Date: Thu, 24 Jul 1997 10:13:26 -0700
From: Dan Gray <dgray@justin-siena.napanet.net>
To: pinhole@exploratorium.edu
Subject: Re:Reflecting on reflections
Dave:
You are quite right. The horizontal distance makes no difference to the
size of a mirror needed to reflect yourself. Think about it this way:
Light must travel from your toes to your eyes in order for you to see
your toes. At the half way point of the light's journey, it will be
half way up between your toes and eyes. This half way point is where
the mirror is located, since half of the light's journey is travelling
to the mirror and half is travelling from the mirror back to you. So no
matter how far away the mirror is, the light (from your toes) that
bounce off of the mirror at a point that is half way up from your toes
to your eyes is the light that will reflect into your eyes. The same
works for the light from the top of your head. It will travel half way
down from the top of your head to your eyes, hit the mirror, then travel
the rest of the way down to your eyes. So the minimum height of the
mirror = 1/2 toe to eye distance + 1/2 eye to top of head distance.
Since half of part of your height + half of the rest of your = half of
all of your height, the mirror needs to be at least 1/2 of your height.
For example, let's say you are 88 cm in height and your eyes are located
80 cm above your toes and 8 cm below the top of your head. The light
from your toes that hits the mirror 40 cm below your eyes, will reflect
into your eyes. The light from the top of your head that hits the mirror
4 cm above your eyes, will reflect into your eyes. So the mirror's total
minimum height = 44 cm.
There are a couple of ways to shorten the needed mirror height: Use a
convex or concave mirror, or lean toward or away from a plane mirror,
but these violate the parameters of the problem, don't they?
The example of the moon that was given also violates the requirements of
the problem in that the reflection must be that of the observer, not
some other object. Not to mention that the mirror in a reflecting
telescope is concave, not planar.
Dan Gray
dgray@justin-siena.napanet.net
http://justin-siena.napanet.net/dgray/danhome.htm
Pinhole Listserv wrote:
>
> A question of reflection to reflect upon.
>
> I was presenting an elementary teacher workshop on light reflection today
> and asked the questions: "How tall must a (normal) mirror be, mounted flat
> against the wall, in order for a person to see their whole body (head to
> toe)? Does the distance from the mirror play a role?"
>
> I maintained that the distance away from the mirror does not matter, that
> the height of the mirror must be approximately one-half the person's
> height, and that the top of the mirror should be approximately level with
> the top of the person's head.
>
> We seemed to find this answer suitable through experimentation with
> different size mirrors and distances away from the mirror. However, there
> were two high school physics teachers in the room who insisted that
> distance DOES matter, one giving the example of looking through a relector
> telescope and being able to see the moon (and comparing that to my mirror
> question) and, that if a person looks in a mirror s/he can observe the
> entire moon, which is very large, because it is so far away, so odstance
> MUST matter. I think THEY have the misconception, but I'm not sure and
> intuitively we are all experiencing cognitive conflict even after "seeing"
> the evidence. They maintained that if we got a mirror far enough away from
> the observer then the only problem with the observer seeing his/her whole
> body in the mirror would be our inability to see oneself from such a great
> distance (they suggested using binoculars to look back at your reflectin in
> the mirror!)
>
> I think their responses are addressing a different question, but couldn't
> argue against their position on the spot. I'd like to know what advice
> pinhole folks have to offer. I am presenting this workshop 'till Friday and
> if I could get your responses on Thursday, I could share them with the
> teachers. We all want to know!
> Thanks!!!
> Dave Nickles
>
> *****************************
> Dave Nickles
> Science Education
> 177 Chambers Bldg.
> Penn State University
> University Park, PA 16802
> 814-863-1691 (office)
> 814-861-2093 (home)
> dan7@psu.edu
> personal homepage is http://www.personal.psu.edu/users/d/a/dan7/
>
> Thought of the Week:
> The Genesis of Ideas
> "Some weeks or months go by, and then, suddenly, an idea that represented a
> solution to the problem or the germ of a solution to the problem would
> burst into my unconsciousness."
> Linus Pauling (1963)
> **********************************************************