POWER OF A LENS

A lens is a transparent medium usually made of glass bounded by two spherical surfaces or by one spherical surface plane surface.

The line joining the center of curvature of the two spherical surfaces is known as the principal axis. A plane through the principal axis is known as the principal section of the lens.

A point on the principal axis through which all the incident and emergent rays which are parallel to each other will pass is called as an optical center of the lens.

POWER OF A LENS

It is the measure of the ability of the given lens to produce convergence of a parallel beam of light that falls on it. A convex lens of large focal length produces a small converging effects and a convex lens of small focal length produce a large converging effect to the incident rays of light. Due to this, the power of a convex lens is taken as +ve and that of a concave lens is taken as -ve.

For example: 

A convex lens of focal length 1m has a power = + 1 diopter and a convex lens of focal length 2 ms has a power = + ½ diopter.

Here diopter (D) represents the unit in which the power of the lens is measured.

Power= 1/focal length in meters
Note:
  1.  When two thin lenses of focal lengths ƒ₁ and ƒ₂ are in contact, then the equivalent focal length (F) is given by \frac{1}{F} = \frac{1}{f_1}+\frac{1}{f_2} and the equivalent power of lens is given by P= P₁+P₂, where P₁ and P₂ are the powers of the lens. Where P is the equivalent power.
  2.  When the two thin lenses of focal lens ƒ₁ and ƒ₂ are placed coaxially and are  separated by a distance ‘d’, then the equivalent focal length (F) is given by \frac{1}{F} = \frac{1}{f_1}+\frac{1}{f_2}-\frac{d}{f_1f_2} Here, P= P₁ + P₂ – d. P₁ P₂, where P is the equivalent power.

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