Question

An object is placed 4 cm in front of a +2 cm focal length lens. If a second identical lens is now placed 8cm behind the first, where will the final image be located? a) 2 cm behind the second lens b) 4 cm behind the first lens c) 10 cm in front of the first lens. d) -5 cm from the second lens.

Answer 1

The final image be located 2 cm behind the second lens.

(a) is correct option.

Step-by-step explanation:

Given that,

Focal length = +2 cm,

Object distance = 4 cm

If a second identical lens is now placed 8 cm behind the first

We need to calculate the image distance

Using formula of focal length

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

Put the value into the formula

`(1)/(2)=(1)/(v)+(1)/(-4)`

`(1)/(v)=(1)/(2)+(1)/(4)`

`(1)/(v)=(3)/(4)`

`v=1.333\ cm`

Where two lens are separated by 8 cm

The image of first lens become object for second lens

Then object distance is

`u = 8 -1.33= 6.67 cm`

Where two lens are same means have same focal length then image distance is

Using formula of lenses

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

Put the value into the formula

`(1)/(2)=(1)/(v)+(1)/(-6.67)`

`(1)/(v)=(1)/(2)+(1)/(6.67)`

`v=1.54\ cm`

Round off value of v is 2 cm

Hence, The final image be located 2 cm behind the second lens.