SOLUTION: 1. The lens equation for a camera is 1/f = 1/di + 1/do , where f is the focal length of the lens, di is the distance between the lens and the film, and do is the distance betwee

Algebra ->  Rational-functions -> SOLUTION: 1. The lens equation for a camera is 1/f = 1/di + 1/do , where f is the focal length of the lens, di is the distance between the lens and the film, and do is the distance betwee      Log On


   

Question 279631: 1. The lens equation for a camera is 1/f = 1/di + 1/do , where f is the focal length of the lens, di is the distance between the lens and the film, and do is the distance between the lens and the object. For a certain camera, an object that is 18 cm from the lens is in focus when the lens is 9 cm from the film. What is the focal length of the lens?
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
1/f = 1/di + 1/do
f is the focal length of the lens
di is the distance between the lens and the film.
do is the distance between the lens and the object.

object is 18 cm from the lens.
lens is 9 cm from the film.

do = 18
di = 9

1/f = 1/9 + 1/18

1/9 is the same as 2/18 so this equation becomes:

1/f = 2/18 + 1/18 = 3/18

you have:

1/f = 3/18

since this is in the form of a ratio, you can cross multiply to get:

3f = 18

divide both sides of this equation by 3 to get:

f = 6

your answer is that the focal length of the lens is 6.

you confirm by plugging that value into the equation to see that it is true.

the equation is 1/f = 1/di + 1/do

we had di = distance from lens to the film = 9 cm.

we had do = distance from object to the lens = 18 cm.

we have f = 6

equation becomes:

1/6 = 1/9 + 1/18

convert all to denominator of 18 to get:

3/18 = 2/18 + 1/18 which becomes:

3/18 = 3/18 which is true confirming that the value of f = 6 is good.