Question

What requirements must be met for the central maximum of the envelope of the double-slit interference pattern to contain exactly 9 fringes?

Answer 1

The required condition will be met if the fifth minimum of the interference factor coincides with the first minimum of the diffraction factor. The fifth minimum of the interference factor occurs when  β = 9/2 π. The first minimum in the diffraction term occurs for α = π. Thus, we get 

β/α = d/α = 9/2  as the required condition.