Question

12.

A Pole 4m Long is laid along the principal axis of a convex mirror of
focal length 1m the end of the pole nearer the mirror is 2m from it.
Find the length of the image of the pole.
Ans: 0.19m
​

Answer 1

The length of the image of the pole is 4/3 m

Step-by-step explanation:

The given parameters are;

The length of the Pole = 4 m

The type of mirror = Convex mirror

The distance of the pole from the mirror = 2 m

The mirror formula for convex mirrors is presented here as follows;

`(1)/(U) - (1)/(V) = - (1)/(F)`

Where;

U = The object (pole) distance from the mirror = 2 m

V = The image of the objects (pole) distance from the mirror

The focal length of the mirror

Therefore, by substitution, we have;

`(1)/(2) - (1)/(V) = - (1)/(1)`

`(1)/(2) + 1 = (1)/(V)`

`(1)/(V) = (1)/(2) + 1 = (3)/(2)`

`V = (2)/(3)`

We have;

`Magnification = (Image \ height)/(Object \ height ) = (Length \ of \ the \ Image \ of \ the \ Pole)/(Length \ of \ the \ of \ the \ Pole ) =(-V)/(U)`

Which by substitution gives;

`Magnification = (Length \ of \ the \ Image \ of \ the \ Pole)/(4) =(-(2)/(3) )/(2) = (2)/(6)`

`{Length \ of \ the \ Image \ of \ the \ Pole}{} = 4 * (2)/(6) = (4)/(3)`

The length of the image of the pole = 4/3 m