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
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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