Question

An LED emitting at $1\mu \text{m}$ with a spectral width of $50\text{nm}$ is used in a Michelson interferometer. To obtain a sustained interference, the maximum optical path difference between the two arms of the interferometer is

• A. $200\mu \text{m}$
• B. $1\mu \text{m}$
• C. $20\mu \text{m}$
• D. $50\text{nm}$

Answer 1

The correct option is C $20\mu \text{m}$

$\because \Delta \lambda =\frac{({\lambda }_{\text{avg}}{)}^2}{2re}$
$x=\frac{({\lambda }_{\text{avg}}{)}^2}{2\Delta \lambda }=\frac{(1\times {10}^{-6}{)}^2}{2\times 50\times {10}^{-9}}=10\mu \text{m}$

Maximum distance $=2\times 10\mu \text{m}=20\mu \text{m}$