For Fraunhofer diffraction at a single slit would be represented by:
a sinθ = mλ
It should be noted that the angle needs be halved because we are only concerned with the angle between m=1 and m=0 and they gave you the angle between m=1 to the right of the center and m=1 on the left of the center. We calculate as follows:
a sin(45/2)=(1)(470)
a = 1228 nm
Hope this answers the question. Have a nice day.
