Given:
The wavelength of the microwave is
[tex]\begin{gathered} \lambda=9.33\text{ cm} \\ =9.33\times10^{-2}\text{ m} \end{gathered}[/tex]
The width of the window is,
[tex]\begin{gathered} a=34.55\text{ cm} \\ =34.55\times10^{-2}\text{ m} \end{gathered}[/tex]
The distance between the wall from the window is,
[tex]d=5.73\text{ m}[/tex]
To find:
the distance from the central maximum to the first order minimum
Explanation:
For destructive interference,
[tex]sin\theta=n\frac{\lambda}{a}[/tex]
Here, for the first order, minima n=1.
[tex]\begin{gathered} sin\theta=\frac{9.33\times10^{-2}}{34.55\times10^{-2}} \\ \theta=15.67\degree \end{gathered}[/tex]
The distance from the central maximum to the first order minimum is
[tex]\begin{gathered} y=dtan\theta \\ =5.73\times tan15.67\degree \\ =1.61\text{ m} \end{gathered}[/tex]
Hence, the required distance is 1.61 m.