Extremely simple spherical mirrors question

[Jim Kata]

Homework Statement

A 3cm tall object is a distance 24cm from the center of a mirror, the focal distance is 6cm from the center of the mirror. What is the images distance from the center of the mirror?
How tall is the image?

Homework Equations

The Attempt at a Solution

Since the object's distance is further away than the focal length you know that the image is real so the sign on i, the image distance is positive

1/24 + 1/i = 1/6

1/i = 3/24 = 1/8

i = 8cm

The magnification is m = -8/24 = -1/3

So the height of the image is 3cm(-1/3) = -1cm.

Is this right?

 

[anathema]

I would like to confirm that your solution is correct. Your use of the thin lens equation (1/f = 1/o + 1/i) and the magnification equation (m = -i/o) are both accurate and appropriate for solving this problem. Based on your calculations, the image distance is indeed 8cm from the center of the mirror, and the image height is -1cm. This makes sense since the image is inverted and smaller than the object. Keep up the good work!

 

[ogb p]

I would say that your approach and calculations are correct. However, it is important to note that the image distance and height are negative, indicating that the image is inverted. Additionally, the image height is smaller than the object height, which is expected in a concave mirror. Overall, your solution is accurate and demonstrates a good understanding of the principles of spherical mirrors.