# Lateral magnification in mirrors, simple issue

In summary, the equation for calculating magnification with a spherical mirror depends on the conventions used for calculating coordinates. The standard convention is to use all lengths without signs and add signs according to whether the image is imaginary or real. However, different conventions may result in different formulas being used. It is important to clarify how lengths are measured, whether in terms of heights or distances from the pole of the mirror, to avoid confusion.
Homework Statement
An object at point p reflects in a convex or concave mirror at origin.
Given that m = 0.4 (lateral magnification), p = +30
The image is inverted. Find i (distance from orgin to reflected image).
Relevant Equations
m = -i/p
The equation gives us that
i = -mp = -0.4 * 30 = -12

Did I miss something here?

Well, you have to be careful with signs. Also it is important whether the mirror is convex or concave, that's not the same thing. Assuming it is convex, if your object is between the focus and the pole of the mirror, you will get an imaginary image, that is not inverted. If it is behind the focus, you get a real image and it's inverted. Magnification should always be defined as ## m = i/p##, where we take ##i## to be negative if the image is imaginary, and positive if it is real.

In case I'm using a term that's not used in English, what I mean by real image - it's image created at intersection of real rays that come from the object. Imaginary image is image created by extensions of rays(the real rays diverge but their extensions converge and the intersection is called imaginary image).

So in your case since you're told the image is inverted, you conclude that it is real, because imaginary image with spherical mirror is never inverted. And then you can get the right coordinate ##i## of the image.

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I agree with what you're saying except the formula in my book is m = -i/p, should I've used m = i/p then I'd get wrong answer on previous questions.
m and p are given with + or - signs infront of them, all I do is put them into the equation.

What you're saying is basically that if the image is inverted then m = -i/p isn't valid. But that formula is for 'lateral magnification produced by a spherical mirror' which is exactly what I'm calculating.

No, I'm saying that that formula depends on how you calculate those coordinates. So my formula basically uses all those lengths without signs and attaches signs according to whether the image is imaginary or real. That's the standard thing I've found in optics books. Your formula probably just uses a different convention, but I can't compare since I have no access to your literature.

That's why I gave you the principle, so you can understand if there's a difference in conventions.

Edit: Also there can be a confusion arising from whether ##i## and ##p## are heights of image and object, or their distances from the pole of the mirror. By similarity of triangles those quotients should be the same, but the sign convention can play a role there depending on how you calculate heights etc. In my definition I used horizontal distances, not heights.

For example, if you say that non inverted height of an object/image is positive, and inverted one is negative, then in this case, where you have inverted image, magnification would have that extra minus sign(in general it is defined as ratio of absolute heights of image vs object). So you need to take into account how you defined those lengths you measure in optics, that's the only issue here.

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## What is lateral magnification in mirrors?

Lateral magnification in mirrors is the ratio of the size of an object's image to the size of the object itself. It is a measure of how much larger or smaller an object appears when reflected in a mirror.

## How is lateral magnification calculated?

Lateral magnification can be calculated by dividing the image distance by the object distance. The image distance is the distance between the mirror and the image, while the object distance is the distance between the mirror and the object. The formula for lateral magnification is M = -d_i/d_o, where M is the magnification, d_i is the image distance, and d_o is the object distance.

## What is the difference between positive and negative magnification?

Positive magnification means that the image is upright and appears larger than the object. Negative magnification means that the image is inverted and appears smaller than the object. This is determined by the sign of the magnification value calculated using the formula M = -d_i/d_o.

## How does the distance between the object and mirror affect lateral magnification?

The distance between the object and the mirror affects lateral magnification because the closer the object is to the mirror, the larger the image will appear. This is because the image distance decreases while the object distance remains constant, resulting in a larger magnification value.

## How does the type of mirror affect lateral magnification?

The type of mirror, whether it is concave or convex, affects lateral magnification because it determines the curvature of the mirror and the way light is reflected. Concave mirrors produce larger and inverted images, while convex mirrors produce smaller and upright images. This means that the lateral magnification will be different for each type of mirror.

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