# 2.8 Microscopes and telescopes  (Page 6/16)

 Page 6 / 16

## Summary

• Many optical devices contain more than a single lens or mirror. These are analyzed by considering each element sequentially. The image formed by the first is the object for the second, and so on. The same ray-tracing and thin-lens techniques developed in the previous sections apply to each lens element.
• The overall magnification of a multiple-element system is the product of the linear magnifications of its individual elements times the angular magnification of the eyepiece. For a two-element system with an objective and an eyepiece, this is
$M={m}^{\text{obj}}{M}^{\text{eye}}.$

where ${m}^{\text{obj}}$ is the linear magnification of the objective and ${M}^{\text{eye}}$ is the angular magnification of the eyepiece.
• The microscope is a multiple-element system that contains more than a single lens or mirror. It allows us to see detail that we could not to see with the unaided eye. Both the eyepiece and objective contribute to the magnification. The magnification of a compound microscope with the image at infinity is
${M}_{\text{net}}=\text{−}\frac{\left(16\phantom{\rule{0.2em}{0ex}}\text{cm}\right)\left(25\phantom{\rule{0.2em}{0ex}}\text{cm}\right)}{{f}^{\text{obj}}{f}^{\text{eye}}}.$

In this equation, 16 cm is the standardized distance between the image-side focal point of the objective lens and the object-side focal point of the eyepiece, 25 cm is the normal near point distance, ${f}^{\text{obj}}$ and ${f}^{\text{eye}}$ are the focal distances for the objective lens and the eyepiece, respectively.
• Simple telescopes can be made with two lenses. They are used for viewing objects at large distances.
• The angular magnification M for a telescope is given by
$M=\text{−}\frac{{f}^{\text{obj}}}{{f}^{\text{eye}}},$

where ${f}^{\text{obj}}$ and ${f}^{\text{eye}}$ are the focal lengths of the objective lens and the eyepiece, respectively.

## Key equations

 Image distance in a plane mirror ${d}_{\text{o}}=\text{−}{d}_{\text{i}}$ 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 $m=\frac{{h}_{\text{i}}}{{h}_{\text{o}}}=\text{−}\frac{{d}_{\text{i}}}{{d}_{\text{o}}}$ 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 $m\equiv \frac{{h}_{\text{i}}}{{h}_{\text{o}}}=\text{−}\frac{{d}_{\text{i}}}{{d}_{\text{o}}}$ Optical power $P=\frac{1}{f}$ Optical power of thin, closely spaced lenses ${P}_{\mathrm{total}}={P}_{\text{lens}1}+{P}_{\text{lens}2}+{P}_{\text{lens}3}+\text{⋯}$ 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 ${M}_{\text{net}}={m}^{\text{obj}}{M}^{\text{eye}}=\text{−}\frac{{d}_{\text{i}}^{\text{obj}}\left({f}^{\text{eye}}+25\phantom{\rule{0.2em}{0ex}}\text{cm}\right)}{{f}^{\text{obj}}{f}^{\text{eye}}}$

## Conceptual questions

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.

A round diaphragm S with diameter of d = 0.05 is used as light source in Michelson interferometer shown on the picture. The diaphragm is illuminated by parallel beam of monochromatic light with wavelength of λ = 0.6 μm. The distances are A B = 30, A C = 10 . The interference picture is in the form of concentric circles and is observed on the screen placed in the focal plane of the lens. Estimate the number of interference rings m observed near the main diffractive maximum.
A Pb wire wound in a tight solenoid of diameter of 4.0 mm is cooled to a temperature of 5.0 K. The wire is connected in series with a 50-Ωresistor and a variable source of emf. As the emf is increased, what value does it have when the superconductivity of the wire is destroyed?
how does colour appear in thin films
in the wave equation y=Asin(kx-wt+¢) what does k and w stand for.
derivation of lateral shieft
hi
Imran
total binding energy of ionic crystal at equilibrium is
How does, ray of light coming form focus, behaves in concave mirror after refraction?
Sushant
What is motion
Anything which changes itself with respect to time or surrounding
Sushant
good
Chemist
and what's time? is time everywhere same
Chemist
No
Sushant
how can u say that
Chemist
do u know about black hole
Chemist
Not so more
Sushant
DHEERAJ
Sushant
But ask anything changes itself with respect to time or surrounding A Not any harmful radiation
DHEERAJ
explain cavendish experiment to determine the value of gravitational concept.
Cavendish Experiment to Measure Gravitational Constant. ... This experiment used a torsion balance device to attract lead balls together, measuring the torque on a wire and equating it to the gravitational force between the balls. Then by a complex derivation, the value of G was determined.
Triio
For the question about the scuba instructor's head above the pool, how did you arrive at this answer? What is the process?
as a free falling object increases speed what is happening to the acceleration
of course g is constant
Alwielland
acceleration also inc
Usman
which paper will be subjective and which one objective
jay
normal distributiin of errors report
Dennis
normal distribution of errors
Dennis
acceleration also increases
Jay
there are two correct answers depending on whether air resistance is considered. none of those answers have acceleration increasing.
Michael
Acceleration is the change in velocity over time, hence it's the derivative of the velocity with respect to time. So this case would depend on the velocity. More specifically the change in velocity in the system.
Big
photo electrons doesn't emmit when electrons are free to move on surface of metal why?
What would be the minimum work function of a metal have to be for visible light(400-700)nm to ejected photoelectrons?
give any fix value to wave length
Rafi
40 cm into change mm
40cm=40.0×10^-2m =400.0×10^-3m =400mm. that cap(^) I have used above is to the power.
Prema
i.e. 10to the power -2 in the first line and 10 to the power -3 in the the second line.
Prema
there is mistake in my first msg correction is 40cm=40.0×10^-2m =400.0×10^-3m =400mm. sorry for the mistake friends.
Prema
40cm=40.0×10^-2m =400.0×10^-3m =400mm.
Prema
this msg is out of mistake. sorry friends​.
Prema
what is physics?