# Image Distance of a concave mirror (need help with algebra!)

## Homework Statement

A concave mirror with a focal length of 34.4 cm produces an image whose distance from the mirror is one-third the object distance. Calculate the object distance.

## Homework Equations

(1/f)=(1/do) + (1/di)

## The Attempt at a Solution

I know that i have to use the mirror equation (posted above). I substitute 1/3(do) in for Di, because the problems states that "... produces an image whose distance from the mirror is one-third the object distance" so my equation now looks like this: (1/f)=(1/do) + [1/(1/3)do].
My problem, sad as it seems, comes during the algebra work. I can't for the life of me get the do terms by themselves to solve. Could someone please help refresh my memory? Basically what i've been doing is adding the do terms to get (1 and 1/3)do = .344m and then divide 1 by the answer that i get solving for do. Thanks for any help you can give!

LowlyPion
Homework Helper

## Homework Statement

A concave mirror with a focal length of 34.4 cm produces an image whose distance from the mirror is one-third the object distance. Calculate the object distance.

## Homework Equations

(1/f)=(1/do) + (1/di)

## The Attempt at a Solution

I know that i have to use the mirror equation (posted above). I substitute 1/3(do) in for Di, because the problems states that "... produces an image whose distance from the mirror is one-third the object distance" so my equation now looks like this: (1/f)=(1/do) + [1/(1/3)do].
My problem, sad as it seems, comes during the algebra work. I can't for the life of me get the do terms by themselves to solve. Could someone please help refresh my memory? Basically what i've been doing is adding the do terms to get (1 and 1/3)do = .344m and then divide 1 by the answer that i get solving for do. Thanks for any help you can give!

Doesn't it work out from your equation that 4/3*f = do ?

Yes, that's how it works out. But solving for do, i get a wrong answer. Perhaps i have my equation set up wrong?

LowlyPion
Homework Helper
Yes, that's how it works out. But solving for do, i get a wrong answer. Perhaps i have my equation set up wrong?

To be clear, if you arrived at
(1 and 1/3)do = .344m
this is incorrect. It should be 3/4*do = .344

(1/f)=(1/do)+(1/di)
(1/f)=(1/do)+(1/((1/3)do))
(1/f)=(1/do)+(1/(do/3))
(1/f)=(1/do)+(3/do)
(1/f)=(4/do)
do=4f

remember:
[1/(1/3)do]
is equal to 1/(do/3)=3/do

Thanks v_bachtiar, that helped a lot!

LowlyPion
Homework Helper
remember:
is equal to 1/(do/3)=3/do

Yikes. You're right. I took it as 1/(3*do) which is wrong. Good catch.