Question

Question #143ab

Answer 1

`1/f=1/u+1/u^'`

Explanation:

`"triangle "" EFO "" is similar to ""triangle "OIH`

`(bar (IH))/(bar (EF))=(bar(OI))/(bar(OF))`

`g:"image height"`

`c:"object height"`

`u:"distance between object and lens"`

`u^':"distance between image and lens"`

`color(red)(g/c)=u^'/u`

`"triangle "" EFC "" is similar to ""triangle "COG`

`(bar (OG))/(bar (EF))=(bar(OC))/(bar(FC))`

`color(red)(g/c)=f/(u-f)`

`u^'/u=f/(u-f)`

`u^'(u-f)=u f`

`u^' u-u^' f=u f`

`u f+u^' f=u^' u`

`f(u+u^')=u^' u`

`f=(u^' u)/(u+u^')`

`1/f=(u+u^')/(u^' u)`

`1/f=cancel(u)/(u^' cancel(u))+cancel(u)^'/(cancel(u)^' u)`

`1/f=1/u+1/u^'`