Question

Light shines through a single slit whose width is 5.6 × 10-4 m. A diffraction pattern is formed on a flat screen located 4.0 m away. The distance between the middle of the central bright fringe and the first dark fringe is 3.3 mm. What is the wavelength of the light?

Answer 1

462 nm

Step-by-step explanation:

Given: width of the slit, d = 5.6 × 10⁻⁴ m

Distance of the screen, D = 4.0 m

Fringe width, β = 3.3 mm = 3.3 × 10⁻³ m

First dark fringe means n =1

Wavelength of the light, λ = ?

`\beta = (\lambda D)/(d)\\ \Rightarrow \lambda = (d \beta)/(D) =(5.6* 10^(-4) * 3.3 * 10^(-3))/(4.0) = 4.62 * 10^(-7)m = 462 nm`