Question

An object of size `7.0 cm` is placed at `27 cm` in front of a concave mirror of focal length `18 cm`. At what distance from the mirror, should a screen be placed, so that a sharp focussed image can be obtained ? Find the size and nature of the image ?

Answer 1

Here, object size, `h_(1) = 7.0 cm` object distance, `u = - 27 cm`
focal length, `f = - 18 cm` image distance, `v = ?`
image size, `h_(2) = ?`
As `(1)/(v) + 1/u = (1)/(f), (1)/(v) = (1)/(f) - 1/u = 1/(-18) + 1/27 = (- 3 + 2)/54 = (-1)/54 = -54 cm`.
`:.` The screen should be held in front of the mirror at a distance of `54 cm` from the mirror. The image obtained on the screen will be real.
As `m = (h_(2))/(h_(1)) = -v/u, (h_(2))/(7.0) =-((-54))/((-27))`
or `h_(2) = - 14.0 cm`
Negative sign of `h_(2)` shows that the image is inverted.