Question

You are using a magnifier that gave you a lateral magnification of 1/2. If the object distance is 0.5 cm, calculate the focal length of the magnifier.

Answer 1

`- 0.5` cm

Step-by-step explanation:

`M` = Lateral Magnification = 0.5

`d_(o)` = Distance of the object = 0.5 cm

`d_(i)` = Distance of the image = ?

Lateral magnification is given as

`M = (- d_(i))/(d_(o))`

`0.5 = (- d_(i))/(0.5)`

`d_(i) = - 0.25` cm

`f` = focal length of the magnifier

Using the equation

`(1)/(d_(o)) + (1)/(d_(i)) = (1)/(f)`

`(1)/(0.5) + (- 1)/(0.25) = (1)/(f)`

`f = - 0.5` cm

Answer 2

The focal length is -0.5.

Step-by-step explanation:

Given that,

Magnification
`m=(1)/(2)`

Object distance u = 0.5 cm

We need to calculate the image distance

Using formula of magnification

`m=-(v)/(u)`

Put the value into the formula

`(1)/(2)=-(v)/(0.5)`

`v=-(1)/(2)*0.5`

`v=-0.25\ cm`

We need to calculate the focal length

Using formula for focal length

`(1)/(f)=(1)/(u)+(1)/(v)`

`(1)/(f)=(v+u)/(vu)`

`f=(uv)/(v+u)`

`f=(0.5*(-0.25))/(-0.25+0.5)`

`f=-0.5\ cm`

Hence, The focal length is -0.5.