Answer
The distance between the two first-order fringes is $~~12.75~cm$
Work Step by Step
We can find the distance between the slits:
$d = \frac{1~mm}{500} = 0.002~mm$
We can find the distance of the first-order red fringe from the center:
$y_r = \frac{\lambda_r~L}{d}$
$y_r = \frac{(656\times 10^{-9}~m)(1.50~m)}{2.0\times 10^{-6}~m}$
$y_r = 0.492~m$
We can find the distance of the first-order blue fringe from the center:
$y_b = \frac{\lambda_b~L}{d}$
$y_b = \frac{(486\times 10^{-9}~m)(1.50~m)}{2.0\times 10^{-6}~m}$
$y_b = 0.3645~m$
We can find the distance between the two first-order fringes:
$\Delta y = y_r-y_b$
$\Delta y = (0.492~m)-(0.3645~m)$
$\Delta y = 0.1275~m$
$\Delta y = 12.75~cm$
The distance between the two first-order fringes is $~~12.75~cm$
