Confused about image size in plane, concave, or convex mirrors

In summary, based on the equations given, when an object is placed in front of a concave or convex mirror with the same focal length, the magnification (m) is always smaller than 1. This means that the image produced by both mirrors would appear to be about the same size. However, if a plane mirror is used instead, the magnification (m) would be 1, resulting in a larger image compared to the concave or convex mirrors. This is because a plane mirror does not have a curvature, unlike the other two types of mirrors.
  • #1
lowellite
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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...)
 
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  • #2
Yes to all.
 

Related to Confused about image size in plane, concave, or convex mirrors

1. What is the difference between image size in a plane mirror versus a concave or convex mirror?

In a plane mirror, the image size remains the same as the object size. In a concave mirror, the image can be either larger or smaller than the object depending on the distance between the object and the mirror. In a convex mirror, the image is always smaller than the object.

2. Why does the image in a plane mirror appear to be the same distance behind the mirror as the object is in front of it?

This is due to the law of reflection, which states that the angle of incidence (the angle between the incident ray and the normal line) is equal to the angle of reflection (the angle between the reflected ray and the normal line). This creates a virtual image that appears to be behind the mirror at the same distance as the object is in front of it.

3. How does the curvature of a concave or convex mirror affect the size of the image?

The curvature of the mirror affects the focal length, which is the distance between the mirror and the focal point. A more curved mirror will have a shorter focal length, resulting in a larger image for objects placed further away from the mirror. A less curved mirror will have a longer focal length, resulting in a smaller image for objects placed further away.

4. Can the size of the image in a mirror be controlled?

Yes, the size of the image can be controlled by adjusting the distance between the object and the mirror (for concave and convex mirrors) or by changing the curvature of the mirror (for concave and convex mirrors). The size of the image can also be affected by the size of the object and the angle at which it is placed in front of the mirror.

5. How does the position of the object in relation to the focal point affect the size of the image in a concave mirror?

If the object is placed beyond the focal point, the image will be smaller than the object. If the object is placed between the focal point and the mirror, the image will be larger than the object. If the object is placed at the focal point, the image will be infinitely large. This is known as the principle of conjugate foci.

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