As per the question the object is placed at a distance of 8 mm from a concave spherical mirror.
Hence the object distance [u] = 8 mm.
As object distance is measured opposite to the direction of light,the sign for u will be negative.
Hence u = -8 mm
The image is formed at a distance of 16 mm in front of the mirror.
Hence the image distance [v ]= 16 mm.
As V is measured opposite to the direction of light,its sign convention will be negative.
Hence v = -16 mm
The height of object is given as 4 mm.Let the object height is denoted as - \(h_{o}\)
The transverse measurement above the principal axis is positive.hence object height will be positive.
\(h_{i} = + 4 mm\)
As per the question we are asked to calculate the image height.Let the image height is denoted as - \(h_{i}\)
The transverse magnification m of for spherical mirror is given as below-
\(\frac{-v}{u} =\frac{h_{i} }{h_{o} }\)
Putting the values of respective quantities we will get-
\(-[\frac{-16 mm}{-8 mm} ]=\frac{h_{i} }{4}\)
\(-2 =\frac{h_{i} }{4}\)
\(h_{i} = -8 mm\)
Here negative sign indicates that the image is below the principal axis i.e the image is inverted.
Hence option D is right.
