Locating the image for curved mirrors

Defining the Parts Focal point – where parallel light rays that reflect off a mirror come together. Principle axis– a line through the middle of the mirror. The bottom of the object always is touching the principle axis.

Defining the parts – cont’d Concave mirror Principle axis Focal point Center of curvature The center of curvature is twice the focal length. It is like the Center of a circle that makes the mirror.

How does a concave mirror reflect light? Parallel light rays that strike a curved mirror pass through the focal point. At each point on the mirror, the angle of incidence = angle of reflection Principle axis Focal point

Convex mirrors The rays from a convex mirror appear to come from a focal point inside the mirror.

So, how do we locate an image? There are four rays you can draw, but you only have to draw two – the third and fourth are optional. All rays will converge on the same place, and that is where the image will form. The easiest one to draw goes from the top of the object, through the center of curvature, and reflects on itself.

The first ray From the top of the object through the center of curvature. Cf

The second ray Draw the ray from the top of the object, parallel to the principle axis. When it reflects, it will go out through the Focal point. Say, “in parallel, out through focal point. Cf

You have already located your image!! Where these two rays meet, shows you where the top of the image is. Cf

The third ray (Extra Credit!!) Let’s make the other 2 rays lighter so they don’t interfere In through the focal point, out parallel. See, they still all meet up in the same place. Say, “in through focal point, out parallel. Cf

The Fourth Ray In through the vertex, angle of incidence = angle of reflection Cf When you draw this one, you should show your angle measurements.

Let’s draw the rays one at a time again. Cf 1. In and out through C 2. In parallel, out through f 3. In through f, out parallel 4. In through vertex, Angle of incidence = Angle of reflection

And where the four meet, there’s the top of your image (since that’s where all the light rays began. Cf

So how do we describe this image? It’s inverted – which means upside down It’s reduced – which means its smaller– you would show measurements to prove it. It’s real – which means it can be projected onto a screen – like the overhead projector. Cf

Is it always this easy? No. Here is another example: Ray 1- in and out through C Ray 2 – in parallel, out through the focal point But wait!! They won’t meet up!!! Bring back the reflected ray!

The refracted rays meet up inside the mirror This image is upright It is magnified – bigger – that’s how makeup mirrors work It is a virtual image – since it’s IN the mirror, It can’t be projected onto a screen

What about the extra rays? Ray 3 – In through the focal point, out parallel. Don’t worry if it misses the mirror, just extend the mirror and pretend it’s there. Now you know why it’s extra credit!!

Extra Ray 4 In through the vertex, angle of incidence = angle of reflection

Keep the four rays in mind– all begin at the top of the object. Ray 1 In and out through C Ray 2 In parallel, out through the focal point Ray 3 In through the focal point, out parallel. Ray 4 In through the vertex, angle of incidence = angle of reflection WRITE THE FOUR RAYS DOWN NOW!!!

We still draw the same four rays Ray 1: Straight through C and back. Remember, our focal point is inside the mirror. Ray 2 – In parallel, out through the focal point All rays inside the mirror should be reflected rays and should be dotted, since they are not real light rays Here is our image

How would you describe this image? Real/virtual? Upright/inverted? Magnified/reduced? virtual Upright reduced Virtual b/c it’s in the mirror Upright b/c it is above the axis Reduced b/c it is smaller than the original object

The Third ray In through the focal point, out parallel

The fourth ray? In through the vertex, angle of incidence = angle of reflection

Altogether In through the vertex, angle of incidence = angle of reflection

Now apply this If you are going to draw your own setups to practice –Use the edge of a protractor to make your mirror –Make a mark at 90 degrees and at the t-point where you line up the protractor. –The t-point is C, and the 90 deg mark is your vertex. Connect these two to make your principle axis. –Measure the halfway point between C and the vertex for your focal point.

vertex Center of curvature Principle Axis You can also flip the Protractor the other Way around and do the Same thing