Question

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?

Answer 1

Given:

The wavelength of the microwave is

`\begin{gathered} \lambda=9.33\text{ cm} \\ =9.33*10^(-2)\text{ m} \end{gathered}`

The width of the window is,

`\begin{gathered} a=34.55\text{ cm} \\ =34.55*10^(-2)\text{ m} \end{gathered}`

The distance between the wall from the window is,

`d=5.73\text{ m}`

To find:

the distance from the central maximum to the first order minimum

Step-by-step explanation:

For destructive interference,

`sin\theta=n(\lambda)/(a)`

Here, for the first order, minima n=1.

`\begin{gathered} sin\theta=(9.33*10^(-2))/(34.55*10^(-2)) \\ \theta=15.67\degree \end{gathered}`

The distance from the central maximum to the first order minimum is

`\begin{gathered} y=dtan\theta \\ =5.73* tan15.67\degree \\ =1.61\text{ m} \end{gathered}`

Hence, the required distance is 1.61 m.