Question

A 9.0 cm object is 3.0 cm from a lens, which has a focal length of –12.0 cm.

Answer 1

The correct answers should be -2.4, 7.2, concave in that order

Answer 2

The question is missing, but I guess the problem is asking for the distance and the size of the image.

Let's find the distance first, by using the lens equation:

`(1)/(f)= (1)/(d_o)+ (1)/(d_i)`
where f is the focal length,
`d_o` the distance of the object from the lens,
`d_i` the distance of the image from the lens. Using
`f=-12.0 cm` and
`d_o=3.0 cm`, we find

`- (1)/(12)= (1)/(3)+ (1)/(d_i)`

`d_i=- (12)/(5)=-2.4 cm`
where the negative sign means the image is virtual, so located in front of the lens.

Now we can find the size of the image, using the relationship:

`(h_i)/(h_o) =- (d_i)/(d_o)`
where
`h_i` and
`h_o` are the size of the image and of the object, respectively.
By using
`h_o=9.0 cm`, we can find
`h_i`, the size of the image:

`h_i=-h_o (d_i)/(d_o)=-(9.0 cm) ((-2.4 cm))/(3.0 cm)=7.2 cm`
where the positive sign means the image is upright.