What is the distance between an object and its real image formed by a thin converging lens with focal length f = 21 cm, if the object distance is 100 cm? (b) What is the minimum object-image distance for a real image formed by that lens?

Answer 1

1/do+1/di=1/f
1/di= 1/0.21 – 1/1 = 3.76
di=0.26 m
D=di+do =0.26+1 = 1.26 m

(b)
1/do+1/di=1/f
di =f•do/(do-f)
D=do+di =
=do+ f•do/(do-f) =do²/(do-f)
For finding D(min) let differentiate D(do)
D´={do²/(do-f)}´={2•do(do-f) -do²(1-f)}/(do-f) ²
D´=0 =>
2•do²- 2•do•f-do²+do²•f=0
do(do-do•f-2•f) =0
d0(1-f) = 2f
d0 =2f/(1-f) = 2•0.21/(1-0.79) = 0.532 m
D(min) = do+di =do + f•do/(do-f)=
=0.532 +{0.21•0.53/(0.53-0.241) =
=0.532+0.348 = 0.88 m