Image size in plane, concave, or convex mirrors

[powerof0]

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So I know these equations

1/f = 1/p + 1/i
m = -i/p

f: focal length
p: object distance from mirror
i: image distance from mirror
m: magnification

Let's say that I have an object in front of a concave or convex mirror with the same |f|. p is much larger than the radius of curvature. Based on the equations above, |m|<1. Also, |m| should be nearly same for both mirrors. Does this mean that the images produced by the two mirrors would appear to be about the same size?

Also, if I replace the concave or convex mirror with a plane mirror (while keeping p the same), |m| would be 1 for the image. Does this mean that the image produced by the plane mirror would appear to be larger than the image produced by the concave/convex mirrors?

(I tried to check this using a spoon, but the spoons I have are not very reflective...)

 

[milski]

Well, you need a silver spoon for experiments like that. 😉

Your conclusions are correct - the images from concave/convex mirrors will be smaller and about the same size to each other. Flat mirror will get you a larger image.

The only difference is that the image from the concave mirror will be inverted and the other two will not.


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[powerof0]

Thanks so much, milski!

If you (or anyone else viewing this thread) have time, would you mind explaining the concept of magnification a bit more? It seems like magnification is defined as "the ratio of the height of the image to the height of the object." However, I'm not sure how this works because if an object that is 1 m tall is placed very far away from a plane mirror, its image will not appear to be 1 m tall. However, plane mirrors have a magnification of 1... It seems that I am missing something...

 

[milski]

You have to account for the distance to the image. Whenever you are talking about a image like that, it is projected at a certain distance from the observer. For example, the image in the plane mirror case will be at twice as for from the observer as is the mirror.

When talking about magnification you are really comparing the size of the image with how big the object would look if it was that far away. So if the mirror is 10 m away from you, your image in the mirror will look as big as you would look if somebody was looking at you from 20 m away.

 

[powerof0]

Thanks for explaining. So for a concave mirror and object for which m = 0.5 and i = 1 (just making up random numbers), the image would appear to be an object that is 50% smaller than the real thing and located at a distance of 1 m in front of the mirror. For a convex mirror with the same |f|, then the image would appear to be an object that is 50% smaller than the real thing and located at a distance of 1 m behind the mirror. Is this right?

If there is an observer in front of the mirror, would the convex mirror image appear to be smaller than the concave mirror image? Since the convex mirror image is located behind the mirror, it is farther away from the observer than the concave mirror image, which is in front of the mirror. This would seem to indicate that the concave mirror image is bigger, but this does not appear to be the case in real life...

Sorry for not understanding this still!