Case I Concave Mirror
Back to Top
To Show that f = R/2 for a Concave 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
BF = CF --------- (3)
If the aperture of the mirror is small then B will be very close to P.
BF = PF --------- (4)
From equations (3) and (4) we conclude that
But by definition PF = f (focal length) and PC = R (radius of curvature)
Note: While Deriving the Relation we have considered only one of the incident rays
Case II Convex Mirror
Back to Top
Let a ray of light AB be incident, parallel to the principal axis, on a convex mirror. After reflection the ray AB appears to come from F. BC is the normal to the convex mirror at B.
From equations (2) and (3)
Hence triangle BCF is isosceles
BF = CF ------- (4)
If the aperture of the mirror is small then B will be very close to P.
BF = PF ------- (5)
From equations (4) and (5) we conclude that
By definition PF = f (focal length) and
PC = R (radius of curvature)
From the above relation we conclude that the radius of curvature of a mirror is twice its focal length.
