When the movable arm of a Michelson interferometer in vacuum (n = 1) is moved by 325 μm, the number of fringe crossings is 1000. The wavelength of the laser used in nanometers is ____.

Concept:-

Applications of Michelson interferometer

(i) Find the wavelength of the monochromatic light

nλ = 2 (Δx)

Δx = x₂ - x₁

where, n = no. of fringes

λ = wavelength of monochromatic light

Δx = micrometer screw movement

x₂ = final position, x₁ = initial position

(ii) Calculation of thickness and the refractive index (μ) of any transparent sheet.



nλ = 2t [μ - 1]

t = thickness of sheet

μ = Refractive index of steel material.

(iii) Resolution of spectral lines.

$\Delta \lambda ={\lambda }_1-{\lambda }_2=\frac{{\lambda }_1{\lambda }_2}{2x}=\frac{({\lambda }_{av}{)}^2}{2x}$

(iv) calculation of thickness of sheet width by young's method



nλ = t (μ - 1)

thickness 't' = $\frac{n\lambda }{\mu -1}$

Calculation:-

Given, μ = 1

Δx = 325 μm

n = 1000

λ = ?

By the first application of michelson interferometer

nλ = 2 + (μ - 1) = 2Δx

nλ = 2Δx

1000 × λ = 2 × 325 × 10⁻⁶

λ = 650 × 10⁻⁹

λ = 650 nm.