waves

Question

Monochromatic light is incident on two slits separated by 0.17mm. An interference pattern is observed on a screen 4.0m away. The distance between the 3^rd dark fringe and the central antinode is 4.20 x10^-2 m. The wavelength of the light is ___x10^-7m

Answer 1

The Distance between two slits d is 0.17 mm = 0.17 * 10^-3 m

Distance between screen and slit L is 4.0 m

Third Dark Fringe means m = 2.5

Distance between third Dark Fringe and Central antinode y = 4.2 * 10^-2 m

Young's Equation is λ = ( y * d) / (m * L)

λ = (4.2 * 10^-2 * 0.17 * 10^-3) / (2.5 * 4.0)

λ = 7.14 * 10^-7 m

λ = 714 * 10^-9 m

λ = 714 nm

Therefore the wavelength of light is 714 nm.