Question

Light from two lasers is incident on an opaque barrier with a single slit of width 4.0 x 10^-4 m. One laser emits light of wavelength 480 nm and the other is 640 nm. A screen to view the light intensity pattern is 2.0 m behind the barrier. The distance from the center of the pattern to the nearest completely dark spot (dark for both colors) is ____ cm. (include 2 digits after the decimal point)

Answer 1

a) y = 2.4 x 10⁻³ m = 0.24 cm

b) y = 3.2 x 10⁻³ m = 0.32 cm

Step-by-step explanation:

The formula of Young's Double Slit experiment will be used here:

`y = (\lambda L)/(d)\\\\`

where,

y = distance between dark spots = ?

λ = wavelength

L = distance of screen = 2 m

d = slit width = 4 x 10⁻⁴ m

a) FOR λ = 480 nm = 4.8 x 10⁻⁷ m:

`y = ((4.8\ x\ 10^(-7)\ m)(2\ m))/(4\ x\ 10^(-4)\ m)`

y = 2.4 x 10⁻³ m = 0.24 cm

a) FOR λ = 640 nm = 6.4 x 10⁻⁷ m:

`y = ((6.4\ x\ 10^(-7)\ m)(2\ m))/(4\ x\ 10^(-4)\ m)`

y = 3.2 x 10⁻³ m = 0.32 cm