Image in a Plane Mirror

What happens when you see and object?

You see a point on an object when your eye detects rays of light diverging from that point.

You already know the law of reflection, that

angle of incidence = angle of reflection

Now, we will apply that to all the rays that leave point O on the object and strike a mirror.

In particular, we will look carefully at the rays that leave O and strike the mirror at points P and Q. Notice that the object O is located at a distance d_o from the mirror; this is called the "object distance".

All the rays of light strike the mirror and are reflected according to the Law of Reflection,

angle of incidence = angle of reflection

Now extend those reflected rays back to see where they intersect. This is the image point I. The reflected rays of light look likethey are diverging from this point. And that is just the criteria we need to "see" something. When we detect rays diverging from point I, our eyes and brain conclude that there is something there for us to see. That is what an image is or what having an image means. Notice that the image is located behind the mirror a distance d_i; this is called the image distance.

Now look at the right triangles OPQ and IPQ,

FF

For a plane mirror, the image distance is equal to the object distance; that is,

d_i = d_o

The image is just as far behind the mirror as the object is in front of the mirror.

Reflections from the smooth surface of a lake or a reflecting pool behave just as from a mirror.

How many images are produced by two mirrors placed at 60° to each other?

Symmetry is an important aspect of Physics. Symmetry will often allow an easy solution to an otherwise difficult problem. Instead of looking at all the individual rays and their reflections, we will apply symmetry to this problem.

Object O is place between Mirror #1 and Mirror #2. Rays that undergo a single reflection on Mirror #1 produce image I₁; a single reflection from Mirror #2, image I₂. Mirror #1 produces an image of Mirror #2; this is labeled M₁₂. There is an image in that mirror, I₁₂. That image is the result of two reflections--from Mirror #1 and then Mirror #2. Likewise, image I₂₁ is also the result of two reflections from Mirror #2 and then Mirror #1. Three reflections are also possible and produce one more image, labeled I₁₂₁ or I₂₁₂. This is the principle of a Kaleidoscope. Each point on the object appears as five images for a total of six things to look at!

Remember that images in a mirror are "flipped" left for right,

 

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(c) Doug Davis, 2002; all rights reserved