1.prove that R=2F for a concave or convex mirror.
Let a ray of light AB be incident, parallel to the principal axis, on a concave mirror. After reflection, the ray AB passes along BD, through the focus F. BC is normal to the concave mirror at B.
We know that AB and PC are parallel to each other.
From equations (1) and (2) we get
Hence triangle BCF is isosceles
If the aperture of the mirror is small then B will be very close to P.
From equations (3) and (4) we conclude that
But by definition PF = f (focal length) and PC = R (radius of curvature)