When a butterfly lands 12 cm from a concave mirror, it's image is 18 cm behind the mirror.
Find the focal length
1/f=(1/do)-(1/di)
1/f=(1/12)-(1/18)
1/f=0.0833-0.0555
1/f=0.0277
f=36
I'm pretty confident w/ my math but as I understood, it's do-di if it's behind the mirror, which it is, & f is also negative if it's behind the mirror. So my question is, is it not always negative? or do I make 36 negative to show that it's in the other direction?
Thanks a bunch :)
If you are using this convention:
https://apps.spokane.edu/InternetContent/AutoWebs/AsaB/Phys103/MirrorsThinLens.pdf
then your calculations are correct
di=-18
do=+12
1/12-1/18=1/36
=> f=36 cm
Ok thank you :)
You're welcome!
Great job on solving the equation and finding the focal length! Your calculations are correct, and you have found the focal length to be 36 cm.
Now, let's address your question about the sign convention for the focal length. In the equation 1/f = (1/do) - (1/di), the sign convention for the distances is as follows:
- The object distance (do) is positive when the object is located in front of the mirror.
- The image distance (di) is positive when the image is formed in front of the mirror.
- The focal length (f) is positive for a concave mirror and negative for a convex mirror.
In your case, the object distance (do) is positive because the butterfly is located in front of the mirror. The image distance (di) is positive because the image is formed behind the mirror, which is considered the positive direction in the sign convention.
So, since you have found f = 36 cm (positive), it means that the focal length of the concave mirror is 36 cm and the image is formed behind the mirror.
Therefore, you do not need to make the value of 36 negative in this case. It is a positive value and indicates the distance from the mirror to its focal point.
I hope this clarifies your question! Let me know if there's anything else I can help you with.