Lenses and Image Formation

Introduction to Lenses

• A lens is a clear device that bends light.

• Made of glass or plastic.

• Used in glasses, cameras, etc.

Types of Lenses

• Converging (Convex):

  • Thicker in the middle.

  • Focuses light.

• Diverging (Concave):

  • Thinner in the middle.

  • Spreads light.

Physical Properties

• Optical Center (O):

  • Center of the lens.

  • Light passes straight.

• Principal Axis:

  • Line through the center.

• Focal Point:

  • Point where light converges (convex) or appears to diverge from (concave).

• Focal Length (f):

  • Distance from center to focal point.

• Center of Curvature (C):

  • Point at $2f$ from the center.

Image Formation

• Convex Lenses:

  • Real Image:

    • Light rays meet.

    • Can be shown on screen.

    • Upside down.

  • Virtual Image:

    • Light rays appear to meet.

    • Cannot be shown on screen.

    • Right side up.

• Concave Lenses:

  • Always virtual, upright, and smaller.

Applications

• Convex Lenses:

  • Glasses for farsightedness.

  • Magnifying glasses.

  • Cameras & telescopes.

• Concave Lenses:

  • Glasses for nearsightedness.

  • Peepholes.

  • Flashlights.

Sign Convention

• Focal Length, $f$

  • $+f$: Convex

  • $-f$: Concave

• Object Distance, $d_O$

  • $-d_O$: In front of lens

• Image Distance, $d_i$

  • $+d_i$: Opposite side, real

  • $-d_i$: Same side, virtual

• Image Height, $h_i$

  • $+h_i$: Upright

  • $-h_i$: Inverted

• Magnification, $M$

  • $+M$: Upright

  • $-M$: Inverted

  • M > 1: Magnified

  • M < 1: Diminished

Lens Equations

• Lens Equation: $\frac{1}{f} = \frac{1}{d<em>i} - \frac{1}{d</em>o}$

• Magnification: $M = \frac{d<em>i}{d</em>o} = \frac{h<em>i}{h</em>o}$

  • $f$ = focal length

  • $d_o$ = object distance

  • $d_i$ = image distance

  • $h_o$ = object height

  • $h_i$ = image height

Sign Convention for Mirrors

• Focal Length, $f$

  • $+f$: Convex

  • $-f$: Concave

• Object Distance, $d_O$

  • $-d_O$: In front of mirror

• Image Distance, $d_i$

  • $+d_i$: Behind, virtual

  • $-d_i$: In front, real

• Image Height, $h_i$

  • $+h_i$: Upright

  • $-h_i$: Inverted

• Magnification, $M$

  • $+M$: Upright

  • $-M$: Inverted

  • M > 1: Magnified

  • M < 1: Diminished