Optical Instruments: Microscopes and Telescopes
Angular magnification M = θ/θ₀, simple microscope (magnifying glass), compound microscope in normal and near-point adjustment, astronomical telescope, tube length, and resolving power considerations.
Marking a lesson complete represents finishing your study of the topic; it does not denote tested mastery.
Learning Objectives
- Derive angular magnification formulas for simple and compound microscopes in both near-point adjustment and normal adjustment.
- Calculate magnifying power M = f_o / f_e and separation L = f_o + f_e for astronomical telescopes in normal adjustment.
Core Theory & Concepts
Optical instruments combine multiple lenses to increase the visual angle subtended by distant or minute objects at the eye, producing apparent magnification without physical approach.
Compound Microscope Magnification
The objective forms a real, magnified intermediate image inside the eyepiece focal length. Total angular magnification for final image at near point D is M = -(v_o / u_o)(1 + D / f_e). In normal adjustment (final image at infinity), M = -(L / f_o)(D / f_e).
Astronomical Telescope Normal Adjustment
Objective (f_o, large aperture) forms a real intermediate image at its second focal point, which coincides with the first focal point of the eyepiece (f_e). The final image is at infinity: M = f_o / f_e, and separation distance L = f_o + f_e.
Common Misconceptions
In an astronomical telescope, the eyepiece should have a larger focal length than the objective to produce higher magnification.
Syllabus Topic Outline
- 1Visual angle and angular magnification M = θ / θ₀
- 2Simple microscope: M = 1 + D/f (near point) and M = D/f (infinity)
- 3Compound microscope: objective and eyepiece lenses, ray diagram
- 4Compound microscope magnification: M = m_o × M_e = -(v_o / u_o)(1 + D / f_e)
- 5Astronomical telescope in normal adjustment: M = f_o / f_e and tube length L = f_o + f_e