Spherical Mirror Formula, Detail, Concave and Convex Mirrors (For CBSE, ICSE, IAS, NET, NRA 2022)

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Spherical Mirror Formula

  • Curved mirrors come in two basic types:
    • The one which converge parallel incident rays of light
    • That which diverge parallel incident rays of light.
  • One of the easiest shapes to analyze is the spherical mirror.
  • Typically, such a mirror is not a complete sphere, but a spherical cap - a piece sliced from a larger imaginary sphere with a single cut.
  • An object placed in front of a mirror generates an image. If light rays from the object falls on the mirror and are then reflected and converge to form an image, the image thus formed is a real image
  • But one could argue that this statement is quantifiably false, since ball bearings are complete spheres and they are shiny and plentiful. Nonetheless as far as optical instruments go, most spherical mirrors are spherical caps.
  • If the reflected light rays do not converge but have to be extrapolated backwards to form an image, the image is called a virtual image.
  • As such, using ray diagrams, it is possible to determine the type of image formed, while using concave and convex mirrors, based on the distance of object from the mirror.

Detail

Paraxial Rays of Light
  • To start with trace a line from the center of curvature of the sphere through the geometric center of the spherical cap.
  • Extend it to infinity in both directions.
  • This imaginary line is called the principal axis or optical axis of the mirror.
  • Any line through the center of curvature of a sphere is an axis of symmetry for the sphere, but only one of these is a line of symmetry for the spherical cap.
  • The adjective “principal” is used because it՚s the most important of all possible axes.
  • The point where the principal axis pierces the mirror is called the pole of the mirror.
  • Compare this with the poles of the Earth, the place where the imaginary axis of rotation pierces the literal surface of the spherical Earth.
  • To obtain exact information about the size and magnification of image, and the distance of the image from the spherical mirror, we can use the mirror formula.

The Mirror Formula

The Mirror Formula (also referred to as the mirror equation)

Where,

  • F = the focal length
  • V = distance of object forms the mirror
  • U = the distance of image forms the mirror
  • The mirror formula for a concave mirror is given below.
  • The magnification image formed by a spherical mirror is given by height of image divided by height of object.

Concave and Convex Mirrors

  • Distances are to be measured from the pole (vertex) of the mirror marked by point V in the figure.
  • Distances measured along the direction of the incident ray are positive.
  • Distances measured opposite the direction of the incident ray are negative.
  • Distances measured above the principal axis are positive. Distances measured below the principal axis are negative.

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