Question

In a particular case of an object in front of a spherical mirror with a focal length of +12.0 cm, the magnification is +4.00.(a) Determine the object distance.(b) Determine the image distance.

Answer 1

9 cm

-36 cm

Step-by-step explanation:

u = Object distance

v = Image distance

f = Focal length = 12

m = Magnification = 4

`m=-(v)/(u)\\\Rightarrow 4=-(v)/(u)\\\Rightarrow v=-4u`

Lens equation

`(1)/(f)=(1)/(u)+(1)/(v)\\\Rightarrow (1)/(12)=(1)/(u)+(1)/(-4u)\\\Rightarrow (1)/(12)=(3)/(4u)\\\Rightarrow u=9\ cm`

Object distance is 9 cm

`v=-4* 9=-36\ cm`

Image distance is -36 cm (other side of object)