Question

In a Young’s experiment, two coherent sources are placed 0.90 mm apart and the fringes are observed one metre away. If it produces the second dark fringe at a distance of 1mm from the central fringe, then the wavelength of monochromatic light used will be ______.

Options

• 60 × 10⁻⁴ cm

• 10 × 10⁻⁴ cm

• 10 × 10⁻⁵ cm

• 6 × 10⁻⁵ cm

Answer 1

In a Young’s experiment, two coherent sources are placed 0.90 mm apart and the fringes are observed one metre away. If it produces the second dark fringe at a distance of 1mm from the central fringe, then the wavelength of monochromatic light used will be 6 × 10⁻⁵ cm.

Explanation:

Distance of n^th dark fringe from central fringe

x_n = `((2"n"-1)lambda"D")/(2"d")`

x₂ = `((2xx2-1)lambda"D")/(2"d")=(3lambda"D")/(2"d")`

10^-3 = `(3xxlambdaxx1)/(2xx0.9xx10^-3)`

⇒ λ = 6 × 10⁻⁵ cm