Chapter 16.1, Problem 6PP

To determine

The minimum luminous flux that the light must produce if the illuminance at the surface of each student’s desk is 160 lx.

Answer to Problem 6PP

  $\boxed{P=8.0\times {10}^3\text{lm}}$

Explanation of Solution

Given:

The distance is $r=2.0\text{m}$ .

Illuminance at the surface of each student’s desk is $E=160\text{lx}$ .

Formula used:

The expression for illumination is given by

  $E=\frac{P}{4\pi r^2}$  ...... (1)

Here, $P$ and $r$ are luminous flux and the distance of the object from the light source respectively.

Calculation:

It is assumed that the light from the source strikes perpendicular to the surface of the disk.

From equation (1), after rearranging:

  $P=\left(4\pi r^2\right)E$  ....... (2)

Substitute $2.0\text{m}$ for $r$ and $160\text{lx}$ for $E$ in equation (2)

  $\begin{array}{l}P=4\pi {\left(2.0\text{m}\right)}^2\times \left(160\text{lx}\right)\\ \boxed{P=8.0\times {10}^3\text{lm}}\end{array}$

Conclusion:

Hence, the required minimumluminous flux that light must produce is $\boxed{P=8.0\times {10}^3\text{lm}}$ .