The illumination at a point on a working plane directly below the lamp is to be 80 lumens/m². The lamp gives 180 C.P. uniformly below the horizontal plane. Determine the height at which the lamp is suspended.

Concept:

• Luminous flux (ϕ): Luminous flux is the light energy radiated per second from a luminous body in the form of light waves. It is measured in lumen.
• Illumination (I): The luminous flux falling per unit area on a surface is known as illumination and is expressed in Lumen/m².
• Candle power (C.P): The light radiating capacity of a source is called its candle power. The number of lumens given out by a source per unit solid angle in a given direction is called its candle power.
• Solid angle (ω): The angle subtended by the partial surface area of a sphere at its center is called as solid angle. It is measured in steradians and it is equal to the ratio of area of surface to the square of radius of sphere.

C.P = luminous flux /solid angle

Illumination = luminous flux / area

\(C.P = \frac{\phi }{\omega }\)

\(I = \frac{\phi }{A}\)

\(\omega = \frac{A}{{{R^2}}}\)

Where R = distance of the point from the point of source.

In the given problem R= height at which the lamp is suspended.

\(C.P = \phi \times \frac{{{R^2}}}{A}\)

\(C.P = I \times {R^2}\)

\(180 = 80 \times {R^2}\)

\(R = \frac{3}{2} = 1.5\;meters.\)