Question

(For Medals)
2. A lens has a focal length of +20cm and a magnification of 4. How far apart are the object and the image?

Answer 1

The equation for magnification is:

\[M=-{i \over o}\]
I'm just going to use i instead of d(i) and o instead of d(o) to make it easier to type out.

Since the focal length is positive, we're dealing with a converging (convex) lens.
Since, according to the equation above, -i/o = 4, meaning i=-4o, the image is 4 times further away from the lens and virtual (i.e. on the same side of the lens as the object).

Now we can plug these values into the lens equation and solve:

\[{1 \over f}={1 \over o}+{1 \over i}\]\[{1 \over f}={1 \over o}-{1 \over 4o}\]
Solve for o to to get the distance of the object from the lens. Then, plug that value into i=-4o to find the distance of the image from the lens. Finally, find o-i to get the distance between the object and the image.

Answer 2

So then would the formula that has to be used would be
d(o)- 1/ (1/f)-(1/d(i))
So then 1/ (1/20) - (1/(-4))

Answer 3

So what's your final answer for d(o)?

Answer 4

I get d(o) to be 3.333 cm

Answer 5

Hmm that's not what I got - check your math

Answer 6

Hmm because I get (1/20)-(1/-4) to equal 0.3.
Then I put that under 1 so it will be (1/0.3) which then equals to 3.333 *I'm using a TSI calculator that we have to use for physics ><

Answer 7

If you multiply the entire equation I wrote above by o, you get:

\[{o \over f}={o \over o}-{o \over 4o}\]\[{o \over 20}=1-{1 \over 4}\]\[{o \over 20}={3 \over 4}\]\[o=15\]

Does that make sense? And if the object distance is 15, what is the image distance?

Answer 8

Would it be -60?

Answer 9

Right! but remember, the negative symbol for the image indicates it's on the SAME side of the lens as the object (it's virtual). So, the object is 15 cm away from the lens, while the image is 60 cm away from the lens, on the SAME SIDE. So what's the distance between the image and the object?

Answer 10

45?

Answer 11

Yup!

Answer 12

Ok then thank you once more *^*

Answer 13

No problem!