What is the minimum size of a mirror for a person to see their whole image?

[rambo5330]

Homework Statement

Quick question I can visualise but not determine mathematically..
The question in my text says:
Determine the MINIMUM size of a flat vertical mirror that a person 178 cm can see his whole image. It suggest that a ray diagram will help.

The Attempt at a Solution

well I could tell that the mirror should be less than the total 178 cm.. but even with the use of a ray diagram i keep getting a 1 to 1 thing going on... if object height equals 178cm and image height equals 178cm...my only thoughts are with the use of a ray diagram i guess there must be some critical for the reflected rays i should be looking for?

 

[zhermes]

Excellent and classic question.

In your ray diagram, don't worry about the size of the image (per se). The mirror has to be big enough so that all of the required light rays pass through the mirror.

Maybe, try drawing a stick-figure person, in front of a flat mirror. Draw the rays so that the person can see their feet and the top of their head (from their eyes--of course). Where do those rays bounce off of the mirror?