A helium-neon laser illuminates two narrow slits separated by a distance \(d\), producing an interference pattern on a screen located a distance \(L\) from the slits. The distance between adjacent bright fringes near the center of the interference pattern is \(\Delta y\). If the setup is modified so that the slit separation is reduced to \(\dfrac{1}{2}d\) and the distance from the slits to the screen is increased to \(2L\), what is the new separation between adjacent bright fringes?