Concave mirror image distance with 24mm object at 12cm

[mhl2188]

Hello, here is the problem i am having trouble with. The sun falls on a concave mirror and forms an image 3 cm from the mirror. If an object 24mm high is placed 12 cm from the mirror, where will its image be formed? So far, i have decided that since 1/f = 1/do + 1/di...
1/f = 1/do + 1/3 = 1/12 + 1/di
I also decided that hi/2.4 = -di/12... The problem is...even if i solve for di in terms of hi and plug that into my first equation i don't have enough information to solve for do. I am stuck and this problem is due tomorrow... please help
thanks
mhl

 

[OlderDan]

Hello, here is the problem i am having trouble with. The sun falls on a concave mirror and forms an image 3 cm from the mirror. If an object 24mm high is placed 12 cm from the mirror, where will its image be formed? So far, i have decided that since 1/f = 1/do + 1/di...
1/f = 1/do + 1/3 = 1/12 + 1/di
I also decided that hi/2.4 = -di/12... The problem is...even if i solve for di in terms of hi and plug that into my first equation i don't have enough information to solve for do. I am stuck and this problem is due tomorrow... please help
thanks
mhl

You need to use the "sun" information to find the focal length of the mirror. The sun is an object at distance ___________ that forms an image at 3cm. What is f?

 

[thepatientmental]

Hello mhl,

Thank you for reaching out for help with your problem. It seems like you have made some progress in understanding the problem and utilizing the lens/mirror equation 1/f = 1/do + 1/di. However, you are correct in realizing that you do not have enough information to solve for do.

To solve this problem, we need to use the magnification equation, m = -di/do = hi/ho. This equation relates the height of the image (hi) to the height of the object (ho) and the distances of the image (di) and object (do) from the mirror or lens.

Since we know the height of the object (24mm) and the height of the image (3cm = 30mm), we can set up the equation as follows:

m = -di/do = hi/ho
m = -30/do = 30/24
m = -5/4

Now, we can use this value of m to solve for do:

m = -di/do
-5/4 = -30/do
do = 24 cm

Therefore, the object must be placed 24 cm away from the concave mirror in order to form an image 3 cm away from the mirror. I hope this helps and good luck with your assignment!