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

Answer:

$\frac{d}{\lambda} = 1.54$

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 :

$d \sin \theta=\left(m+\frac{1}{2}\right) \lambda$

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

$d \sin \theta=\left(\frac{1}{2}\right) \lambda$     (since, m = 0)

$d \sin \theta=\frac{\lambda}{2}$

$\frac{d}{\lambda} = \frac{1}{2 \sin \theta}$

$\frac{d}{\lambda} = \frac{1}{2 \sin 19^\circ}$

$\frac{d}{\lambda} = 1.54$

Therefore, the ratio is $\frac{1}{1.54}$  or 1 : 1.54