Chapter 12.8, Problem 3E

To determine

To calculate: How far the object is placed from a table surface to the illumination that is provided $24$ lx, a lamp gives $216$ cd lamp.

Answer to Problem 3E

The distance from the table surface is: $3$m.

Explanation of Solution

Given information:

How far the object is placed from a table surface to the illumination that is provided $24$ lx, a lamp gives $216$ cd lamp.

Formula used:

For find the illumination,

  $E=\frac{l}{r^2}$

Calculation:

Consider a surface provided illumination that is provided $24$ lx, a lamp gives $216$ cd lamp.

Recall that for find the illumination,

  $E=\frac{l}{r^2}$

Here the values are:

  $r=?\text{,E=24,l=216}$

Therefore, the illumination given by,

  $\begin{array}{c}E=\frac{l}{r^2}\\ 24=\frac{216}{r^2}\\ r^2=\frac{216}{24}\\ r^2=9\end{array}$

Simplified further:

  $\begin{array}{c}{r}^2=9\\ r=\sqrt{9}\\ r=3\end{array}$

Thus, the distance from the table surface is: $3$m.