Two gratings A and B have slits separations dA and dB, respectively. They are us

Question

Two gratings A and B have slits separations dA and dB, respectively. They are used with
the same light and the same observation screen. When grating A is replaced with grating B, it is
observed that the first-order maximum of A is exactly replaced by the second-order maximum
of B.
a) Determine the ratio dB/dA of the spacings between the slits of the gratings.
b) Find the next two principal maxima of grating A and the principal maxima of B that
exactly replace them when the gratings are switched. Identify these maxima by their order
numbers.

my equations:
dasin(?) = m1?
dbsin(?) = m2?

I just divided the two equations and got db/da =
m2/m1 = 2.

While this answers part a I still need help with part b?

Explanation / Answer

The grating equation is nL = d.sin(w) where L is wavelength and w is the diffraction angle. sin(w[A]) = L/d[A] sin(w[B]) = 2L/d[B] sin(w[A]) = sin(w[B]) L/d[A] = 2L/d[B] d[B]/d[A] = 2

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