How far from a converging lens with a focal length of 15 cm should an object be placed to produce a real image which is half the size of the object?
How do you solve this?
Thanks!
M = -1/2 = - di/do
di = 1/2 do
then
1/15 = 1/(0.5 do) + 1/do = 3/do
do/3 = 15/1
do = 45 cm
Old Science Guy gave you this.
To solve this problem, we can use the lens formula:
1/f = 1/v - 1/u
Where:
f = focal length of the lens
v = image distance
u = object distance
We are given the focal length of the lens, which is 15 cm. We also know that the image formed is real and half the size of the object. This means the magnification (m) is -1/2 (since it is a real image). Magnification is given by the equation:
m = -v/u
Now let's substitute the given values in the magnification equation:
-1/2 = -v/u
From this, we can say that v = u/2.
Now substitute this value of v in the lens formula and solve for u:
1/f = 1/v - 1/u
1/15 = 1/(u/2) - 1/u
1/15 = 2/u - 1/u
1/15 = 1/u
u = 15 cm
Therefore, the object should be placed 15 cm from the lens to produce a real image that is half the size of the object.