You shine light with a wavelength of 400 nm at two small slits (I and II) and observe an interference pattern on a screen. What is the difference in path lengths between the light that travels from slit I to the first dark fringe of the pattern and the light that travels from slit II to the same dark fringe?

2 x 10⁻⁷ m

Explanation:

Since the light from two slits interfere to form dark fringe on the screen,

the path difference must be odd multiple of λ / 2.

Since it is the first dark fringe the factor of odd multiple must be one.

So path difference must be

(2n + 1) x λ / 2.

for first dark fringe

n = 0

path difference = λ / 2

400 x 10⁻⁹ / 2 m

= 2 x 10⁻⁷ m