Image size in concave mirror

[roam]

Homework Statement

An object 23.0 mm high is 31.0 cm away from a concave spherical mirror with a radius of curvature of 54.0 cm. What is the absolute size of the image?

Homework Equations

Maybe these are relevant

Mirror equation in terms of focal length:
$$\frac{1}{p}+\frac{1}{q}=\frac{1}{f}$$

Magnification of image:
$$M=\frac{h'}{h}=-\frac{q}{p}$$

The Attempt at a Solution

I have already calculated the distance of the image from the mirror to be 209 cm. But how do I calculate the size of the image? Is there a special formula or do I need to use some kind of trigonometry? I had no luck using the trying the above equations...

The correct answer must be 155.

 

[ehild]

Explain the notations you used: What is p and q and f? And what is a concave mirror? What about the signs of p,q and f? How is f related to the curvature of the mirror?
You know both the image distance and the object distance. How are they related to the ratio of the image height to the object hight?

ehild

 

[roam]

Explain the notations you used: What is p and q and f? And what is a concave mirror? What about the signs of p,q and f? How is f related to the curvature of the mirror?
You know both the image distance and the object distance. How are they related to the ratio of the image height to the object hight?

ehild

Thank you! I got the right answer using the ratio $$\frac{h'}{h}=-\frac{q}{p}$$, but I had to exclude the minus '-' sign. Is that because the resulting image is upright (not inverted)?

 

[ehild]

The real image is inverted (h' is negative), the virtual image is upright (h' is positive). The image distance is positive when the image is real, and negative when the image is imaginary. You got q=209, a positive number, so h'/h was negative, h' negative, the image was real. To get the absolute size, you have to take the absolute value of h'.

ehild

 

[rwisz]

4 mm.



To calculate the absolute size of the image, you can use the magnification equation M=-q/p, where q is the image distance and p is the object distance. In this case, q is 209 cm and p is 31.0 cm. Plugging these values into the equation, we get M = -209/31 = -6.7419. This means that the image is about 6.7419 times larger than the object. To find the absolute size of the image, we can multiply the magnification by the object size. So, the absolute size of the image is 6.7419 * 23.0 mm = 155.4 mm. This is the same as the correct answer provided. Therefore, the absolute size of the image in this scenario is 155.4 mm.