Shortcut Methods
Microscopes
1. Magnifying Power
- Shortcut: Multiply the magnifying power of the eyepiece lens by the magnifying power of the objective lens.
- Formula: $$M=m_e\times m_o$$
2. Resolving Power
- Shortcut: Divide 1.22 by the numerical aperture of the objective lens, then multiply the result by the wavelength of light used.
- Formula: $$R=\frac{1.22 \lambda}{NA}$$
Telescopes
1. Magnifying Power
- Shortcut: Divide the focal length of the objective lens by the focal length of the eyepiece lens.
- Formula: $$M=\frac{f_o}{f_e}$$
2. Light-Gathering Power
- Shortcut: Square the diameter of the objective lens, then multiply the result by pi and divide by 4.
- Formula: $$G=\frac{\pi d^2}{4}$$
Additional Numericals
Microscopes
- Objective lens diameter: 4-10 mm
- Eyepiece lens focal length: 10-25 mm
- Eyepiece lens magnifying power: 5x-10x
- Objective lens magnifying power: 4x-100x
- Resolving power: 0.2-2.0 µm
Telescopes
- Objective lens diameter: 50-200 mm
- Eyepiece lens focal length: 20-50 mm
- Magnifying power: 10x-1000x
- Light-gathering power: 100x-100000x
