All rays of light obey the laws of reflection when the strike a surface a mirror is just another surface.
A) Angle of incidence = angle of reflection
B) Incident ray reflected ray and Normal lie in the same plane.
This is a convex mirror so the centre of curvature lies behind the mirror
1) Any ray striking a surface normally comes back along its own path so all rays going in as if they were going to reach the centre of curvature are reflected back along their own path ---- radius is always normal to the surface of a circle.
2) All rays close and parallel to the principal axis will be reflected so that they appear to come from a point behind the mirror --- the focal point. This is called a virtual point since the rays don't actually come from it.
3) All incident rays going towards the mirror as if they were going to reach the virtual focal point will be reflected parallel to the PA (principal axis)
Finding the Centre of curvature & focal point is possible as follows:
A darkened room is essential!
You will need a ray box with a screen surrounding the pinhole; the pinhole will have to be the same height as the centre of the mirror, mirror holder, meter stick graph paper and pencil.
Place a large sheet of graph paper on the bench.
Draw a long straight line to represent the PA.
Mark and position the the mirror at right angles to the PA about half way along.
Draw a line at right angles to the PA at this position. Mark two intervals of 5mm along this line on either side of the pa.
Put the mirror in place at right angles to the PA
Use the ray box to direct a ray of light towards the mirror to strike it at the first interval from pa; adjust the angle of the ray so that the reflected ray comes back along its own path, using the screen to see where this happens.
Very carefully transfer the position of the pinhole to the graph paper.
If this point is joined to the 1st interval at the mirror and projected through to where it meets the PA behind the mirror at the Centre of curvature.
Repeating this procedure for the other 3 interval points will check the position for accuracy.
To obtain the location of F:
Position the ray box at 20cm from the mirror; direct a ray Parallel to the PA to strike the mirror corresponding to the first interval mark. Carefully transfer the reflected rays position from he screen to the graph paper; call this point A.
Now move the ray box to a position 40cm from the mirror but still aimed at the 1st interval mark and parallel to the PA. Now transfer from the screen to the graph paper call this point B
Join B to A and project the line until it meets the PA behind the mirror giving the Focal Point.
Repeating this procedure for the other 3 interval marks will give further checks on the accuracy.
I know this has been wordy but it relies on what was stated at the start 1 & 2 in particular
In practise depending on the size of the mirror the dimensions may need changing.
What do you think?
It would of course be easier with a cylindrical convex mirror!