Chapter 7.3, Problem 49PPS

(a)

To determine

To Find: How many $f$ stop setting should be move to accommodate less light if his camera is set up to take pictures in a direct sunlight, but it is a cloudy day. If the amount of the sunlight on the cloudy day is $\frac{1}{4}$ as bright as direct sunlight.

Answer to Problem 49PPS

  $2$

Explanation of Solution

Given: The formula $n={\log }_2\frac{1}{p}$ represents the change in the $f$ stop setting to $n$ to use in less light where $p$ the fraction of sunlight.

Given: $n={\log }_2\frac{1}{p}$

Substitute $p=\frac{1}{4}$

We get

  $\begin{array}{l}n={\log }_2\frac{1}{p}\\ n={\log }_2\frac{1}{\frac{1}{4}}\\ n={\log }_{2}4\\ n={\log }_2{2}^2\\ n=2{\log }_{2}2\\ n=2\times 1\\ n=2\end{array}$

Hence, $2$

  $f$ stop setting should be move to accommodate less light

(b)

To determine

To Draw: Graph the function.

Answer to Problem 49PPS

  

Explanation of Solution

Given: The formula $n={\log }_2\frac{1}{p}$ represents the change in the $f$ stop setting to $n$ to use in less light where $p$ the fraction of sunlight.

Given: $n={\log }_2\frac{1}{p}$

Solving

  $\begin{array}{l}n={\log }_2\frac{1}{p}\\ n=-{\log }_{2}P\end{array}$

The graph of the function is

  

(c)

To determine

To Find: Use the graph to predict what fraction of daylight Benito is accommodating if he moves $3$

  $f$ stop settings. Is he following more or less light into the camera?

Answer to Problem 49PPS

  $\frac{1}{p}=8$

Explanation of Solution

Given: The formula $n={\log }_2\frac{1}{p}$ represents the change in the $f$ stop setting to $n$ to use in less light where $p$ the fraction of sunlight.

Using graph

  

Substitute $n=3$ in $n={\log }_2\frac{1}{p}$

We get

  $\begin{array}{l}n={\log }_2\frac{1}{p}\\ 3={\log }_2\frac{1}{p}\\ 2^3=\frac{1}{p}\\ 8=\frac{1}{p}\\ \frac{1}{p}=8\end{array}$

Hence, $\frac{1}{p}=8$