A converging lens has a focal length of 40 cm . Calculate the size of the real image of an object, 4.0 cm in height, for the object distance:
50 cm
Given `f = 40 cm, h _(0) = 4 cm, and u` in different cases. Find: `h _(1)` in each case corresponding to the given value of u.

Explanation

From the magnification formula,
`m = ( h _(1))/( h_(0)) = (-v)/( u)`
`therefore h _(1) = (-v)/(u) xx h _(0) " "(1)`
From the mirror formula,
`(1)/(f) = (1)/(u) + (1)/(v) implies v = (uf)/(u-f)" "(2)`
Subsituting (2) in (1),
`h _(1) = ( - u f h _(0))/( u ( u-f)) =( - u f h _(0))/( u - f)" "(3)`
If `u _(2) = 60 cm,` from Eq, (3),
`h _(1) = ( - 40 cm xx 4 cm )/( 60 cm - 40 cm) = - 8 cm`