Question

The ceiling of a large symphony hall is covered with acoustic tiles which have small holes that are 4.35 mm center to center. If a person with a pupil of diameter 5.10 mm walks into the hall when it is illuminated by 550 nm wavelength light and they can just distinguish the individual holes, what is the distance between their eye and the ceiling?

Answer 1

Answer:

33.0 m

Explanation:

We are given that

Wavelength,$\lambda=550nm=550\times 10^{-9} m$

$1nm=10^{-9} m$

Diameter of pupil=d=5.1 mm=$5.1\times 10^{-3} m$

$1mm=10^{-3} m$

$y=4.35 mm=4.35\times 10^{-3}m$

By Rayleigh criteria

$sin\theta=1.22\frac{\lambda}{d}$

$\frac{y}{L}=1.22\frac{\lambda}{d}$

$L=\frac{yd}{1.22\lambda}$

Substitute the values

$L=\frac{4.35\times 10^{-3}\times 5.1\times 10^{-3}}{1.22\times 550\times 10^{-9}}$

$L=33.0 m$