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

[Samr28]

Homework Statement

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

Homework Equations

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

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.

 

[Daniel Gallimore]

Homework Statement

[/B]
View attachment 200090

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

Homework Equations

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

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.

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.

 

[andrevdh]

the image is 20x smaller than the object so

h_i = 1/20 h_o

giving us

h_i/h_o = 1/20

but h_i/h_o = d_i/d_o

so we also have that

d_i/d_o = 1/20

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

d_o = ... ?

 

[Daniel Gallimore]

the image is 20x smaller than the object so

h_i = 1/20 h_o

giving us

h_i/h_o = 1/20

but h_i/h_o = d_i/d_o

so we also have that

d_i/d_o = 1/20

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

d_o = ... ?

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 $d_o$.