Answer
The required wavelength is $~~648~nm$
Work Step by Step
We can write an expression for the angular separation:
$\Delta \theta = \frac{\lambda}{d}$
We can see that the angular separation will increase by 10% if we increase the wavelength by 10%
We can find the required wavelength:
$(1.10)(589~nm) = 648~nm$
The required wavelength is $~~648~nm$
