# Converging lens solve for all variables given f, Hi, and Ho

1. May 7, 2017

### Samr28

1. The problem statement, all variables and given/known data

What is directly given in the problem:
Converging lens with f=1.43m
Hi = 2m

2. Relevant equations

Hi/Ho = di/do
M = Hi/Ho = di/do
1/f = 1/do + 1/di

3. The attempt at a solution

Ho = 2m * 20 = 40m
Not sure how I can get do from this. All of the equations seem to need di.

2. May 7, 2017

### Daniel Gallimore

You can get the object height from the magnification. Since the image is $20$ times smaller than the object, $M=1/20$. We also know that $H_i=2 \, m$.

To get the distance to the coaster, multiply $$\frac{1}{f}=\frac{1}{d_o}+\frac{1}{d_i}$$ through by $d_o$ and substitute $1/M=20$ for $d_o/d_i$. You know the focal length, so it shouldn't be difficult to solve for $d_o$ from there.

3. May 8, 2017

### andrevdh

the image is 20x smaller than the object so

hi = 1/20 ho

giving us

hi/ho = 1/20

but hi/ho = di/do

so we also have that

di/do = 1/20

so that we have that the object distance in terms of the image distance is

do = .... ?

4. May 8, 2017

### Daniel Gallimore

Multiply the equation $$\frac{1}{f}=\frac{1}{d_o}+\frac{1}{d_i}$$ through by $d_o$. This gives you the equation $$\frac{d_o}{f}=\frac{d_o}{d_o}+\frac{d_o}{d_i}$$ $d_o/d_o=1$ and $d_o/d_i=1/M$ Solve for the remaining $d_o$.