Question

A Michelson inteferometer illuminated with a source of central wavelength ${\lambda }_0$ & spectral width $\Delta \lambda$ is adjusted for equal path difference for the beams returning from the two mirrors. When one of the mirrors is moved by a distnace of $0.1mm$ from this position 200 fringes move past the field of view. When the mirror is moved further, the fringes completely disappear when the mirror is approximately $5cm$ from the initial position. The spectral width of the source $\Delta \lambda$ (in pm) is

• A. 10

Answer 1

The correct option is A 10
we know
$n\lambda =2\Delta x$
$\lambda =\frac{2\Delta x}{n}=\frac{2\times 0.1\times {10}^{-3}}{200}=1\mu m$
Spectral width $\Delta \lambda =\frac{({\lambda }_{avg}{)}^2}{2x}$
$=\frac{({10}^{-6}{)}^2}{2\times 5\times {10}^{-2}}$
$=10pm$