Question

A point source emitting light uniformly in all directions is placed 60 cm above a table-top. The illuminance at a point on the table-top, directly below the source, is 15 lux. Find the illuminance at a point on the table-top 80 cm away from the first point.

Answer 1

Given,
Distance of the source from the table-top (r) = 60 cm or 0.6 m
Let I_o be the intensity of illumination.
Illuminance directly below the source $\left(E_A\right)$ is given by,
$E_A=\frac{I_0}{(0.6{)}^2}$
⇒ I₀ = 15 × (0.6)²
= 5.4 candela

Let E_B be the illuminance at a point 80 cm away from the initial point.
So, $E_B=\frac{I_0\cos \theta }{{\left(OB\right)}^2}$
From the figure, we get
cos$\theta$ = $\frac{0.6}{1}$
OB = 1 m
Substituting the respective values in the above formula, we get
E_B $$\begin{gathered} =5.4\left(\frac{0.6}{1}\right) \\ =3.24\mathrm{lux} \end{gathered}$$
So, the illuminance at a point on the table-top 80 cm away from the first point is 3.24 lux.