the wall of a large room is covered with acoustic tile in which small holes are drilled 1.9 mm from center to center. how far can a person be from such a tile and still distinguish the individual holes, assuming ideal conditions? assume the diameter of the pupil of the observer's eye to be 4.00 mm and the wavelength of the room light to be 515.0 nm.

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MonikaNandal MonikaNandal · Answer 1 · 2022-12-18T08:15:30+01:00

To distinguish the individual holes, the minimum distance between the person and the tile is 29.8mm ≈30 mm.

Wavelength can be defined as the distances between 2 successively Crest or the throughs of any wave.

According to Rayleigh's criterion, the angular separation between two point sources is given as follows.

8 = 1.22A d

Here, λ = wave length,

d =circular aperture diameter.

Since the regular separatione is very small, the value of sine is nearby equal to e=㏑

Where D is the center-to-center distance between two point lights and L is the distance from the screen to the light source.

Substitute for e in the above equation 1.22A

8 =d

To obtain the expression for L as

D /L= 1.22A /d

Rearrange the mentioned equation for L as follows:

L = Dd d1.22A

Substitute 0.005m for D, 0.004m for d, and

550 × 10⁻⁹m for λ in the above equation

L = (Dd)/(1.22lambda) to obtain the values of L as follows:

L = ((0.005m)(0.004m))/(1.22(550 × 10 ⁻⁹ m))

L =29.8mm

Thus, the distance between the person from the tile distinguishes the individual holes.

(Rounding off to two significant figures) is 30 m.

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