A point source, positioned at the origin, emits 628 lumen of luminous flux uniformly in all directions. Determine the illuminance on a small area located at (1.0 m , 0, 0) , given that the normal to this area forms an angle of 37^ with the X -axis.

Step-by-step solution

The luminous intensity I of the point source is given by the total luminous flux divided by the total solid angle: I = 4 = 628 4 3.14 = 50 cd The illuminance E on a surface is given by: E = I r^2 where r is the distance from the source and is the angle between the normal to the surface and the direction of the incident light. The light travels along the X-axis, so the angle of incidence is = 37^ . Substituting the given values: E = 50 37^ (1.0)^2 E = 50 4 5 = 40 lux