Question

Microwaves of wavelength 4.60 cm enter a long, narrow window in a building that is otherwise essentially opaque to the incoming waves. If the window is 34.5 cm wide, what is the distance from the central maximum to the first-order minimum along a wall 6.35 m from the window?

Answer 1

Answer:

The distance from the central maximum is 0.854 m.

Explanation:

Given that,

Wave length = 4.60 cm

Width d= 34.5 cm

Distance L= 6.35 m

We need to calculate the angle

Using relation width and wavelength

$d\sin\theta=n\lambda$

$\sin\theta=\dfrac{n\lambda}{d}$

$\theta=\sin^{-1}\dfrac{n\lambda}{d}$

$\theta=sin^{-1}\dfrac{4.60}{34.5}$

$\theta=7.66^{\circ}$

We need to calculate the distance from the central maximum

$y=L\tan\theta$

$y=6.35\times\tan7.66$

$y=0.854\ m$

Hence, The distance from the central maximum is 0.854 m.