As illustrated in the figure, a small diffused plane source S is positioned 2.4 m above a horizontal table-top, such that its plane is parallel to the table-top. At point A , which lies directly beneath the source, the illuminance is 25 lux . Determine the illuminance at a point B on the table, situated 1.8 m away from A .

Step-by-step solution

For a small diffused plane source, the luminous intensity in a direction making an angle with the normal is given by Lambert's cosine law: I( ) = I₀ The illuminance E at a point on a surface is given by: E = I( ) r^2 where r is the distance from the source to the point, and is the angle of incidence. Since the source plane is parallel to the table-top, the angle of emission is equal to the angle of incidence . Thus: E = I₀ ^2 r^2 At point A , the point is directly beneath the source, so = 0^ and r_A = 2.4 m . E_A =