The radius of curvature of a concave mirror is 30 cm. Following Cartesian Sign Convention, its focal length is expressed as ________.

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  1. + 30 cm
  2. + 15 cm
  3. – 30 cm
  4. – 15 cm

Answer (Detailed Solution Below)

Option 4 : – 15 cm
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CONCEPT:

Concave mirror: 

  • If the inner surface of the spherical mirror is the reflecting surface, then it is called a concave mirror. It is also called a focusing mirror/converging mirror.
    • The size of the image produced by these mirrors can be larger or smaller than the object, depending upon the distance of the object from the mirror.
    • The concave mirror can form both real as well as virtual images of any object.

Sign convention in mirrors

  • All distance are measured from the pole of the mirror.
  • The distance measured from the pole (p) to the left side of the mirror is taken as negative.
  • The distance measured from the pole (p) to the right side of the mirror is taken as positive.
  • The heights measured upwards and perpendicular to the principal axis of the mirror is taken as positive.
  • The heights measured downwards and perpendicular to the principal axis of the mirror is taken as negative.

​EXPLANATION:

Given - Radius of curvature (R) = - 30 cm

  • The relationship between the focal length (f) and the radius of curvature (R) is given by -

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