Question

An object 2.0 cm in size is placed at 30.0 cm in front of a concave mirror of focal length 15.0 cm. At what distance from the mirror should a screen be placed in order to obtain a sharp image, Find the nature and the size of the image formed?

Answer 1

h $=$2$·$0 cm
u $=$ $-$30cm
f $=$ $-$ 15cm
v $=$ ?
using the mirror formula 1$/$v $+$ 1$/$u $=$1$/$f
1$/$v $=$1$/$( $-$30) $-$ 1$/$($-$15)
1$/$v $=$$-$1 $/$ 30
v $=$$-$ 30 cm
So the screen should be placed at 30 cm from the mirror.
m $=$image size $/$ object size = $-$v $/$u
Image size $=$$-$( $-$30 )$\times$2 $/$ ( $-$ 30)
Image size $=$$-$2 cm
So the image is real, inverted and is of the same size as that of the object.