A. To solve for part A, we use the formula of Young’s double slit equation:
x = λ L m / d
Where,
x = distance between adjacent dark lines or fringes = 12.5 cm = 0.125 m
λ = wavelength of light = 600 × 10^-9 m
L = distance from the two sources of light to the screen = 1.2 m
m = number of fringes = 10 (tenth) – 1 (first) = 9
d = separation of slits = unknown
Rearranging the equation in terms of d and plugging in the values:
d = λ L m / x
d = (600 × 10^-9 m) (1.2 m) (9) / 0.125 m
d = 5.184 × 10^-5 m
d = 51.84 μm
B. The formula for path difference is:
path difference = (2 m + 1) (λ / 2)
path difference = (2 * 9 + 1) (600 × 10^-9 m / 2)
path difference = 5.7 × 10-6 mpath difference = 5.7 μm