Question #143ab

1 Answer
Oct 20, 2016

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

Explanation:

enter image source here

"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^'