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Microwaves of wavelength 9.33 cm are incident on a narrow window that is 34.55 cm wide. If the far wall is 5.73 m away from the window, what is the distance from the central maximum to the first order minimum?

Sagot :

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.