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Spherical Mirrors

The reflecting surface of a spherical mirror may be curved inwards or outwards.A spherical mirror, whose reflecting surface is curved inwards, is called as a concave mirror. A spherical mirror, whose reflecting surface is curved outwards, is called as a convex mirror.
 
 
 
Mirror Versus Shining spoon:
 
The curved surface of the shining spoon will act as a curved mirror. The spherical mirror is the most commonly used mirror. The surface of the spoon curved inwards can be approximated to a concave mirror and the surface of the spoon bulged outwards can be approximated to a convex mirror.

Solar energy concentrated by a concave mirror:
 
Actually solar energy concentrated by a concave mirror at its focus is sufficient to burn the paper. Take a concave mirror of focal length 15 cm or 20 cm. Hold the mirror facing the sun and focus on the paper. Try to obtain the brightest and sharpest spot of concentrated rays on the paper. If you hold your hand steady, you will observe that the piece of paper will begin to burn. This effect is illustrated in the following visual and animation.
 

In order to discuss the formation of images in spherical mirror, it is necessary to define few terms related to spherical mirrors.

  

  1. Pole
     
    The centre of the spherical surface of the mirror is called the pole O of the mirror.
  2. Centre of Curvature
     
    The centre of curvature C is the centre of the sphere of which the spherical mirror is a part.
  3. Radius of Curvature
     
    The radius of curvature R is the radius of the sphere of which the mirror is a part. In the above figure, one such radius is shown. The distance of any point on the surface of the mirror from the centre of curvature is equal to R. The radius at any point is normal to the mirror at the point.
  4. Principal Axis
     
    The line OC (produced on both sides) joining the pole and the centre of curvature of the mirror is called the principal axis of the mirror.
  5. Focus and Focal Length
     
    The focus or the principal focus (F), at a concave mirror is that point on the principal axis to which all the rays parallel to the axis converge after reflection from the mirror. However, the focus of the convex mirror is that point on the principal axis from which all the rays parallel to the axis appear to diverge after being reflected from the mirror.
The distance OF, of the focus and the pole of the spherical mirror, is called its focal length, which is denoted by the letter f.
 
There is a relationship between the radius of curvature R, and focal length f, of a spherical mirror. For spherical mirrors of small apertures, the radius of curvature is found to be equal to twice the focal length.
 
R=2f
 
This implies that the principal focus of a spherical mirror lies midway between the pole and centre of curvature.




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