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 central wavelength of the source is

• A. $632.8\text{nm}$
• B. $667\text{nm}$
• C. $540\text{nm}$
• D. $720\text{nm}$

Answer 1

The correct option is B $667\text{nm}$

$n\lambda =2\left(\mu x\right)$
$\lambda =\frac{2\left(\Delta x\right)}{n}=\frac{2\times 0.1\times {10}^{-3}}{300}=0.66666\times {10}^{-6}$
$=666.66\text{nm}=667\text{nm}$