Find the two maxima for a double grate diffraction

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SUMMARY

The discussion focuses on determining the ratio of slit separations (dB/dA) for two diffraction gratings, A and B, based on their maxima. The first-order maximum of grating A is replaced by the second-order maximum of grating B, leading to the conclusion that the ratio dB/dA equals 2. Additionally, the next two principal maxima for grating A and their corresponding maxima for grating B are to be identified by their order numbers, following the established equations dasin(θ) = m1λ and dbsin(θ) = m2λ.

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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


dasin(θ) = m1λ
dbsin(θ) = m2λ

The Attempt at a Solution


I just divided the two equations and got db/da =
m2/m1 = 2.
 
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Can someone please help me I have done part a I am just struggling with b
 

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