Question

Light shines through a single slit whose width is 5.7 x 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 4.0 mm.

What is the wavelength of the light?

Answer 1

`\lambda = 570\ nm`

Step-by-step explanation:

Given,

Width of slit, W = 5.7 x 10⁻⁴ m

Distance between central bright fringe, L = 4 m

distance between central bright fringe and first dark fringe, y = 4 mm

Diffraction angle

`tan \theta = (y)/(L)`

`tan \theta = (4)/(4* 10^3)`

`\theta = 0.0572`

Now.

`W sin \theta = m \lambda`

m = 1

`5.7 * 10^(-4) * sin (0.0572) = 1 * \lambda`

`\lambda = 569.99 * 10^(-9)\ m`

`\lambda = 570\ nm`