Five Chapter 11

Lenses

Refraction of Light in Lenses

• Lenses are used in cameras, telescopes, microscopes, projectors, eyeglasses, etc.
• Lens – a piece of transparent material with uniformly curved surfaces that change the direction of light passing through it.
• Converging lens – a lens that causes parallel rays to refract inwards.
  • Convex lens
• Diverging lens – A lens that causes parallel rays to refract outwards
  • Concave lens
• Optical Centre (O) – the geometric centre of a lens.
  • Same as vertex for mirrors
• Just as for mirrors, lenses have various terms that relate to them.
  • Optical centre (O)
  • Principal axis (PA)
  • Principal focus (F)
  • Focal length (f)
  • Focal plane
  • Secondary principal focus (F’)

• Note these differences with the terminology used with mirrors.
  • Principal focus – the refracted light passes through this.
  • Secondary principal focus – the refracted light does not pass through it, but would if the light went through the lens from the other side.
  • Optical centre replaces vertex.
• Just as with mirrors, parallel rays not parallel to the principal axis converge at different focal points not on the principal axis. The set of all of these makes up the focal plane.
• With converging lenses, a real image of distant objects is formed at or near the principal focus
• In diverging lenses, rays are refracted as if they were radiating from a virtual focus (virtual image) at the principal focus.

Images in Lenses

• The rules used for locating the image of an object formed by a lens are:
  1. A ray that is parallel to the principal axis is refracted so that it passes through or can be projected back through, the principal focus.
  2. A ray that passes through (or is projected through) the secondary principal focus (F’), is refracted parallel to the principal axis.
  3. A ray that passes through the optical centre goes straight through without bending.
  4. The image forms where any two of these rays intersect, or their projections intersect.

• The following is a summary of image characteristics for different object locations for converging lenses.

• Diverging lenses use the same rules as converging lenses except the principal focus is virtual instead of real. The image is always between F and the lens, virtual, erect, and smaller than the object.

Thin Lens Equations

• The equations which apply to lenses are:

• M = magnification, h_i = image height, h_o = object height, d_i = image distance, and d_o = object distance.
• Proof of these equations:

• Sign convention
  1. All distances are measured from the optical centre of the lens.
  2. Distances of real objects and images are positive.
  3. Distances of virtual objects and images are negative.
  4. Objects and images are measured from the principal axis and are positive if up and negative if down.
• For diverging lenses, a virtual principal focus is present (negative) and a negative focal length.
• For a converging lens, a real principal focus is present (positive) and a positive focal length.
• Magnification is positive for erect images and negative for inverted images.

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Movember 20, 2013