How Much Can a 6ft Man See of His Image in a Mirror?

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In summary, a 6ft tall man standing 4ft away from a mirror 4ft above the ground can only see an image of himself that is 4ft below his head. This is due to the laws of geometric optics, where the angle of reflection is equal to the angle of incidence. The distance between the man and the mirror does not affect the image he sees.
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SAWiz
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A 6ft tall man stands in front of a mirror (2ft tall)
The mirror is 5ft away from the man and 4 ft above the ground.
How much of his image can he see?



A 6ft tall man stands in front of a mirror (2ft tall)
The mirror is 10 ft away from the man and 4 ft above the ground.
How much of his image can he see?
 
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By the laws of geometric optics the angle of reflection is equal to the angle of incidence. Both are measured to the normal (an imaginary line perpendicular to the mirror).

The 6ft tall man looks at the bottom of a mirror 2 feet below his head. Therefore a light ray entering his eye needs to have an angle of reflection of arctan(2/5). If you draw this out it becomes clear that the image that appears in the bottom of the mirror is a point 4 ft below the man's head.

Do the same as above for the next part and prove to yourself that it doesn't matter how far the man stands away from the mirror. He still can only see 4 ft below his head. (You can demonstrate this using a bathroom mirror).
 

1. How does the height of a person affect what they can see of themselves in a mirror?

The height of a person does not directly affect what they can see of themselves in a mirror. However, it may affect the angle at which they are viewing themselves, which can impact their perception of their image.

2. Does a taller person see more of themselves in a mirror compared to a shorter person?

No, the amount of a person's image that they can see in a mirror is determined by the size of the mirror and the distance between the person and the mirror, not their height.

3. How much of a person's image can a 6ft man see in a mirror?

This depends on the size of the mirror and the distance between the man and the mirror. Generally, a 6ft man standing about 2 feet away from a standard-sized bathroom mirror (3ft x 2ft) can see about 2/3 of their body in the mirror.

4. Does the angle of the mirror affect how much a person can see of themselves?

Yes, the angle of the mirror can impact the perception of a person's image. For example, a person standing directly in front of a mirror will see a more accurate reflection compared to someone standing at an angle where their reflection may be distorted.

5. Can a person see their entire body in a mirror if they are 6ft tall?

It is unlikely that a person can see their entire body in a mirror if they are 6ft tall, as most standard-sized mirrors are not tall enough to accommodate a person's full body length. They may be able to see most of their body, but certain areas such as the top of their head may not be visible.

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