Question

Microwaves of wavelength 5.03 cm are incident on a narrow window that is 30.48 cm wide. If the far wall is 7.27 m away from the window, what is the distance from the central maximum to the first order minimum?

Answer 1

`122\text{ cm}`

Step-by-step 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:

`\sin\theta=m(λ)/(a)`

where θ = angle of the first fringe from the central axis.

m = order = 1

Solve for θ:

`\begin{gathered} \sinθ=1*(5.03)/(30.48)=0.1650 \\ \\ \theta=\sin^(-1)(0.1650) \\ \\ θ=9.50\degree \end{gathered}`

Now, find the distance between the central maximum and the first order minimum by applying the formula for the position of the fringe:

`\begin{gathered} (y)/(L)=\tanθ \\ \\ y=L\tanθ \end{gathered}`

Solve for y:

`\begin{gathered} y=7.27*\tan9.5 \\ \\ y=1.22\text{ }m=122\text{ }cm \end{gathered}`

That is the distance from the central maximum to the first order minimum.