A red laser beam \((\lambda=650 \mathrm{~nm})\) is sent through a double slit to a screen that is \(400 \mathrm{~mm}\) wide and \(1.00 \mathrm{~m}\) away from the slits.

(a) If the separation distance between the slits is \(4000 \mathrm{~nm}\), how many bright fringes appear on the screen?

(b) Verify your answer to part \(a\) by calculating the distance between adjacent bright fringes.