Question

A laser beam of wavelength 439.4 nm is inci- dent on two slits 0.306 mm apart.

Answer 1

Constructive interference happens when this condition is satisfied:
$dsin(\theta)=m\lambda; m=1,2,3,4,5,...$
This means that the difference in the distance traveled by the waves, from the slit to the screen, is equal to the whole multiple of the wavelength.
If we say that the distance between two interference fringes is much smaller than the distance from the slit to the screen, we can use the following approximation:
$sin(\theta)=\frac{y}{L}$
Finally for the bright spots we have:
$y=\frac{m\lambda L}{d}$
The spacing between bright spots is:
$y=\frac{\lambda L}{d}=\frac{6.08\cdot 439.4\cdot 10^{-9}}{0.306 \cdot 10^{-3}}=8.73mm$