Question

n a double-slit experiment, the slit separation is 6.03x10-5 meters. The slits are illuminated with a laser beam of wavelength 5.37x10-7 meters. A screen is located 2.14 m from the slits. Calculate the distance on the screen from the first dark fringe on one side of the central maximum to the second dark fringe on the other side.

Answer 1

D = 3.81 x 10⁻² m = 3.81 cm

Step-by-step explanation:

We can use the formula of fringe spacing from Young's Double Slit experiment to answer this question:

`\Delta x = (\lambda L)/(d)\\`

where,

Δx = distance between two consecutive dark fringes

λ = wavelength of light beam = 5.37 x 10⁻⁷ m

L = Distance between screen and slits = 2.14 m

d = slit separation = 6.03 x 10⁻⁵ m

But, we need the distance between first dark fringe on 1 side to 2nd dark fringe on other side. It means we need twice the distance between two dark fringes:

`D = 2\Delta x = 2(\lambda L)/(d)\\`

where,

D = distance between first dark fringe on one side and 2nd dark fringe on other side of central maximum = ?

Therefore,

`D = ((2)(5.37\ x\ 10^(-7) m)(2.14\ m))/(6.03\ x\ 10^(-5)\ m )`

D = 3.81 x 10⁻² m = 3.81 cm