Optical Instruments

We will briefly review how certain optical

instruments work. We will look at:

• the eye

• the simple magnifying glass

• the compound microscope

• the telescope

The Eye

Cornea

Iris

Lens Retina

The Eye

➜ most of the refraction is done

by the cornea

➜ the lens can change its shape

and thus its focal length

Near Point

➜ we usually make an object

seem larger by bringing it

closer to our eye (this allows

us to resolve more detail)

➜ however, at some point we

reach the near point of our

eye, and bringing the object

any closer causes it to blur

near

pointmax.

strain

near

pointmax.

strain

Myopia - “nearsightedness”

➜ far point is not at infinity

➜ rays from objects past the

far point get bent too much by

the relaxed lens

➜ can be adjusted for by

using a diverging lens to

diverge the rays enough to

place an intermediate image

at the far point ➜ if you’re nearsighted you should be wearing

glasses/contacts featuring diverging lenses

Hyperopia - “farsightedness”

➜ near point is far away from

the eye

➜ rays from objects inside the

near point can’t be bent

enough even by the lens

under maximum strain

➜ can be adjusted for by

using a converging lens to

converge the rays enough to

place an intermediate image

outside the near point➜ if you’re farsighted you should be wearing

glasses/contacts featuring converging lenses

Magnifying glass

➜ we usually make an object

seem larger by bringing it

closer to our eye (this allows

us to resolve more detail)

➜ however, at some point

we reach the near point of

our eye, and bringing

the object any closer causes

it to blur

near

pointmax.

strain

near

pointmax.

strain

Magnifying glass at the near point

➜ we can bring the object closer than the near point if we bring in some

external focusing power - a converging lens will do the trick

near

point

max.

strain

virtual

image

Magnifying glass at infinity➜ if we put the virtual

image at the far point

(infinity for most people),

then the eye can be

relaxed

➜ achieved if the object

is at the focal point of

the magnifying lens

near

point

no

strain

virtual

image

at infinity

Magnifying glass –

angular magnification

Magnifying glass

We define the

power or strength

of a lens as the

inverse of the focal

length in meters, in

units of ‘diopters’.

Spherical aberration

For lenses made with

spherical surfaces, rays

which are parallel to the

optic axis but at different

distances from the optic

axis fail to converge to the

same point.

For a single lens, spherical

aberration can be

minimized by bending the

lens into its best form. For

multiple lenses, spherical

aberrations can be canceled

by overcorrecting some

elements.

Chromatic aberration

A lens will not focus different

colors in exactly the same place

because the focal length depends

on refraction and the index of

refraction for blue light (short

wavelengths) is larger than that of

red light (long wavelengths). The

amount of chromatic aberration

depends on the dispersion of

the glass.

One way to minimize this

aberration is to use glasses of

different dispersion in a doublet or

other combination

The Compound Microscope

The objective lens forms an enlarged real

image which is the object for the eyepiece.

The eyepiece forms an even larger virtual

image:

eye

Objective Eyepiece

O

I1

I2

The Microscope➜ physical limitations of lensmaking prevent

really large magnifications with a simple

magnifying glass - the microscope beats this

by using two lenses

Fobj

objective

eyepiece

Fobj

Feye

Feye

The Microscope

Fobj

objective

eyepiece

Fobj

Feye

Feye

the objective lens produces a real image

of an object placed at or near its focal point

this image should be formed inside or on

the focal point of a second lens, called

the eyepiece

The Microscope

Fobj

objective

eyepiece

Fobj

Feye

Feye

the eyepiece forms a virtual image that

is much magnified (in an angular sense)

The Microscope

Fobj

objective

eyepiece

Fobj

Feye

Feye

The Telescope

There are two main types of telescopes:

• the refracting telescope (uses lenses)

• the reflecting telescope (uses mirrors)

The refracting telescope has an optical layout

similar to the compound microscope (two

convex lenses).

The Refracting Telescope

Fobj

objective eyepiece

Feye

Feye

foca

l p

lan

e

The distance between

the lenses is fo + fe

Fobj

objective eyepiece

Feye

Feye

foca

l p

lan

e

➜ magnification in the angle subtended

angular

magnification

The Refracting Telescope

22

The Telescope

objective eyepiece

➜ magnification in the angle subtended

angular

magnification

image of the

middle of the object

these rays from the

middle of the object

The Refracting Telescope

Exercise: A telescope is constructed from two lenses:

an objective of focal length 100 cm and an eyepiece

of focal length 10 cm.

The telescope is used in normal adjustment.

a) Calculate the angular magnification

b) What is the distance between the lenses?

Exercise: A telescope has an objective of focal

length 50 cm. What focal length eyepiece should be

used to give a magnification of 10?

Exercise: The moon has a diameter of 3500 km and

is 400,000 km from Earth. Calculate the angle

subtended by the moon at an observer’s eye on

Earth.

Reflecting telescopes: mirrors?

• In spherical mirrors, parallel

rays only reflect through the

focal point when they are

close to the principal axis.

Otherwise, the form a

caustic curve.

• This problem does not exist

for parabolic mirrors.

Uses a combination of mirrors (and lenses).

Advantages:

• Using mirrors allows larger telescopes,

since it’s easier to make large mirrors than

large lenses.

• Using parabolic mirrors removes spherical

aberration, and mirrors don’t have

chromatic aberration.

Problem: To view the image we need to block

some incoming light

The Reflecting Telescope

• Newtonian mounting

The Reflecting Telescope

• Cassegrain mounting

The Reflecting Telescope

Modern Telescopes

Add a CCD camera at the

focus to capture a digital

image launched the

development of

astrophysics.

Remove atmospheric effects

(such as “twinkling” and

electromagnetic pollution)

by building in high places

or in outerspace

Hubble telescope

Modern TelescopesRadio Telescopes: The resolving power is limited by

diffraction at the aperture of the instrument need larger

reflecting surfaces

Fortunately, because of the larger wavelengths involved, the

surface doesn’t have to be so precisely made.

Arecibo

Observatory

in Puerto Rico

Modern TelescopesRadio Interferometer Telescopes:

Using interference signals from two

or more radio telescopes, we can

construct images using a process

known as “aperture synthesis”.

The resulting increase in resolving

power is equivalent to building one

huge telescope with diameter equal to

the separation of the telescopes.

This would allow in principle to

make telescopes with “aperture” the

size of Earth.

Very Large Array in

New Mexico

Modern Telescopes

Radio

Interferometer

Telescopes