5. Lenses

Chapter 5: Lenses

Types of Spherical Lenses

  • Two types of spherical lenses:

    • Concave (Diverging): Curves inwards; rays diverge after passing through the lens.

    • Convex (Converging): Curves outwards; rays converge after passing through the lens.

Convex Lenses and Ray Diagrams

  • Ray diagram rules for convex lenses:

    1. Ray parallel to the principal axis, refracts through the focal point on the opposite side.

    2. Ray passing through the focal point, refracts parallel to the principal axis.

    3. Ray towards the center of curvature continues straight.

  • Image formation:

    • Object outside the focus (f): Produces a real image (inverted, on opposite side).

    • Object inside the focus: Produces a virtual image (upright, on the same side).

Concave Lenses and Ray Diagrams

  • Ray diagram rules for concave lenses:

    1. Ray parallel to the principal axis, refracted as if coming from the focal point.

    2. Ray towards the center continues straight.

  • Image characteristics:

    • Always diminished, upright, and virtual regardless of object distance.

Lens Formulas and Conventions

  • Focal length (f), object distance (u), and image distance (v) relationship:

    • Sign conventions:

      • Convex lens: f positive.

      • Concave lens: f negative.

      • Real image: v positive.

      • Virtual image: v negative.

      • Object distance (u) is always positive.

  • Magnification:

    • If v is virtual, make the value negative in the problem for concave lenses or convex lenses with objects inside focal length.

Power of a Lens

  • Power of a lens formula:

    • Power = 1/focal length (m^-1)

  • Sign conventions:

    • Converging lens: positive power.

    • Diverging lens: negative power.

  • Combining lenses:

    • If two lenses with powers P1 and P2 are in contact: P = P1 + P2.

    • Focal length of combination follows similar sign conventions.

The Eye and Its Optical Structure

  • Components of the eye:

    • Retina: Light-sensitive screen at the back.

    • Cornea & Lens: Focus light onto the retina.

    • Iris: Controls light entry.

  • Power of accommodation: Ability to focus real images of objects at varying distances onto the retina.

Vision Defects

  • Short-sightedness:

    • Difficulty focusing on distant objects; can see near objects clearly.

  • Long-sightedness:

    • Difficulty focusing on nearby objects; can see distant objects clearly.

Measurement of Focal Length (Convex Lens)

  • Apparatus needed:

    • Converging lens, screen, lamp-box, metre stick, retort stand.

  • Procedure for measurement:

    1. Place ray-box outside approximate focal length.

    2. Move screen to obtain clear inverted image.

    3. Measure u (distance from cross-wire to lens) and v (distance from screen to lens).

    4. Repeat for varied u values and calculate average focal length.

  • Precautions:

    • Sharp focus determination, parallax error mitigation, measurements from lens center.

Extra Credit: Confusion Between Mirrors and Lenses

  • Differences to remember:

    • Concave mirrors vs. convex lenses produce real images; virtual images differ in formation position.

  • Watering plants advice:

    • Water droplets act as converging lenses, burning leaves.

Up Close with History

  • Historical use of optics in art:

    • Artists like Van Eyck may have used lenses and mirrors to create projections.

  • Upside-down glasses research:

    • Investigated by George Stratton in the 1890s; findings on visual perception adjustments through inversion.

Key Exam Questions and Solutions

  • Ray diagrams: Render different lens images.

  • Power calculation: Use formulas to ascertain values based on objects and distances.