Question

Use the mirror formula to show that an object lying between the pole and focus of a concave mirror, the image formed is virtual in nature

Answer 1

let v = image distance from pole,
u = object distance from pole
and, f = focal length of the mirror .

Mirror formula :- (1/v) + (1/u) = (1/f)
given conditions:- u = -ve , f = -ve and f > u
we have to find the sign of v .
so, (1/v) = (-1/f) - (-1/u)
=> 1/v = 1/u - 1/f
=> 1/v = (f - u)/(f x u)
since , f > u => ( f-u ) is positive ..
=> v = positive ...
hence, image will form at the right side of mirror,
=> image is virtual