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Chapter 5: Q. 101 (page 285)

Optics If a single pane of glass obliterates 3% of the light passing through it, the percent p of light that passes through n successive panes is given approximately by the function

p(n)=100(0.97)n

(a) What percent of light will pass through 10 panes?
(b) What percent of light will pass through 25 panes?

Short Answer

Expert verified

(a) 73.74%

(b)46.69%

Step by step solution

01

Step 1.Giveninformation

Let us consider a pane which blocks3% of the light.
This means that the light passing through the pane is97% of the actual.
Thus the percentage of light that passes through n panes

p(n)=100(0.97)n

02

Step 2.(a) What percent of light will pass through 10 panes? 

Let us consider 10 panes.
Therefore light passing through 10 panes will be

p(10)=100(0.97)10=100(0.7374)=73.74%

03

Step 3. (b) What percent of light will pass through 25 panes? 

Let us consider 25 panes
Therefore light passing through 25 panes will be

p(25)=100(0.97)25=100(0.4669)=46.69%

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