Finding height of image for a concave mirror

[chester89]

Ok, there's something I just don't understand. I know that to find the height of an image (hi), you need to use the magnification equation m = -di/do = hi/ho. And for this question, the focal length (f), distance of object (do), and distance of image (di) are given. Now, if I want to find the height of the image (hi), I would need the height of the object (ho) to finish the equation, but I don't, so now I'm stumpted on what to do with this question.

I know 'hi = -diho/do' is the equation but if I don't have ho, than how can I find hi.

Any help would be greatly appreciated.

 

[mezarashi]

Edited, misinterpretation.

I don't believe you can find the height of the image without the height of the object. The focal length and a given object distance will determind the image distance. No other focused distance is possible. We cannot arbitrarily choose some image distance.

 

[quicknote]

Hello, thank you for reaching out with your question. I understand your confusion with finding the height of an image for a concave mirror. Let me explain the process in more detail.

Firstly, the magnification equation m = -di/do = hi/ho is correct. However, in order to find the height of the image (hi), we do not necessarily need the height of the object (ho). This equation can also be rearranged to solve for hi, as shown below:

hi = -m * ho

This means that the height of the image (hi) is equal to the magnification (m) multiplied by the height of the object (ho). So, if the magnification is known, we can calculate the height of the image without knowing the height of the object.

In your case, if the focal length (f), distance of object (do), and distance of image (di) are given, you can use the formula 1/f = 1/do + 1/di to find the magnification. Once you have the magnification, you can use the above equation to find the height of the image.

I hope this helps clarify the process for finding the height of an image for a concave mirror. Let me know if you have any other questions. Keep up the good work in your studies as a scientist!