Above the center of a round table with a radius of 1 m at a height of 1.5 m hangs a lamp with a luminous intensity of 300 KD.

Above the center of a round table with a radius of 1 m at a height of 1.5 m hangs a lamp with a luminous intensity of 300 KD. Determine the illumination at the edge of the table.

The radius of the round table is denoted by r, and the distance from the lamp to the center by h. Then, according to the condition of the assignment, r = 1 m and h = 1.5 m. In addition, the luminous intensity of the lamp I = 300 cd is known. It is required to determine the illumination at the edge of the table, which we denote by E (in lux).
Since it is required to determine the illumination at the edge of the table, we immediately find the distance from the lamp to the edge of the table, which we denote by R. Since the lamp is on a line that is perpendicular to the plane of the table surface, we are dealing with a right-angled triangle, the hypotenuse of which is equal to R, and the legs are equal r and h. By the Pythagorean theorem, we have: R² = r² + h² = (1 m) ² + (1.5 m) ² = (1 + 2.25) m² = 3.25 m², whence R = √ (3.25) m …
According to the generalized law of illumination, E = I * cosα / R². The figure shows that, by the definition of cosine, cosα = h / R. So, the required illumination at the edge of the table is E = I * cosα / R² = I * (h / R) / R² = I * h / R³ = (300 * 1.5) / (√ (3.25)) ³ ≈ 76.8 lx.
Answer: 76.8 lux.