The focal length of a spherical mirror, whether it is concave or convex, is equal to half of its radius of curvature.
Focal length = Radius of curvature/2
f = R/2
In the diagram given above, M and N represent the spherical mirror. However, P is the principal axis, C is the centre of curvature, F is the focal point where the two rays meet each other. In addition, the distance between the C and P is called the radius of curvature, and the distance between F and P is called the focal length.
![](https://df0b18phdhzpx.cloudfront.net/ckeditor_assets/pictures/1760215/original_10a.png)
The ray of light incident on the mirror is parallel to the principal axis. The ray of light AB generally strikes on the surface. CP is equal to R (radius of curvature ). However, when the two parallel rays A and B strike on the mirror, they reflect and pass through the focus point. As the law of reflection is followed, i = r,
According to the figure of the geometry,
∠BPC = θ = i
Also, θ = r
BF = FC (according to the law of reflection i = r)
When the mirror’s aperture is smaller than, B lies near to P, and therefore, the condition becomes BF = PF.
FC = FP = Pf,
PC = PF + FC = PF + PF
R = 2 PF = 2f
So, f = R/2