Lenses

A lens is a transparent piece of glass or plastic that refracts light rays to form an image.

Types of Lenses:

• • Convex Lens (Converging Lens): Thicker at the center than at the edges. It brings parallel rays of light together (converges them) to a point called the principal focus.
  • Concave Lens (Diverging Lens): Thinner at the center than at the edges. It spreads parallel rays of light outward (diverges them) as if they are coming from a point called the principal focus.

Key Terms:

• • Principal Axis: A straight line passing through the optical center and the centers of curvature of the lens surfaces.
  • Optical Center (O): A point on the lens through which light passes without deviation.
  • Principal Focus (F): The point where parallel rays of light either converge (convex lens) or appear to diverge from (concave lens).
  • Focal Length (f): The distance between the optical center and the principal focus.
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Lens Formula:

\(\dfrac{1}{f} = \dfrac{1}{v} – \dfrac{1}{u}\)

where \(f\) = focal length, \(v\) = image distance, \(u\) = object distance (sign convention applied).

Magnification (M):

\( M =- \dfrac{\text{Image height}}{\text{Object height}} =- \dfrac{v}{u} \)

Ray Diagrams for Lenses:

For converging lenses:

• A ray parallel to the principal axis passes through the focal point after refraction.
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• A ray passing through the center of the lens continues in a straight line.
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• A ray through the focal point emerges parallel to the axis.
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For concave lenses:

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  • Parallel ray → appears to diverge from the focus.
  • Ray through optical center → passes undeviated.

Applications of Lenses:

• • Convex lenses: magnifying glasses, cameras, microscopes, human eye.
  • Concave lenses: spectacles for short-sightedness, peepholes in doors.