Find the two maxima for a double grate diffraction

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θ

Homework Statement

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.
2

Homework Equations

d_asin(θ) = m₁λ
d_bsin(θ) = m₂λ

The Attempt at a Solution

I just divided the two equations and got d_b/d_a =
m₂/m₁ = 2.

 

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Can someone please help me I have done part a I am just struggling with b