At what height above the center of the table should a lamp with a total luminous flux of 1300

At what height above the center of the table should a lamp with a total luminous flux of 1300 lm be hung so that the illumination of the center of the table is 26 lm?

To find out the height of the suspension of the lamp taken above the center of the table (φ (angle of incidence of the considered luminous flux) = 0º), we use the formula: I = E * r ^ 2 / cosφ = E * r ^ 2, from where we express: r = √ (I / E) = √ ((Ф / ω) / E) = √ (Ф / (ω * E)).

Data: Ф – the received luminous flux (Ф = 1300 lm); ω – solid angle (ω = 4Π); E – required illumination (E = 26 lux).

Let’s perform the calculation: r = √ (Ф / (ω * E)) = √ (1300 / (4 * Π * 26)) ≈ 1.995 m.

Answer: The height of the suspension of the taken lamp above the center of the table should be 1.995 m.