Question

Calculate the illuminance at sea level from the sun at zenith, using the following information: The luminance of the sun at zenith at sea level is: Ls=1600 x 10 cd/m² (149x10 cd/ft?); The diameter of the sun's photosphere is 8.64 x 10 miles (45.62 x 108 ft); The distance from the sun to the earth is 92.9 x 10 miles (49.05 x 100 ft). Show all formulae and calculations.

Answer 1

346.01 × 10² Lux

Step-by-step explanation:

Given:

luminance of the sun at zenith at sea level, Ls = 1600 × 10 cd/m²

The diameter of the sun's photosphere = 8.64 × 10 miles = 45.62 × 10⁸ ft

or

Radius, r =
`\frac{45.62*10^8\ ft}{\textup{2}}`

or

r = 22.81 × 10⁸ ft

The distance from the sun to the earth = 92.9 × 10 miles = 49.05 x 10¹⁰ ft

Now,

Lumen = Luminance × 4πr²

or

Lumen = 1600 × 10 cd/m² × 4πr² .....................(1)

also,

Illumination =
`\frac{\textup{Lumen}}{\textup{4}\pi\textup{Distance}^2}`

on substituting lumen from 1

Illumination =
`\frac{1600*10*4\pi r^2}{\textup{4}\pi\textup{Distance}^2}`

or

Illumination =
`\frac{1600*10^6*4\pi*(22.81*10^8\ ft)^2}{\textup{4}\pi\textup{49.05*10^10 ft}^2}`

or

Illumination = 346.01 × 10² Lux