Mirror question

[Jwinsler7]

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A woman of height h can see her entire body in a flat mirror. What's the minimum length of the mirror?

A. 1/4 h
B. 1/2 h
C. h
D. Any mirror will work depending how far woman stands

My guess was D. But the correct answer is B. Why does a flat mirror have to be 1/2 h?

 

[cloak25]

Going to take a guess on this.

When the woman looks into the mirror, her image will be on the other side of the mirror with the same distance the real woman is to the mirror. So if the woman's distance from the mirror is x, her image will be a distance of 2x away from her.

assuming magnification of mirrors is 1, you can use m = i/o = hi/ho where hi = mirror's height and ho = height of woman.

m = 2x/x = hi/ho
m = 2 = hi/ho

but this is wrong though because you would get 2ho.....?????

 

[Jwinsler7]

Going to take a guess on this.

When the woman looks into the mirror, her image will be on the other side of the mirror with the same distance the real woman is to the mirror. So if the woman's distance from the mirror is x, her image will be a distance of 2x away from her.

assuming magnification of mirrors is 1, you can use m = i/o = hi/ho where hi = mirror's height and ho = height of woman.

m = 2x/x = hi/ho
m = 2 = hi/ho

but this is wrong though because you would get 2ho.....?????

With your logic, di and do would be the same, wouldn't it? I am inclined to say that di is the distance from the image to the mirror, not the distance from woman all the way to the image.

 

[thelullaby99]

A woman of height h can see her entire body in a flat mirror. What's the minimum length of the mirror?

A. 1/4 h
B. 1/2 h
C. h
D. Any mirror will work depending how far woman stands

My guess was D. But the correct answer is B. Why does a flat mirror have to be 1/2 h?

Apparently it's a well known fact, and should be memorized, that the required length of a plane mirror to view one's own entire image is h/2 😱 (after some googling)

 

[Eastfolding]

Draw a picture! A mirror on the wall, and a little lady standing in front of it.

First of all, how do you see yourself in the mirror? Light bounces off your body, and then bounces off the mirror into your eyes.

So let's think about this. In order to see your feet, there must be enough mirror so that light will be able to bounce off the wall and into your eyes. Also, because of snell's law, we know that the angle of incidence = angle of reflection. So if the light originates at your feet, where must it bounce off the wall so that it can get into your eyes?

Since Incidence = Reflection and assuming you're standing perfectly straight, the vertical distance traveled before the light hits the mirror must be the same as the vertical distance traveled after it hits the wall. Thus, it must bounce right in the half way point between the floor and the top of your head. thus, mirror = h/2

 

[richkaj]

The distance of the object is the same distance as the image behind the "plane" mirror. A person standing in front of a plane mirror can see her whole reflection because she is seeing twice her distance. The mirror only has to be 1/2 her height to see herself from head to toe.

 

[Pigglyjuff]

Can someone explain this in a MS Paint picture 🙂

 

[richkaj]

I hope this helps... Just imagine if you were the chess pieces. You are x away from the mirror as an object but also the image is x away. The true distance would be 2x from object to image. The person only needs 1/2 a mirror to see her entire body...

 

[abhik143]

In order to view his image, the man must look as low as point Y (to see his feet) and as high as point X (to see the tip of his head). The man only needs the portion of mirror extending between points X and Y in order to view his entire image. All other portions of the mirror are useless to the task of this man viewing his own image.

The diagram depicts some important information about plane mirrors. Using a cm-ruler, measure the height of the man (the vertical arrow) on the computer screen and measure the distance between points X and Y. What do you notice? The man is twice as tall as the distance between points X and Y. In other words, to view an image of yourself in a plane mirror, you will need an amount of mirror equal to one-half of your height. A 6-foot tall man needs 3-feet of mirror (positioned properly) in order to view his entire image.