Figuring out what image distance (lens and mirror) formula to use?

Clomo4star

I was practicing hw and I came across these two derived equations from 1/f=1/d0+1/di
1st one 1/di=1/d0-1/f
2nd one di=d0(f)/d0-f
How do distinguish which one to use? and how did they get that derivation for the 2nd equation?

Simon Bridge

I wouldn't worry about memorizing the different forms of the equations to use for which situation, focus on understanding the physics.

Note - the second one is just what happens to the lensmakers formula if you solve it for d_i. The first one is incorrect.

jtbell

1st one 1/di=1/d0-1/f

Are you sure the right-hand side wasn't reversed, that is,

$$\frac{1}{d_i} = \frac{1}{f} - \frac{1}{d_o}$$

This is just a re-arrangement of your first equation. It's good algebra practice. First, get the 1/d_i all by itself on the left as in my equation above. Can you see where to go from there? (hint: how do you add or subtract fractions?)

Clomo4star

Oh yeah sorry oops I was just wondering about the 2nd one.

Simon Bridge

No worries - did you have a go at the derivation yet? How did you get on?