Question

When an object is placed 8 millimeters from a concave spherical mirror, a clear image can be projected on a screen 16 millimeters in front of the mirror. If the object has a height of 4 millimeters, the height of the image is
A. 12 millimeters.
B. 4 millimeters.
C. 2 millimeters.
D. 8 millimeters.

Answer 1

M = i / p

m = 16 mm / 8 mm

m = 2 mm

2 x 4 mm = 8 mm

Answer D

hope this helps!

Answer 2

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.