Two gratings A and B have slit 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.) I already found that the ratio of db/da is 2
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

mA=2,mB=4

mA=2,mB=4 and

mA=3,mB=6

Explanation:

First of all we need to write the equation of the networks

sin θ = mA λ / dA

sin θ = mB λ / dB

Equating we have

mA λ/ dA = mB λ / dB

We are given the ratio as

dB / dA = 2

So

mA 2 = mB

Finally overlapping orders

We have

mA=2,mB=4

mA=2,mB=4

and mA=3,mB=6

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