After a laser beam passes through two thin parallel slits, the first completely dark fringes occur at 19.0 with the original direction of the beam, as viewed on a screen far from the slits. (a) What is the ratio of the distance between the slits to the wavelength of the light illuminating the slits

Explanation:

Given :

The first dark fringe is for m = 0

Now we know for a double slit experiments , the position of the dark fringes is give by :

The ratio of distance between the two slits, d to the light's wavelength that illuminates the slits, λ :

    (since, m = 0)

Therefore, the ratio is  or 1 : 1.54

50 inches should be the resultant vector