Question

Can someone PLEASE help me with this question!?
A diverging lens of focal length -12cm projects the image of an object onto a wall. What is the object distance if the image is virtual, upright, and 80% of the object size? The answer is 3cm, but I am not sure how to get it. PLEASE HELP!

Answer 1

For lenses

1 1 1 v
-- = ----- - ----- and magnification = -------
f v u u

here

magnification is 80% = 0.8
so
0.8 = v/u
or
0.8v = u



1 1 1
---- = ----- - ------
-12 v 0.8v
12 12
-1 = ----- - -----
v 0.8v
12 120
-1 = ------ - -----
v 8v
96 - 120
-1 = ----------
8v

-8v = -24
v = -24/-8
v = 3