How do you find the width needed for a plane mirror

[angiep410]

Homework Statement

a) You wish to have a plane pocket mirror that is as discreet as possible but with which you can see the whole width of your face. If your face is 23.0 cm wide, what is the minimum width, in cm, of the mirror for you to be able to see the whole width of your face in one eye?

b) What would be the minimum width of the mirror if you are willing to accept that you must use two eyes to see the full width of your face? (Take the distance between the centers of your eyes to be 6.60 cm.)

Homework Equations

I know that for a plane mirror the height needs to only be half the height of the person, but I haven't learned about width.

The Attempt at a Solution

I think part a's answer is 11.5 cm because that is half the width of the face and for the height you only need half the distance, but I don't know if that's right

 

[BruceW]

That is the correct answer for part a), but you should probably find out the reason behind it. Would your teacher expect you to use reasoning based on the rules of reflection of light? Or is it OK to just use the rule that the height of the mirror only has to be half the height of the object?

 

[angiep410]

I would like to know the reason behind it and how to solve part B

 

[BruceW]

Well, you know the rule for reflection of a ray of light from a flat mirror? (What are the angles of the incident and reflected ray?)

 

[angiep410]

They aren't given. All that is given is what I have posted

 

[BruceW]

Its a general rule, I'm sure you must know it. (Or I don't know why your teacher would have given out this problem).

To explain more clearly: I am talking about two angles. First: the angle between the incident ray and the normal to the mirror. Second: the angle between the reflected ray and the normal to the mirror. There is a very simple rule about these two angles.

 

[angiep410]

The angle of incident=the angle of reflection

 

[BruceW]

That's the one :) In fact, that is the only equation you need. You need to draw a picture of the situation (where the person's eye is effectively a point), and using the equation, you can work out the area which can be viewed when he uses a given mirror size.

 

[angiep410]

Ah! That makes sense. But how do I find part B since I'm trying to find the width of the mirror?

 

[BruceW]

You are finding the minimum width of the mirror (while still being able to see his whole face) for part A and B. The only difference is that in part B he has two eyes.

 

[angiep410]

So would it still be 11.5?

 

[BruceW]

no, he has two eyes now. You should draw the situation again, keeping in mind that light going into both eyes contributes to the picture he is able to see.

 

[angiep410]

I drew the picture, but I don't think I did it right. Would it be 18.1?

 

[BruceW]

That's not the correct answer. I'm really sorry, but I'm off to the pub now, I won't be replying for a while. I hope you figure it out!

 

[BruceW]

Did you find out the answer to part b yet? What is your picture like?