Diverging lens problem -image should be between focus & optical centre

1. Aug 17, 2013

s3a

1. The problem statement, all variables and given/known data
Problem:
An object 2.0 cm high is placed in front of a diverging lens of focal length 1.8 cm.

The object is 2.7 cm from the optical centre of the lens.

Questions:
1) Where is the image located with respect to the focus and the optical centre of the lens, qualitatively?

2) Is the image upright or inverted?

3) Is the image real or virtual?

4) Is the image larger or smaller than the object?

1) The image is located between the focus and the optical centre of the lens.

2) The image is upright.

3) The image is virtual.

4) The image is smaller than the object.

2. Relevant equations
$1/f = 1/d_o + 1/d_i$
$h_i/h_o = -d_i/d_o$

3. The attempt at a solution

Modifying $1/f = 1/d_o + 1/d_i$, I get:
(1/(1.8 cm) – 1/(2.7 cm))^(-1) = 5.4 cm = $d_i$

Doesn't that mean that the image should be 5.4 cm – 2.7 cm = 2.7 cm to the left of the object instead of between the focus and the optical centre of the lens?

I'm assuming there's something wrong with the numbers because if what I am reading from this book is correct, the image of a diverging lens should always be between the primary focus and the optical centre, regardless of where the object is located.

Could someone please tell me what I am doing wrong?

Any input would be greatly appreciated!

2. Aug 17, 2013

technician

The lens is diverging.....do you know what this means regarding focal length value?

3. Aug 17, 2013

s3a

Oh! Is it that the focal length is negative such that the distance of the image from the optical centre is -1.08 cm or 1.08 cm leftward of the optical centre?

4. Aug 17, 2013

besulzbach

Exactly. The focus, in this problem, is -1.8cm.

5. Aug 17, 2013

technician

You have got it. You first attempt was for a converging lens

6. Aug 17, 2013

s3a

Alright. Thank you (both) very much! :D