Answer:
19.5 cm
Explanation:
from lens formula which is
[tex]\frac{1}{f} =\frac{1}{u} +\frac{1}{v}[/tex]
f=focal length of the lens
u=object distance
v=the image distance from the lens
since she uses the lens to view far objects and she is short sighted
then [tex]\frac{1}{f} =\frac{1}{-39} +\frac{1}{∞}[/tex]
f=-39cm
susan uses concave lens and its of a focal length 39cm
[tex]\frac{1}{-39} =\frac{1}{-13} +\frac{1}{v}[/tex]
-1/39+1/13=1/v
1/v=2/39
Take inverse of both sides
v=39/2
v=19.5cm
this is the distance of the closest object she can focus on
The closest object on which Susan can focus with her glasses on is 19.5 cm.
Given the following data:
To determine the closest object on which Susan can focus with her glasses on:
Mathematically, the focal length is given by this formula:
[tex]\frac{1}{f} =\frac{1}{u} +\frac{1}{v}[/tex]
Where:
Making f the subject of formula, we have:
[tex]f=\frac{uv}{u\;+\;v}[/tex]
Substituting the given parameters into the formula, we have;
[tex]f=\frac{39 \times 13}{39\;+\;(-13)}\\\\f=\frac{507}{39\;-\;13}\\\\f=\frac{507}{26}[/tex]
f = 19.5 cm.
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