A point source emitting light uniformly in all directions is situated 60 cm above a table-top. At a point on the table-top directly beneath the source, the illuminance is 15 lux . Determine the illuminance at a point on the table-top located 80 cm away from this first point.

Step-by-step solution

The illuminance at a point directly below the source is given by E₀ = I h² . Given E₀ = 15 lux and h = 60 cm = 0.6 m . The illuminance at a point on the table-top at a distance x from the first point is E = I r² , where r = h² + x² and = h r . Substituting I = E₀ h² and , we get: E = E₀ h² r² h r = E₀ ( h r )³ Given x = 80 cm = 0.8 m , the distance r from the source to the point is: r = 0.6² + 0.8² = 1.0 m Therefore, the illuminance at this point is: E = 15 ( 0.6 1.0 )³ = 15 0.216 = 3.24 lux