ANSWER
[tex]122\text{ cm}[/tex]EXPLANATION
Parameters given:
Wavelength of the microwave, λ = 5.03 cm
Width of the window, a = 30.48 cm
Distance of window from the wall, L = 7.27 m
First, we have to apply the condition for destructive interference using the formula:
[tex]\sin\theta=m\frac{λ}{a}[/tex]where θ = angle of the first fringe from the central axis.
m = order = 1
Solve for θ:
[tex]\begin{gathered} \sinθ=1*\frac{5.03}{30.48}=0.1650 \\ \\ \theta=\sin^{-1}(0.1650) \\ \\ θ=9.50\degree \end{gathered}[/tex]Now, find the distance between the central maximum and the first order minimum by applying the formula for the position of the fringe:
[tex]\begin{gathered} \frac{y}{L}=\tanθ \\ \\ y=L\tanθ \end{gathered}[/tex]Solve for y:
[tex]\begin{gathered} y=7.27*\tan9.5 \\ \\ y=1.22\text{ }m=122\text{ }cm \end{gathered}[/tex]That is the distance from the central maximum to the first order minimum.
