Question

In each of the following situations, a wave passes through an opening in an absorbing wall. Rank the situations in order from the one in which the wave is best described by the ray approximation to the one in which the wave coming through the opening spreads out most nearly equally in all directions in the hemisphere beyond the wall.

(a) The sound of a low whistle at 1 kHz passes through a doorway 1 m wide.
(b) Red light passes through the pupil of your eye.
(c) Blue light passes through the pupil of your eye.
(d) The wave broadcast by an AM radio station passes through a doorway 1 m wide. (e) An x-ray passes through the space between bones in your elbow joint.

Answer 1

A) geometric optics, B) geometric optics , c) geometric optics ,

e) geometric optics, f) geometric optics

Step-by-step explanation:

For this exercise we must use the condition for interference and diffraction so that these phenomena are relevant the wavelength must be comparable to the gap spacing

λ> = a

Lam when the spacing is much greater than the wavelength, the description of geometric optics is more and more exact

let's analyze each situation

a) let's find the wavelength

v = λ f

λ= v / f

λ= 343/1000

λ = 0.343 m

0.343 << 1m

therefore the description of the geometric optics of

b) red light passes through the pupil of the eye

red light has a wavelength of 700 num or more, the lojo pupil has a maximum of 8 me

λ = 700 10⁻⁹ m = 7 10⁻⁷ m

a = 8 mm 10⁻³

longitudinal is much less therefore the geometric optics is correct

c) luz azul lam = 450 nm = 450 10⁻⁹ m = 4.5 10⁻⁷ m

again the wavelength is much less than the diameter of the pupil, for which the description with the optics is generally sufficient

d) a radio A transmits up to a maximum of f = 1400 Khz = 1,400 10⁶ Hz

let's find the wavelength

c = λf

λ = c / f

λ= 3 108 / 1,400 106

λ= 2.14 102 m

in this case the wavelength is greater than the width of the gate, so the description of diffraction should be used to explain the phenomenon

e) X-rays have wavelength lam = 10-10 m

the separation of the elbow bones is of the order of a few millimeters, for local the wavelength is much less than the separation, therefore with the relations of geometric optics it is sufficient