The relationship between focal length and radius of curvature of a spherical mirror is
a) f=2r
b) f=r/3
c) f=3r
d) f=r/2
Answers
Explanation:
For a concave mirror:
In figure (a),
∠BP
′
C=∠P
′
CF (alternate angles) and
∠BP
′
C=∠P
′
F (law of reflection,∠i=∠r)
Hence ∠P
′
CF=∠CP
′
F
∴ FP
′
C is isosceles.
Hence, P
′
F=FC
If the aperture of the mirror is small, the point P
′
is very close to the point P,
then P
′
F=PF
∴ PF=FC=
2
PC
or f=
2
R
For a convex mirror:
In figure (b),
∠BP
′
N=∠FCP
′
(corresponding angles)
∠BP
′
N=∠NP
′
R (law of reflection, ∠i=∠r) and
∠NP
′
R=∠CP
′
F (vertically opposite angles)
Hence ∠FCP
′
=∠CP
′
F
∴ FP
′
C is isosceles.
Hence, P
′
F=FC
If the aperture of the mirror is small, the point P
′
is very close to the point P.
Then P
′
F=PF
∴PF=FC=
2
PC
or f=
2
R
Thus, for a spherical mirror {both concave and convex), the focal length is half of its radius of curvature.