Question

A lamp of 250 candles power is hanging at 6m from a wall. The illuminance at a point on the wall at a minimum distance from the lamp will be
A. 9.64 lux
B. 4.69 lux
C. 6.94 lux
D. None of these

Answer 1

Illuminance is the total luminous flux incident on a surface, per unit area. It is a measure of how much the incident light illuminates the surface, wavelength-weighted by the luminosity function to correlate with human brightness perception. From the formula of illuminance, we can directly calculate it.

Complete step-by-step solution : The Inverse Square Law of Illuminance:
This law states that the Illuminance (E) at any point on a plane perpendicular to the line joining the point and source is inversely proportional to the square of the distance between the source and plane.
$I = \dfrac{{power}}{{{{(dis\tan ce)}^2}}}$
$I = \dfrac{{250}}{{{6^2}}} = \dfrac{{250}}{{36}}$
$I = 6.94lux$
Hence, option C is correct.

Note:- The inverse square law can only be used in cases where the light source approximates a point source. For Lambertian light sources, a useful guideline to use for illuminance measurements is the “five times rule”: the distance from the measurement point to the light source should be greater than five times the largest dimension of the source for an accurate measurement. Moreover, for a strongly directional light source the five times rule will not work.
Illuminance was formerly often called brightness, but this leads to confusion with other uses of the word, such as to mean luminance. "Brightness" cannot be used for quantitative description, but for sack of nonquantitative references, we say it is perceptions of light.