Question

An object is 18.0 cm to the left of a lens with a focal length of +9 cm. A second lens of focal length +13 cm is 29.5 cm to the right of the lens. Find the location and size of the object of height 4.0 cm. Location with respect to the second lens?

Answer 1

99.67 cm to the left of second lens

Step-by-step explanation:

For the first lens :

`d_(o)` = Distance of the object = 18 cm

`f` = focal length of the lens = 9 cm

`d_(i)` = Distance of the image

Using the lens equation

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

`(1)/(18) + (1)/(d_(i)) = (1)/(9)`

`d_(i) = 18` cm

`d` = distance between the two lenses = 29.5 cm

For the second lens, the image formed by the first lens acts as the object

For the second lens :

`d_(o)` = Distance of the object =
`d - 18` =
`29.5 - 18` =
`11.5` cm

`d_(i)` = Distance of the image

`f` = focal length of the lens = 13 cm

Using the lens equation

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

`(1)/(11.5) + (1)/(d_(i)) = (1)/(13)`

`d_(i) = - 99.67` cm

The image is located 99.67 cm to the left of the second lens