A researcher is calibrating a double-slit interferometer for a high-precision optical sensor. In the initial configuration, a light source of wavelength $\lambda$ passes through two slits separated by a distance $s$, with a detector array placed at a distance $D$ behind the slits. This setup produces an interference pattern with a fringe spacing of $w$.

Due to temperature variations and realignment:

• The wavelength of the source is decreased to $0.90\lambda$.
• Thermal expansion increases the slit separation to 1.20s.
• The distance between the slits and the detector array is adjusted to $1.60D$ to maintain focus.

What is the new fringe spacing $w^{\prime }$ at the detector array in terms of the original spacing $w$?