To find the separation between the slits in a double slit experiment, we can use the formula for the position of the bright fringes given by:
\[ y_m = \frac{m \lambda L}{d} \]
where:
- \(y_m\) is the distance from the central maximum to the m-th order maximum (in this case, \(y_1\) for the first order),
- \(m\) is the order of the maximum (1 for the first order),
- \(\lambda\) is the wavelength of the light,
- \(L\) is the distance from the slits to the screen,
- \(d\) is the separation between the slits.
Given:
- \(\lambda = 7.2 \times 10^{-7} , \text{m}\)
- \(L = 1.00 , \text{m}\)
- \(y_1 = 0.0655 , \text{m}\)
We need to find \(d\). Rearranging the formula, we get:
\[ d = \frac{m \lambda L}{y_m} \]
Now, substituting in the values for the first order (where \(m = 1\)):
\[ d = \frac{1 \cdot (7.2 \times 10^{-7}) \cdot (1.00)}{0.0655} \]
Calculating the numerator:
\[ d = \frac{7.2 \times 10^{-7}}{0.0655} \]
Now calculating that value:
\[ d \approx \frac{7.2 \times 10^{-7}}{0.0655} \approx 1.097 \times 10^{-5} , \text{m} \]
Now rounding it to two decimal places:
\[ d \approx 1.09 \times 10^{-5} , \text{m} \]
Thus, the separation between the slits is
\[ \boxed{1.09 \times 10^{-5} , \text{m}} \]