Question

At what distance should a book be placed from a $50Cd$ bulb so that the illuminance on the book becomes $2\operatorname{lm} {m^{ - 2}}$
(A) $1m$
(B) $5m$
(C) $10m$
(D) $50m$

Answer 1

Luminance measures the amount of light falling onto and spreading over a given surface area. Illuminance is given by $({{\text{E}}_{\text{v}}}) = \dfrac{I}{{{R^2}}}$

Complete step by step answer:
Illuminance is flux of light per unit area. The SI unit of Illuminance is lux which is also called lumen per meter square ($\operatorname{lm} {m^{ - 2}}$ ). Physically It is measured using an illuminance meter. Mathematically illuminance can be calculated from the formula ${E_v} = \dfrac{I}{{{R^2}}}$ , where $I$ is the luminous intensity which is the amount of light emitted per unit area per unit solid angle, it measured in Candela $\left( {Cd} \right)$ and R is the distance in metre.
Given $I = 50Cd$ and${{\text{E}}_{\text{v}}} = 2\operatorname{lm} {m^{ - 2}}$ .
$\Rightarrow R = \sqrt {\dfrac{{50}}{2}} = 5m$.
Hence the answer is option (B) 5m.

Note: Not be confused with illuminance and luminance. Luminance refers to the amount of light passing through or reflected back from an object and physically it is measured using a luminance meter while illuminance refers to intensity of light falling onto a surface area. SI unit of luminance is candela per metre square (Cd/$m^2$) where as SI unit of illuminance is lumen per meter square ($\operatorname{lm} {m^{ - 2}}$). Luminance and illuminance are not the same with brightness. We can not measure brightness, it's something felt by the human eye, but we can measure luminance and illuminance.