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.

#### Solution

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 (E_{A}) is given by,

`E_A=I_0/(0.6)^2`

⇒* **I*_{0} = 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=(I_0 costheta)/(OB)^2`

From the figure, we get

`cos theta=0.6/1`

OB = 1 m

Substituting the respective values in the above formula, we get

` E_B= 5.4(0.6/1)`

= 3.24 lux

So, the illuminance at a point on the table-top 80 cm away from the first point is 3.24 lux.