\[ d = \frac{(3.9 \times 10^{-7}) \cdot 1.00}{0.0655} \]
Calculating this:
\[ d = \frac{3.9 \times 10^{-7}}{0.0655} \approx 5.95 \times 10^{-6} , \text{m} \]
Thus, the separation between the slits is approximately \( 5.95 \times 10^{-6} , \text{m} \).
Therefore, the correct answer is:
5.95 x 10-6 m