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The distance between the centre of curvature and pole of a convex mirror of 1┬аm focal length is ________.
5 m
1 m
2 m
0.5 m
2 m
The distance between the centre of curvature and the pole of a mirror is called the radius of curvature (R). The relation between the radius of curvature (R) and focal length (f) for a spherical mirror is given by R=2f. Given the focal length f=1┬аm, the distance is R=2├Ч1┬аm=2┬аm.
The distance between the centre of curvature and the pole of a mirror is called the radius of curvature (R). The relation between the radius of curvature (R) and focal length (f) for a spherical mirror is given by R=2f. Given the focal length f=1┬аm, the distance is R=2├Ч1┬аm=2┬аm.
Think of a convex mirror as a slice of a large plastic sphere. If the sphere has a radius of 2┬аm, the distance from the outer surface (pole) to the exact middle of that sphere (centre of curvature) is 2┬аm, while its focal point sits half that distance away at 1┬аm.
Remember: 'Radius is double the focus' (R=2f) or 'Focus is half the curvature' (f=R/2).
R=2f тАФ Radius of curvature is twice the focal length
f=2RтАЛ тАФ Focal length is half the radius of curvature
In spherical mirrors, the principal focus (F) lies midway between the pole (P) and the centre of curvature (C). Therefore, the radius of curvature (PC) is always twice the focal length (PF), expressed as R=2f. This relationship holds true for both concave and convex mirrors under paraxial ray approximations.
The pole (P) is the geometric centre of the reflecting surface of a spherical mirror.
The centre of curvature (C) is the centre of the hollow sphere of which the mirror is a part.
For a convex mirror, both the focus (F) and the centre of curvature (C) lie behind the mirror (virtual).
Sign convention dictates that distances measured behind a convex mirror are taken as positive.
Provides a wider field of view making it ideal for rear-view mirrors in vehicles.
Does not form real images of objects placed in front under normal conditions, limiting usage in focusing light.
Rear-view mirrors in automobiles
Security mirrors in department stores and blind turns
Option C (2┬аm) is obtained directly by doubling the given focal length (1┬аm).
Option A (1┬аm) represents the focal length itself, not the distance between pole and centre of curvature.
Option D (0.5┬аm) represents half of the focal length.
C is correct тАФ The distance between the centre of curvature and the pole of a convex mirror is 2 m.
Always verify whether the question asks for focal length (f) or radius of curvature (R), as students often confuse R with f or vice versa in numerical problems.
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