The image of the first lens acts as the object for the second lens.

Lens power: $P={\displaystyle \frac{1}{f}}\text{diopters,}$ $1\text{D}=1{\text{m}}^{-1}$

The angular resolution of a lens of diameter $D$ is

Rayleigh’s criterion states that two objects separated by an angle $\alpha$ are marginally resolvable if $\alpha ={\theta }_{\text{min}}$.

Form a real, inverted image on a detector. The lens’s f-number is

The light intensity on the detector is

For relaxed-eye viewing, the angular magnification of a lens is

For microscopes and telescopes, angular magnification, not lateral magnification, is the important characteristic. The eyepiece acts as a magnifier to view the image formed by the objective lens.

Refraction at the cornea is responsible for most of the focusing. The lens provides fine-tuning by changing its shape (accommodation).

In normal vision, the eye can focus from a far point (FP) at $\text{∞}$ (relaxed eye) to a near point (NP) at $\approx 25\text{cm}$ (maximum accommodation).

• Hyperopia (farsightedness) is corrected with a converging lens.

• Myopia (nearsightedness) is corrected with a diverging lens.

The object is very close to the focal point of the objective.

The total angular magnification is $M=m_{\text{obj}}{M}_{\text{eye}}$.

The best possible spatial resolution of a microscope, limited by diffraction, is about one wavelength of light.

The minimum spot size to which a lens of focal length $f$ and diameter $D$ can focus light is limited by diffraction to

With the best lenses that can be manufactured, $w_{\text{min}}\approx \text{λ}$.

The object is very far from the objective.

The total angular magnification is $M=-{\displaystyle \frac{f_{\text{obj}}}{f_{\text{eye}}}}$.