Question

A converging lens has a focal length of 20 cm. An object 1 cm tall is placed 10 cm from the center of the lens. What is the height of the image? (note: solve for the image distance first)

Answer 1

Answer: 2 cm

Step-by-step explanation:

Given , for a converging lens

Focal length :
`f=20\ cm`

Height of object :
`h=1\ cm`

Object distabce from lens :
`u=-10\ cm`

Using lens formula:
`(1)/(f)=(1)/(v)-(1)/(u)`, we get

`(1)/(20)=(1)/(v)+(1)/(10)`, where v = image distance from the lens.

On solving aboive equation , we get

`(1)/(v)=(1)/(20)-(1)/(10)=(1-2)/(20)=(-1)/(20)\Rightarrow\ v=-20\ cm`

Formula of Magnification :
`m=(v)/(u)=(h')/(h)` , where h' is the height of image.

Put value of u, v and h in it , we get

`(-20)/(-10)=(h')/(1)\\\\\Rightarrow\ h'=2\ cm`

Hence, the height of the image is 2 cm.