Question

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

Answer 1

`$(d)/(\lambda) = 1.54$`

Step-by-step explanation:

Given :

The first dark fringe is for m = 0

`$\theta_1 = \pm 19^\circ$`

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

`$d \sin \theta=\left(m+(1)/(2)\right) \lambda$`

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

`$d \sin \theta=\left((1)/(2)\right) \lambda$` (since, m = 0)

`$d \sin \theta=(\lambda)/(2)$`

`$(d)/(\lambda) = (1)/(2 \sin \theta)$`

`$(d)/(\lambda) = (1)/(2 \sin 19^\circ)$`

`$(d)/(\lambda) = 1.54$`

Therefore, the ratio is
`$(1)/(1.54)$` or 1 : 1.54