Question

A point source emitting 628 lumen of luminous flux uniformly in all directions is placed at the origin. Calculate the illuminance on a small area placed at (1.0 m, 0, 0) in such a way that the normal to the area makes an angle of 37° with the X-axis.

Answer 1

Given,

Luminous flux = 628 lumen

Angle made by the normal with the x axis (θ) = 37°

Distance of point, r = 1 m

Since the radiant flux is distributed uniformly in all directions, the solid angle will be 4π.

∴ Luminous intensity, l = `"Luminous flux"/"Solid angle"`

`=628/(4pi)=50 "candela"`

I lluminance (E) is given by,

`E=l cos (theta/r^2)`

On substituting the respective values we get,

`E=50xxcos37^o/1^2`

`50xx"(4/5)"/1=40 "lux"`

So, the illuminance on the area is 40 lux.