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 (E_A) is given by,

`E_A=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=(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.