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-

`(-v)/(u) =(h_(i) )/(h_(o) )`

Putting the values of respective quantities we will get-

`-[(-16 mm)/(-8 mm) ]=(h_(i) )/(4)`

`-2 =(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.