Lecture Notes: Types of Lenses and Their Properties

Types of Lenses

• Lenses are categorized based on their shapes:

  1. Concave Lens
  2. Convex Lens
  3. Double Convex (Biconvex) Lens
  4. Double Concave (Biconcave) Lens
  5. Plano-Convex Lens
  6. Plano-Concave Lens
  7. Concavo-Convex Lens

• The names are based on the surfaces' shapes.

• The effect of a lens depends on the curvature and radius of its surfaces.

Common Uses

• Concave lenses are commonly used in glasses.
• Plano concave lenses are mentioned in relation to glasses used for 4 years.

Lens Behavior and Image Formation

Convex Lenses

• Double Convex Lens: Also known as converging or positive lens.

  • Parallel rays converge at the focus.
  • Image characteristics: As an object moves towards the lens, the image moves away and enlarges.
  • Image placement: Between focus (F) and twice the focal length (2F), image is magnified.

• Image Characteristics:

  • Virtual, erect, and magnified on the same side as the object.

Lens Formula

• For thin lenses:
  • Formula: ( \frac{1}{f} = \frac{1}{v} - \frac{1}{u} )
  • Magnification (M): Ratio of height of the image (HI) to height of the object (HO).
  • Convention: Distances are taken from the optical center.
  • Lens power ( P = \frac{1}{F} ) (F in meters), unit is diopter (D).
  • Negative sign in focal length indicates a concave lens.

Image Formation in Concave Lenses

• Concave Lens: Diverging lens.
  • Rays diverge and appear to come from a virtual focus.
  • Image Characteristics: Same side, virtual, erect, and diminished.

Power of a Lens

• Reciprocal of the focal length (in meters).
• Power (P) = 1/F (diopters)
• Example: -5 diopters = -1/5 meter focal length (20 cm), indicating a concave lens.

Combination of Lenses

• Lenses in contact can combine their powers:
  • Total Power ( P = P_1 + P_2 )
  • Total Focal Length: ( \frac{1}{F} = \frac{1}{F_1} + \frac{1}{F_2} )
  • Magnification is the product of individual magnifications.

Example Problem

• Concave lens with focal length -20 cm combined with another lens.

• Given combined power is 2 diopters, find the focal length of the second lens.

  • Calculation:
    1. Power of combination = 1/50
    2. ( \frac{1}{F_2} = \frac{1}{50} + \frac{1}{20} )
    3. Result: F2 = 100/7 cm

Conclusion

• Understanding lens properties, formulas, and image characteristics is crucial for optics.
• Practice problems often involve calculating power and focal lengths in lens combinations.