Chapter 16.1, Problem 7PP

To determine

To Calculate: The distance above the surface where the lights should be placed.

Whether the desired illuminance be achieved if the lights are placed 1.5 m above the keyboard surface.

The change in lamp’s luminous flux required to achieve desired illuminance.

Explanation of Solution

Given:

Luminous flux of the lamp, $I=1750\text{lm}$

Desired illumination on the keyboard, $E=175\text{lx}$

Formula used:

  $E=\frac{I}{d^2}$

Here, Iis the luminous flux, E is the illumination and d is the distance from the source.

Calculation:

The distance from the keyboard where lights should be placed.

  $\begin{array}{l}d=\sqrt{\frac{1750}{175}}\\ d=3.16\text{m}\end{array}$

Illuminance if the lights are placed 1.5 m above the keyboard:

  $\begin{array}{l}E\text{'}=\frac{1750}{{\left(1.5\right)}^2}\\ E\text{'}=777.78\text{lx}\end{array}$

The illumination would exceed the desired illuminous.

The required luminous flux of the lamp to get desired illumination at 1.5 m away from the keyboard is:

  $\begin{array}{l}{I}_n=E\times d^2\\ I_n=175\times {\left(1.5\right)}^2\\ I_n=393.75\text{lm}\end{array}$