Question

Photography The formula n=log2 1/p represents the change in the f-stop setting n to use less light where p is the fraction of sunlight. a. Benitos camera is set up to take pictures in direct sunlight, but it is a cloudy day. If the amount of sunlight on a cloudy day is 1/4 as bright as direct sunlight, how many f-stop settings should he move to accommodate less light? B. Graph the function c. Use the graph in part b to predict what fraction of daylight Benito is accommodating if he moves down 3 f-stop settings. Is he allowing more or less light into the camera.

Answer 1

Since p represents the fraction of sunlight, when we have direct sunligh p equals 1, then for 1/4 as bright as direct sunlight p is 1/4*1=1/4, we can find n by replacing 1/4 into p, like this:

$n=\log _2(\frac{1}{\frac{1}{4}})=\log _2(4)=2$

Then, the number of stop setting that he would move is 2.

The value of p goes from 0 at its minimum value to 1 at its maximum value for direct sunlight. then, we can plot the equation in the interval (0,1], by calculating the value of n for different values of p, like this:

n(0.1)=3.32

n(0.3)=1.74

n(0.5)=1

n(0.7)=0.51

n(0.9)=0.15

n(1)=0

let's plot these values:

From the plot, If Benito moves down 3 f-stop settings his daylight fraction is approximately 0.15