Question

A Michelson interferometer illuminated with a source of central wavelength ${\lambda }_0$, and spectral width $\Delta l$ is adjusted for equal path difference for the beams returning from the two mirrors. When one of the mirrors is moved by a distance of $0.1\text{mm}$ from this position, 300 fringes move past the field of view. When the mirror is moved further, the fringes completely disappear when the mirror is approximately $4\text{cm}$ from the initial position.

The spectral width of the source $\Delta \lambda$ is approximately

• A. $0.1000\text{nm}$
• B. $0.0056\text{nm}$
• C. $0.0500\text{nm}$
• D. $0.0100\text{nm}$

Answer 1

The correct option is B $0.0056\text{nm}$

The spectral width of the source $\left(\Delta \lambda \right)$ is approximately
$\Delta \lambda =\frac{({\lambda }_{\text{av}}{)}^2}{2x}=\frac{(667\times {10}^{-a}{)}^2}{2\times 4\times {10}^{-2}}=0.0056\text{nm}$