Question

5. 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 _________ millimeters.
A. 8
B. 4
C. 12
D. 2

Answer 1

A...............................................................

....

Answer 2

The correct answer to the question is A). 8 mm.

CALCULATION:

As per the question, the object distance u = 8 mm.

The image distance v = 16 mm.

The height of the object $h_{0}=\ 4\ mm.$

As per the rule of sign convention, the distance measured along the direction of light is taken as positive and opposite to the direction of light is taken as negative.

All the transverse measurements above the principal axis are taken as positive, and the transverse measurements below the principal axis are negative.

Hence, the object distance  u = -8 mm

          The image distance v = -16 mm.

          The object height $h_{o}=\ +4\ mm$.

We are asked to calculate the image height $h_{i}$.

The transverse magnification of the spherical concave mirror is given as -

                                  $m=\ \frac{h_{i}} {h_{o}}=\ \frac{-v}{u}$

                               ⇒  $\frac{h_{i}} {h_{0}}=\ \frac{-v}{u}$

                                ⇒   $h_{i} =\ h_{0}\times \frac{-v}{u}$

                                        $=\ 4\times \frac{-(-16)}{(-8)}\ mm$

                                        $=\ -8\ mm$    

The negative sign signifies that the image is inverted in nature.

Hence, the image height will be 8 mm.