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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?

  • phy -

    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

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