Question

An electric bulb is hanging over a table at a height of 1 m above it. The illuminance on the table directly below the bulb is 40 lux. The illuminance at a point on the table 1 m away from the first point will be about
(a) 10 lux
(b) 14 lux
(c) 20 lux
(d) 28 lux

Answer 1

Correct option (b)

$$\begin{gathered} \mathrm{Here}, \\ \mathrm{r}=\sqrt{2} \\ \mathrm{tan\theta }=\frac{\mathrm{BC}}{\mathrm{AB}}=1 \\ {\mathrm{I}}_{\mathrm{o}}=40\mathrm{lux} \\ \mathrm{\theta }={\tan }^{-1}\left(1\right)={45}^0 \\ \mathrm{The}\mathrm{illuminance}\mathrm{is}\mathrm{given}\mathrm{by} \\ \mathrm{E}=\frac{{\mathrm{I}}_{\mathrm{o}}\mathrm{cos\theta }}{{\mathrm{r}}^2} \\ =\frac{40\times \cos \left({45}^0\right)}{{\left(\sqrt{2}\right)}^2} \\ =14\mathrm{lux} \end{gathered}$$