An extended real object is placed perpendicular to the principle axis of a concave of focal length `10 cm`, such that the images found is half the size of object
(a) Find the object distance from the lines
(b) Find the image distance from the lens and draw the ray diagram
(c) Find the laterial magnification if object is moved by `1mm` along the principle axis towards the lens.

Explanation

(a) We have,
`f = -10cm`
`m = (h_(2))/(h_(1)) = 0.5 = (v)/(u)`
So, `(1)/(v) - (1)/(u) = (1)/(f)` gives `rArr (1)/(0.5u) - (1)/(u) = (1)/(-10), :. U = -10cm`
(b) `(v)/(u) = 0.5`
`:. V = 0.5x(-10)cm`
`= -5cm`
Ray dragem:-
(c) `m = (f)/((f+u)^(2)) du = ((+10))/((-10-10)^(2)) (0.1) = 0.0025cm`
so, final laterial magnification `(m+dm) = 0.5025cm`