PHS 121 Optics – Optical Instruments: Microscope, Telescope

The Magnifier (Simple Magnifier)

• A magnifier is a converging lens used to form an image larger than the object.
• The size of an object's image on the retina depends on the angular size (θ) subtended by the object at the eye.
• Angular Magnification (M): The ratio of the angle subtended with the magnifier (θ') to the angle subtended without the magnifier (θ).

  M = θ' / θ

  • θ' = angle subtended with magnifier
  • θ = angle subtended without magnifier
• For a simple single-lens magnifier:

  M = 25 / f

  where:
  • f = focal length in cm.
  • 25 cm = standard near point distance for a human eye.

The Microscope (Compound Microscope)

• Used for greater magnification than a simple magnifier.
• Structure: Comprises an objective lens and an eyepiece.
  • The image formed by the objective lens serves as the object for the eyepiece.
  • Both objective and eyepiece are typically compound lenses with multiple elements.
• Overall Angular Magnification (M): The product of two factors:
  1. Lateral magnification of the objective lens (m₁).
  2. Eyepiece magnification (m₂).

  M = m₁ * m₂

• The final image is inverted with respect to the object.
• Example Problem:

  In a compound microscope:

  • Objective focal length: 8 mm
  • Eyepiece focal length: 40 mm
  • Distance between lenses: 200 mm
  • Final image distance from eyepiece: 250 mm

  a. How far is the object from the objective lens?

  b. What is the total magnification?

Telescopes

• Purpose: To view large objects at large distances (unlike microscopes, which view small objects close by).
• Optical System: Similar to a compound microscope, with an objective forming an image viewed by an eyepiece.
• Objective: Can be a lens or a curved mirror.
• Angular Magnification (M): The ratio of the focal length of the objective to that of the eyepiece.

  M = -f₁ (objective) / f₂ (eyepiece)

  • The negative sign indicates that the final image is inverted.
  • Magnification can be varied by using different eyepieces (f₂).

Resolving Power (RP) of a Telescope

• Definition: The ability to distinctly identify two distant objects that are close to each other.
• Depends on the dimensions of the mirror/objective and the wavelength of light.
• Formula:

  RP = 1.22λ / D

  where:
  • λ = wavelength of light
  • D = diameter of the mirror (objective)

Example Problem: Simple Magnifier

• Focal length of a simple magnifier: 9.0 cm.
• Assume magnifier is a thin lens placed very close to the eye.
• a. How far in front of the magnifier should an object be placed if the image is formed at the observer's near point (25 cm in front of her eye)?
• b. If the object is 1.0 mm high, what is the height of its image formed by the magnifier?