Question

A light source is located at$p_1$ as shown in the figure. All sides of the polygon are equal . the intensity of illumination at $p_2$ is$I_o$ What will be the intensity of illumination at$P_3$

• A. $\frac{3\sqrt{3}}{8}{1}_0$
• B. $\frac{1_0}{8}$
• C. $\frac{3}{8}{1}_o$
• D. $\frac{\sqrt{3}}{8}{1}_o$

Answer 1

The correct option is A $\frac{3\sqrt{3}}{8}{1}_0$

From the geometry of the figure
$p_1{p}_2=2a\sin {60}^o$
so, $I_{p_2}=\frac{L}{p_1{p}_2^2}$
$=\frac{L}{\left(2a\sin {60}^o\right)}=\frac{L}{3a^2}$
and $I_{p_3}=\frac{L}{(P_1{P}_2^2+a^2)}\cos {30}^o$
$=\frac{L}{\left[\right(2a\sin {60}^o)+a^2]}\frac{\sqrt{3}}{2}=\frac{\sqrt{3}L}{8a^2}$

$\Rightarrow I_{p_3}=\frac{3\sqrt{3}}{8}{I}_{p_2}=\frac{3\sqrt{3}}{8}{I}_0$