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

the old price per ounce is c/4.

the new price per ounce is c/3.6.

the ratio of the old price to the new one is

(c/4)/(c/3.6) = (c/c)×(3.6/4) = 0.9 . . = 9/10 . . "nine tenths" in either form