Question

The characters of a stadium scoreboard are formed with closely spaced lightbulbs that radiate primarily yellow light. (Use λ=600nm.) How closely must the bulbs be spaced so that an observer 80 m away sees a display of continuous lines rather than the individual bulbs? Assume that the pupil of the observer’s eye has a diameter of 5.0 mm.

Answer 1

The bulbs in the stadium scoreboard must be spaced close enough so that an observer 80 m away sees a display of continuous lines rather than individual bulbs.

Step-by-step explanation:

In order for an observer 80 m away to see a display of continuous lines rather than the individual bulbs on a stadium scoreboard, the bulbs must be spaced close enough that the diffraction of light is minimized.

The maximum angle of diffraction, θ, is given by the equation sin(θ) = λ/d, where λ is the wavelength of light and d is the distance between the bulbs.

To minimize diffraction, we want the maximum angle of diffraction to be smaller than the angle of the observer's pupil, given by sin(θ) = (0.5 * diameter of pupil) / distance to observer. Solving these equations, we can find the minimum distance between the bulbs, d, as:

sin(θ) = λ/d

d = λ/sin(θ)