# Question #38523

May 24, 2017

$699 n m$

#### Explanation:

As light travels to and from the mirror, for a distance of $\frac{\lambda}{2}$ to the mirror, one full wavelength $\lambda$ shift at the detector will be noted. We know that for $1$ wavelength movement there is constructive interference. Hence, one fringe will move into a position previously occupied by the original fringe.

Fringes moved $= 644$
Mirror moved $= 0.225 m m$
$\text{Number of fringes"xxlambda/2="Distance moved by movable mirror}$
$\implies \lambda = 0.225 \times 2 \times \frac{1}{644} = 6.99 \times {10}^{-} 7 m$

$= 699 n m$