A woman stands 1m in front of a plane mirror. What is the magnification and distance from the woman to her mirror-image?

- 1/2 and 2m
- 1 and 1m
- 2 and 1m
- 1 and 2m

**Explanation**

A flat plane mirror has a radius of curvature that is infinite (it doesn’t curve!) and thus a focal point distance that is also infinite. Thus the equation 1/f = 1/object + 1/image can be simplified to 1/object = -1/image

So a flat plane mirror will always have an image distance that is equal to the object distance. The negative sign tells us that the image is virtual. Using the equation m = -i/o we can also see that a flat plane mirror will always produce an object with a magnification of 1. That is, when you look at yourself in the bathroom mirror, your image is not magnified nor reduced.

If a person is standing 1 m in front of their mirror, then the image will be 1 m away from the mirror as well (“inside” the mirror). So the total distance between the person and the image will be 2 m.

- 1/2 and 2m, incorrect, Uses image distance of 2m rather than 1m and inverts the magnification equation.
- 1 and 1m, incorrect, Does not sum object and image distance for distance between woman and image.
- 2 and 1m, incorrect, Uses image distance of 2m in magnification equation and distance from woman to image also incorrect.
- 1 and 2m, correct.

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Moare explanation with the questions would be nice.

**equations

Of course! Let’s go in order and talk through the equations here:

First, we have the simplification of our standard thin lens equation. Note that we aren’t given certain pieces of information here, like the focal length of the mirror (which we would typically need). However, since we’re dealing with a plane (flat) mirror, the focal length is infinite – the mirror doesn’t curve, so it has an infinite radius of curvature and thus an infinite focal point. The explanation dropped the 1/f term and moved the 1/i term to the other side of the equation.

Next, m = -i/o is the equation for magnification, which is helpful to know. It allows us to calculate the magnification of the final image by using the ratio of image distance to object distance.

Now, let’s actually calculate our answer. We now have the simplified equation 1/object = -1/image. Better yet, we have the object distance – 1 meter. Plugging that in, we find that the image distance is -1 meter, meaning that it is a meter behind the mirror. Since the woman was positioned in front of the mirror, she is a total of 2 meters from her image.

Last of all, we find the magnification. m = -i/o, so m = -(-1 m) / (1 m). Our magnification is simply 1, so the woman’s image is the same size as she is.

Why do we have a virtual image? Why did we consider 1/object= -1/image? I am trying to figure out things.

Sure, I appreciate the questions ðŸ™‚ A plane (flat) mirror ALWAYS produces a virtual image. With mirrors, that means the image is always located behind the mirror. Imagine looking in a flat bathroom mirror – where do you see your image? You see yourself as if you’re standing “behind” the mirror. You can also tell that an image is virtual if the sign of “i” (the image distance) is negative, which it is here.

Now, back to the 1/object = -1/image. Do you remember the typical thin lens equation? It’s 1/f = 1/i + 1/o, and it’s DEFINITELY important to know for the MCAT. But our problem here is that we don’t have “f” (focal length). So, how do we find it?

Well, focal point comes from a measurement known as radius of curvature. Focal length = 1/2 (radius of curvature), to be exact. Think of a curved mirror or lens. Take the curve of that mirror or lens and extend it to form a circle / sphere. The radius of that circle/sphere is the radius of curvature, and the focal length is HALF of that value.

Now, we don’t have to do any of that here. Why? Because our mirror is a plane mirror. It’s flat! So it doesn’t have a curve at all, and thus, it’s focal point is infinite. We can extend that mirror as far as we want, and it’ll never form a circle.

Back to our equation – we now have 1/(infinity) = 1/i + 1/o. Well, what is 1/(infinity)? It’s zero, or at least very, very close to zero, because the denominator is infinitely large. So, we can simplify to 0 = 1/i + 1/o, and -1/i = 1/o.