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Image distance in a plane mirror | ${d}_{\text{o}}=\text{\u2212}{d}_{\text{i}}$ |
Focal length for a spherical mirror | $f=\frac{R}{2}$ |
Mirror equation | $\frac{1}{{d}_{\text{o}}}+\frac{1}{{d}_{\text{i}}}=\frac{1}{f}$ |
Magnification of a spherical mirror | $m=\frac{{h}_{\text{i}}}{{h}_{\text{o}}}=\text{\u2212}\frac{{d}_{\text{i}}}{{d}_{\text{o}}}$ |
Sign convention for mirrors | |
Focal length f | $\begin{array}{c}+\phantom{\rule{0.2em}{0ex}}\text{for concave mirror}\hfill \\ -\phantom{\rule{0.2em}{0ex}}\text{for concave mirror}\hfill \end{array}$ |
Object distance d _{o} | $\begin{array}{c}+\phantom{\rule{0.2em}{0ex}}\text{for real object}\hfill \\ -\phantom{\rule{0.2em}{0ex}}\text{for virtual object}\hfill \end{array}$ |
Image distance d _{i} | $\begin{array}{c}+\phantom{\rule{0.2em}{0ex}}\text{for real image}\hfill \\ -\phantom{\rule{0.2em}{0ex}}\text{for virtual image}\hfill \end{array}$ |
Magnification m | $\begin{array}{c}+\phantom{\rule{0.2em}{0ex}}\text{for upright image}\hfill \\ -\phantom{\rule{0.2em}{0ex}}\text{for inverted image}\hfill \end{array}$ |
Apparent depth equation | ${h}_{\text{i}}=\left(\frac{{n}_{2}}{{n}_{1}}\right){h}_{\text{o}}$ |
Spherical interface equation | $\frac{{n}_{1}}{{d}_{\text{o}}}+\frac{{n}_{2}}{{d}_{\text{i}}}=\frac{{n}_{2}-{n}_{1}}{R}$ |
The thin-lens equation | $\frac{1}{{d}_{\text{o}}}+\frac{1}{{d}_{\text{i}}}=\frac{1}{f}$ |
The lens maker’s equation | $\frac{1}{f}=\left(\frac{{n}_{2}}{{n}_{1}}-1\right)\left(\frac{1}{{R}_{1}}-\frac{1}{{R}_{2}}\right)$ |
The magnification m of an object | $m\equiv \frac{{h}_{\text{i}}}{{h}_{\text{o}}}=\text{\u2212}\frac{{d}_{\text{i}}}{{d}_{\text{o}}}$ |
Optical power | $P=\frac{1}{f}$ |
Optical power of thin, closely spaced lenses | ${P}_{\mathrm{total}}={P}_{\text{lens}1}+{P}_{\text{lens}2}+{P}_{\text{lens}3}+\text{\cdots}$ |
Angular magnification M of a simple magnifier | $M=\frac{{\theta}_{\text{image}}}{{\theta}_{\text{object}}}$ |
Angular magnification of an object a distance
L from the eye for a convex lens of focal length f held a distance ℓ from the eye |
$M=\left(\frac{25\phantom{\rule{0.2em}{0ex}}\text{cm}}{L}\right)\left(1+\frac{L-\mathcal{\ell}}{f}\right)$ |
Range of angular magnification for a given
lens for a person with a near point of 25 cm |
$\frac{25\phantom{\rule{0.2em}{0ex}}\text{cm}}{f}\le M\le 1+\frac{25\phantom{\rule{0.2em}{0ex}}\text{cm}}{f}$ |
Net magnification of compound microscope | ${M}_{\text{net}}={m}^{\text{obj}}{M}^{\text{eye}}=\text{\u2212}\frac{{d}_{\text{i}}^{\text{obj}}\left({f}^{\text{eye}}+25\phantom{\rule{0.2em}{0ex}}\text{cm}\right)}{{f}^{\text{obj}}{f}^{\text{eye}}}$ |
Geometric optics describes the interaction of light with macroscopic objects. Why, then, is it correct to use geometric optics to analyze a microscope’s image?
Microscopes create images of macroscopic size, so geometric optics applies.
The image produced by the microscope in [link] cannot be projected. Could extra lenses or mirrors project it? Explain.
If you want your microscope or telescope to project a real image onto a screen, how would you change the placement of the eyepiece relative to the objective?
The eyepiece would be moved slightly farther from the objective so that the image formed by the objective falls just beyond the focal length of the eyepiece.
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