Chapter 12.7, Problem 6P

To determine

To calculate: The brightness of the light which is 0.4 m closer to the light source. if at a distance of 1.2 m from the light source, the brightness on a book page was measured as $12lm/m^2$ ( lumens per square meter) , also given the brightness of the light on a object varies inversely as the square of the distance from the object to the light source.

Answer to Problem 6P

The brightness of the light is $L=56.3lm/m^2$ .

Explanation of Solution

Given information:

The brightness of the light on a object varies inversely as the square of the distance from the object to the light source.

Let, $L$ is the brightness of the light

  $d$ is the distance

So $L\prec \frac{1}{d^2}$ Given

Let k be a constant

  $L=k\cdot \frac{1}{d^2}$...... (1)

Put the values of L and d to get k .

  $\frac{25}{}=\frac{k}{{\left(1.2\right)}_{}^2}$

Solve further to get k ,

  $\begin{array}{l}k=\left(25\right)\times {\left(1.2\right)}^2\\ k=36\end{array}$

Now book page moves $0.4m$ closer to the light, so new distance is

  $\begin{array}{l}d=\left(1.2-0.4\right)m\\ d=0.8m\end{array}$

Put the value of k and d in equation 1 to get L

  $L=\frac{k}{d^2}$

  $\begin{array}{l}L=\frac{36}{{\left(0.8\right)}^2}\\ L=56.25lm/m^2\end{array}$

To nearest tenth.

  $L=56.3lm/m^2$